ESSAYS IN MARKET DESIGN

By

Pallavi Pal

A DISSERTATION

Submitted to

Michigan State University

in partial fulllment of the requirements

for the degree of

Economics  Doctor of Philosophy

2020

ABSTRACT

ESSAYS IN MARKET DESIGN

By

Pallavi Pal

Chapter 1: Quality Dierentiation and Optimal Pricing Strategy in Multi-sided

Markets

This paper analyzes the generalized quality dierentiation model in multi-sided markets with

positive externalities, which leads to new insights into the optimal pricing structure of the

rm. We nd that quality dierentiation for users on one side leads to a decrease in the

price charged to users on the other side, thereby aecting the pricing structure of multi-sided

rms. In addition, quality dierentiation aects the strategic relationships among the choice

variables for the platform, so that the platform strategically uses quality dierentiation to

raise its prots.

Chapter 2: Dynamic Game with Multidimensional Type: The Case of Carbon-

Credit Market

A signicant problem with the carbon credit market that has become apparent in recent

years is that the market price has been far more volatile than originally envisioned. The

underlying problem is the ill-understood pricing anomalies in a repeated period dynamic

setting. In this paper, we drive the equilibrium price path in a dynamic setting and suggests

ways to overcome price instability. The model setup allows the rms to dier in terms of

their value for the carbon credit as well as the urgency of obtaining it. For example, a rm

with an early deadline for obtaining the carbon credits will have a higher demand urgency.

We nd that the equilibrium price is aected by future demand and supply expectations.

The ndings show that the cap or the supply limit for each period can be used to decrease

price instability. Currently, the government or the carbon credit seller decides a per period

limit on the supply, which decreases over time. However, this paper suggests that to curb

price uctuation the per period supply should be a function of expected future demand. We

show that correlating supply rate with expected future demand leads to a more stable price.

Chapter 3: Revenue-Maximizing Number of Ads per Page in the Presence of

Market Externalities

Firms use advertising as a medium to gain a competitive advantage, which is negatively

aected if the ad appears alongside their rival's ada form of externality. The multiple ad

display setting on search engines, such as Google and Yahoo!, introduces such externalities

in the market. In this paper, I estimate a structural model based on a novel data set of

Yahoo! ads to (i) quantify the eect of externality on an advertiser's willingness to pay

and (ii) simulate the revenue-maximizing number of ads for a search engine. First, I nd

that externality depends on the quality and quantity of competing ads. For example, an

advertiser's willingness to pay decreases by 18.5 percent due to the addition of a second

high-quality ad, but only by 0.15 percent due to the addition of a seventh low-quality ad.

Second, the counterfactual results suggest that the revenue-maximizing number of ads per

page diers across the ad product category, with the average being ve ads per page, and

implementing the suggested number of ads would lead to a 4.5 percent increase in revenue, on

average. These results provide evidence in support of recent changes in the online advertising

market; for example, Microsoft introduced a service called RAIS that provides advertisers

with an option of an exclusive ad display.

Copyright by
PALLAVI PAL
2020

ACKNOWLEDGMENTS

Firstly, I would like to express my sincere gratitude to my advisors Kyoo il Kim and Thomas

D. Jeitschko for the continuous support of my Ph.D study and related research, for their

patience, motivation, and immense knowledge. Besides my advisors, I would like to thank

the rest of my thesis committee: Hanzhe Zhang , Jay Pil Choi and Chenhui Guo, for their

insightful comments and encouragement. A special thanks to Mike Conlin, Ashish Agarwal

and David Croson who provided me an opportunity to discuss and give a fresh prospective

to my research.

I would like to acknowledge nancial support from the Department of Economics, Grad-

uate School, College of Social Sciences, and Council of Graduate Students, along with the

numerous fellowships received through the duration of these PhD years that have been instru-

mental in successful completion of this work. The administrative help and support received

from Lori Jean Nichols and Jay Feight has made navigating this PhD program easier than

it would otherwise have been.

I thank my fellow graduate students Riju Joshi, Sambojyoti Biswas, Haoyang Li, Bhavna

Rai, Katie Harris, Alyssa Carlson, Udita Sanga, Katie Bollman, Akanksha Negi, Tram Hoang

and Ruonan Xu for the stimulating discussions, for the sleepless nights we were working

together before deadlines, and for all the fun we had over the last few years. My warmest

gratitude goes to my family  Mom, Dad, Neha, Sid, and Parikshit as well as my friends

back in India  Ojal, Deeksha, Devangana and Ameya for inspiring me to follow my dreams

and supporting me spiritually throughout writing this thesis and my life in general. Finally,

I would like to thank my best friend and life partner Dhruv Gupta, with whom I shared the

joys and challenges of the PhD life and who motivated me to pursue PhD.

v

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

EGY IN MULTI-SIDED MARKETS†

CHAPTER 1 QUALITY DIFFERENTIATION AND OPTIMAL PRICING STRAT-
. . . . . . . . . . . . . . . . .
1.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Model
1.3.1 Model with one quality case . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Model with two qualities case . . . . . . . . . . . . . . . . . . . . . .
1.4 Equilibrium results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Quality dierentiation and optimal pricing strategy . . . . . . . . . .
1.5.2 Quality dierentiation and extra markup . . . . . . . . . . . . . . . .
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

OF CARBON-CREDIT MARKET†

CHAPTER 2 DYNAMIC GAME WITH MULTIDIMENSIONAL TYPE: THE CASE
. . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
2.2 Model setup
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Symmetric equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . .
2.4 Applications and comparative statics : emission market
2.4.1 Comparison with price control strategies . . . . . . . . . . . . . . . .
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CHAPTER 3 REVENUE-MAXIMIZING NUMBER OF ADS PER PAGE IN THE

PRESENCE OF MARKET EXTERNALITIES† . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
3.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Market environment and theoretical Model . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .
3.3.1 Overview of the search advertising market
3.3.2 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Consumers side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Advertising model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
3.5 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Data details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Characterizing features of the data . . . . . . . . . . . . . . . . . . .
Identication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4.1 Bounds on exclusive ad value

3.4 Equilibrium bid analysis

3.6

vi

1
1
5
9
9
12
15
22
22
23
24

26
26
30
33
36
38
40

41
41
45
47
47
49
49
51
53
56
59
59
62
64

3.7.1
3.7.2
3.7.3

3.6.1 Advertisers value distribution . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Consumers click behavior
. . . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Externality estimation . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.4 Creating market using unsupervised machine learning
. . . . . . . .
3.7 Econometric Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Step 1: Estimate consumer click probability . . . . . . . . . . . . . .
Step 2: Estimate the externality eect on the advertiser's bid . . . .
Step 3: Estimate lower and upper bounds on advertiser's externality-
free value distribution . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.1 Consumers side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.2 Externality eect . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.3 Non-linear eect of externality . . . . . . . . . . . . . . . . . . . . . .
3.8.4 Advertiser willingness to pay for an ad and prot margin . . . . . . .
. . . . . . . . .
3.9.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.9 Counterfactual analysis: revenue-maximizing number of ads

64
65
66
67
69
70
71

73
74
74
75
76
77
78
79
80

APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D
APPENDIX E
APPENDIX F
APPENDIX G
APPENDIX H

83
APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
Figures for Chapter 1 . . . . . . . . . . . . . . . . . . . . . .
85
Proofs for Chapter 1 . . . . . . . . . . . . . . . . . . . . . .
93
Figures for Chapter 2 . . . . . . . . . . . . . . . . . . . . . .
Proofs for Chapter 2 . . . . . . . . . . . . . . . . . . . . . .
94
Figures for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . 101
Tables for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . 117
Proofs for Chapter 3 . . . . . . . . . . . . . . . . . . . . . . 125
Revenue-maximizing number of ads: looking at exible num-
ber of ads . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Robustness Check . . . . . . . . . . . . . . . . . . . . . . . . 135
Data cleaning for Chapter 3 . . . . . . . . . . . . . . . . . . 137

APPENDIX I
APPENDIX J

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

vii

LIST OF TABLES

Table F.1: List of variables available for consumers side data . . . . . . . . . . . . . . 117

Table F.2: List of variables available on advertisers side

. . . . . . . . . . . . . . . . 118

Table F.3: Summary statistics for consumers side data . . . . . . . . . . . . . . . . . 118

Table F.4: Summary statistics for advertisers side data . . . . . . . . . . . . . . . . . 119

Table F.5: Features of dierent categories . . . . . . . . . . . . . . . . . . . . . . . . 119

Table F.6: Externality co-ecient across categories . . . . . . . . . . . . . . . . . . . 120

Table F.7: Quality measure across product categories . . . . . . . . . . . . . . . . . . 120

Table F.8: Estimated average partial eect of position on click probability . . . . . . 121

Table F.9: Results for the revenue-maximizing number of ads per page . . . . . . . . 122

Table F.10: Identifying dierent categories

. . . . . . . . . . . . . . . . . . . . . . . . 123

Table F.11: Robust check: externality co-ecient across categories . . . . . . . . . . . 123

Table F.12: Robust check: dierent externality index denitions

. . . . . . . . . . . . 124

viii

LIST OF FIGURES

Figure A.1: Two-sided rm with quality dierentiation . . . . . . . . . . . . . . . . .

84

Figure C.1: Decrease in uctuation due to price ceiling and oor

. . . . . . . . . . .

93

Figure C.2: Price path for carbon credits for RGGI auction . . . . . . . . . . . . . .

93

Figure E.1: Sample of Yahoo! search result page . . . . . . . . . . . . . . . . . . . . . 101

Figure E.2: Timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Figure E.3: Snapshot of an advertiser's account on Yahoo!

. . . . . . . . . . . . . . . 102

Figure E.4: Percentage of clicks across pages . . . . . . . . . . . . . . . . . . . . . . . 103

Figure E.5: The popularity of the product categories for google in the past ve years

104

Figure E.6: No. of keywords specied by advertisers across days

. . . . . . . . . . . 104

Figure E.7: Average click rate and bid across ad positions

. . . . . . . . . . . . . . . 105

Figure E.8: Revenue per ad across bid . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure E.9: Mean of bids at dierent winning positions . . . . . . . . . . . . . . . . . 106

Figure E.10: Mean click probability for each ad across position . . . . . . . . . . . . . 106

Figure E.11: Relation between the advertiser's bid and percentage of other high-

quality ads on the page

. . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Figure E.12: Eye tracking Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure E.13: Example of sub category within the laptop category . . . . . . . . . . . . 108

Figure E.14: Keywords for Cosine and Euclidean distance . . . . . . . . . . . . . . . . 109

Figure E.15: The predicted click probability across positions

. . . . . . . . . . . . . . 109

Figure E.16: The aect of choosing higher position on click probability . . . . . . . . . 110

Figure E.17: Ad-Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

ix

Figure E.18: Cumulative distribution of Externality Index . . . . . . . . . . . . . . . . 112

Figure E.19: Externality coecient across categories . . . . . . . . . . . . . . . . . . . 113

Figure E.20: Eect of an additional ad on advertisers bid across dierent ad quality . 113

Figure E.21: Diminishing eect of an additional ad on advertisers bid . . . . . . . . . 114

Figure E.22: Upper bound for the cumulative distribution function of the ad value . . 114

Figure E.23: Cumulative distribution of advertiser's ad value . . . . . . . . . . . . . . 115

Figure E.24: Gain in revenue from using the alternate method in appendix(H)

. . . . 116

Figure E.25: Revenue-maximizing number of ads from alternate method suggested in

appendix(H) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

x

CHAPTER 1

QUALITY DIFFERENTIATION AND OPTIMAL PRICING STRATEGY IN

MULTI-SIDED MARKETS†

1.1

Introduction

There has been an increasing shift toward multi-sided rms in many industries. The early

pioneering models of multi-sided platforms were introduced by Armstrong (2006), Caillaud

and Jullien (2003), Parker and Van Alstyne (2005), and Rochet and Tirole (2003).

Im-

portantly, many real-world organizations determine how close or how far they are from a

multi-sided economic model based on changing industrial parameters.

In this paper, we

examine how platforms in multi-sided markets optimally use quality dierentiation as a

business strategy.

As many previous studies emphasize, it is important to establish how multi-sided plat-

forms dier from typical one-sided rms and how such dierences lead to new business

implications. Many markets that have traditionally featured one-sided rms now feature

more two-sided rms due to advanced technology; for example, the taxi industry only had

one-sided rms before Uber appeared. Firms typically begin with an one-sided model and

switch to a multi-sided model as they become more established. Doing so allows poten-

tial platforms to overcome the chicken-and-egg problem by rst providing complementary

goods themselves. For instance, Amazon started o as a pure retailer but has moved closer to

a two-sided model over time by enabling third-party sellers to trade directly with consumers

on its website. We can also nd many other examples in which a rm faces a strategic choice

of how many sides to pursue. For instance, in the personal computer market, Apple produces

its own hardware, whereas Microsoft leaves this to independent manufacturers. As a result,

Apple manages only a two-sided platform with consumers and software providers, while Mi-

†This work is joint with Soo Jin Kim and is unpublished.

1

crosoft manages a three-sided platform with consumers, software providers, and hardware

providers. Indeed, there is an increasing shift from traditional business structures in which

the rm focuses only on one side of users to platforms where the rm serves more than one

side of users.

Given this shift toward multi-sided business, the main strategic choice that we analyze

in this paper is the choice of the quality of interaction between users on two dierent sides.

We focus on platforms that enable interaction between two sides, for example, buyers and

sellers. The term interaction" covers various traditional interactions, such as those observed

in auction houses and those on internet sites in person-to-business transactions, for example,

Amazon. This also includes interactions or exchanges between application developers and

application users on software platforms such as computers (e.g., Apple, Microsoft); mobile

devices (e.g., iPhone, Samsung); and video games (e.g., Sony PlayStation, Xbox). These

markets usually have more than one type of quality access on the buyers' side. For example,

Amazon oers buyers two types of quality access; basic (low-quality) access is free, while

premium access (Prime membership, which is high-quality) is the paid service. It is easy to

see that the interactions or exchanges through the high-quality access have better quality

for example, Prime provides two-day shipping. Many ride-sharing services oer dierentiated

quality tiers for customers. Uber provides riders multiple types of quality services. Although

each region may have dierent availability, there are basically low-quality service at a cheaper

price (e.g. Uber X, Uber Pool ) as well as high-quality service at a little more expensive price

(e.g. Uber XL, Uber Select, Uber Black ). For instance, whereas trips with Uber Pool may

take longer time to nish by sharing the same car with other strangers, Uber Select or

Black is a private car sharing service with more luxurious car. Other ride-sharing services

oer similar quality dierentiation: Didi in China provides three quality tiers with Express,

Premier, and Luxe.

These are examples of quality dierentiation by rms serving two sides. Ultimately, this

paper provides business implications of quality dierentiation in the multi-sided platform

2

market by building a simple model of two-sided monopolists in a market with interactions

between buyers and sellers. The rm chooses the price and the quality of interaction for the

buyers' side.

The rst main nding of the paper is that a rm provides higher quality per dollar

to buyers as it serves more sides. That is, when a rm expands its business from one-

sided service (serving buyers/riders only) to multi-sided service as a platform (serving both

buyers/riders and sellers/drivers), it provides better quality to buyers. Intuitively, if a rm

oers a better quality price menu to buyers, it attracts more buyers. When it serves the

sellers' side at the same time, more demand from the buyers' side makes sellers on the other

side earn more revenue. The platform can extract those additional revenues on the sellers'

side, which incentivizes the platform to oer a better quality price ratio to buyers.

We also nd that the quality dierentiation on the buyers' side decreases the price charged

on the sellers' side compared to the price charged by a single-quality, two-sided rm. The in-

tuition behind this nding is related to product dierentiation and demand elasticity. If the

platform provides multiple quality options for buyers, it means that it provides more dier-

entiated products, which makes buyers more inelastic to price changes because the platform

can extract extra surplus from high-quality buyers without deterring buyer participation. As

the buyers' side becomes more inelastic, it creates an incentive for the platform to extract a

higher rent from the buyers' side and subsidize the sellers' side by lowering the price faced

by sellers.

By providing more quality choices, even if the quality dierentiation is small, the platform

is able to obtain more prots. Given that buyers are heterogeneous in their valuation of

product quality, there is an incentive for the platform to oer dierent levels of product

quality at dierent prices to extract more rents from buyers. Following quality dierentiation,

the platform needs to charge a lower price for low-quality buyers. However, it is able to earn

higher extra markup from the high-valuation group of buyers (who will buy a high-quality

product) if the quality gap is widened. Given that the number of high-quality buyers is

3

suciently large, the platform's ultimate prot is greater with quality dierentiation. Based

on the model predictions, we discuss some business implications concerning how quality

dierentiation in one side of the market helps the platform raise its prot.

Related literature There is a broad literature on the corresponding problem of a

monopolistic rm seeking to maximize prots by oering quality-dierentiated products in

one-sided standard markets. The seminal papers are Spence (1977), Mussa and Rosen (1978),

Maskin and Riley (1984), and M. Itoh (1983). We generalize this problem by varying the

number of sides served by the rm.

This paper is also related to the literature on pricing structure in markets with multi-sided

rms (e.g., Rochet and Tirole (2003), Armstrong (2006b), and Reisinger (2010)). Aside from

being broadly related to the literature on pricing in multi-sided markets, papers on skewed

pricing in multi-sided markets are closely related to our paper in terms of our theoretical

implications. Suarez and Cusumano (2008) discuss the platform's subsidy pricing strategy to

attract greater user adoption, although they do not set up an economic model to conrm this

strategy. Bolt and Tieman (2008), Schmalensee (2011), and Dou and Wu (2018) study skewed

pricing strategies in two-sided markets, i.e., the subsidy and money sides. However, those

papers do not consider forms of product dierentiation, such as the quality dierentiation

examined in our paper, as a means of skewing prices.

Regarding markets with multi-sided rms, few papers have focused on rms choosing the

quality of interaction on their platform. These papers study markets with negative network

externalities and do not endogenize the quality choice. Crampes and Haritchabalet (2009)

examine the choice of oering a pay ads regime and no pay ads packages. Peitz and Valletti

(2004) compare the advertising intensity when media operators oer free services and when

the subscription price is positive. Viecens (2006) is an exception because she studies a

setup with endogenous quality dierentiation on two-sided platforms. However, the quality

dierentiation in her model takes a dierent form from ours in that she focuses on the

quality provided by users on one side and not on the quality provided by the platform itself.

4

Therefore, her results do not provide any implications for the platform's dynamic pricing

structure, such as subsidizing one side at the expense of the other. Another quality-related

aspect explored in the context of two-sided markets is the case in which users care about the

quality of the other users with whom they interact. These papers are relevant for matching

markets such as dating sites. Jeon et al. (2016) examine this problem in a platform setting.

Renato and Pavan (2016) consider this problem in a matching setup. Hagiu (2012) studies

a model in which users value the average quality of other users. The setup in these papers,

however, is dierent from that in ours in that we focus on the quality of interaction and not

on the quality of users.

Our analyses are also related to the literature on product dierentiation in multi-sided

markets, in that quality dierentiation is one form of product dierentiation. Smet and

Cayseele (2010) focus on product dierentiation in platform markets, which still diers from

our paper in that they do not account for its consequences for optimal pricing strategies.

The literature has not focused on endogenizing the choice of network quality in multi-

sided markets with positive externalities. Therefore, our results on how multi-sided markets

are combined with quality dierentiation on a platform provide new insights into the related

business.

1.2 Model setup

We model the interaction between buyers and sellers. Economic value is created through

the interaction between these two sides. We consider the case of a single rm providing

a platform for interactions between buyers and sellers. For instance, Amazon acts as a

transaction-based platform for interactions between sellers and buyers. In addition to charg-

ing an access fee to use the platform, the rm can also control the quality of interaction.

Figure(A.1) displays the structure of the two-sided rm with quality dierentiation on the

buyers' side using Amazon as an example. The two types of access quality oered on the

buyers' side are Amazon Basic and PrimeAmazon Prime is the higher-quality access, as

5

it provides premium services including free two-day shipping.

Specically, we model a two-sided monopolist rm that price discriminates on the buyers'
side by oering two dierent types of access quality: qk ∈ {ql, qh}, where k denotes the
quality provision, either low or high.
In this model, the users' gain from the platform

comes through interaction between users on two sides: buyers and sellers. Both buyers and

sellers obtain utility from interacting with each other. The quality variable controls the gain

from each such interaction. We assume that both buyers and sellers are heterogeneous with

respect to the per-interaction or usage benet. The usage or per-interaction benets are
bb
i (qk) for the buyers' side (for individual buyer i) and bs
seller j), where the superscript b (s) denotes buyers (sellers). For simplicity, we assume

j for the sellers' side (for individual

that bb

i (qk) = Bαb

i qk, where B represents the basic benet for every buyer. This benet

is dependent on the quality of interaction; thus, the monopolist can control the benet by
choosing the quality of platform access qk on the buyers' side. The term αb
i denotes the
heterogeneity among buyers; it follows a distribution function F b with support on [0, 1] and

density f b. Additionally, each buyer pays a price for using the platform, which is denoted pb
k

as a usage or per-transaction fee. For a buyer i, the utility function is given by the following:

U b
ik = [bb
⇔ U b
ik = (Bαb

i (qk) − pb
i qk − pb

k]N s, where k ∈ {l, h}
k)N s.

(1.1)

(Bαb

i qk − pb

The buyers' utility is the net benet from each interaction with the other side, i.e.,
k), multiplied by the number of interactions, which is denoted N s.1 From the
utility specication, it can be shown that the buyer with the highest benet is that with
αb
i = 1, i.e., Bαb
1We assume here that every buyer interacts with every seller and that every seller interacts
with every buyer. We can easily extend this to a model where the number of interactions
is a function of the total number of sellers, such as g(N s). The results are robust to such
extensions.

i = B.

6

We assume that the access fee pb

k is charged per-transaction for simplicity. Indeed, certain

kinds of platforms charge for premium service based on usage: for Uber, a basic service (Uber

X) is cheaper than a premium service (Uber Select) for the same trip. We view that the

per-usage fee for the basic service (low-quality) is zero (i.e., pb

l = 0 in this example) whereas

that for the premium service (high-quality) is the dierence between two riding costs (i.e.,

pb
h > 0). Nevertheless, it is worth noting that many platforms charge an one-time xed

access fee: for instance, Amazon Prime costs either nothing for Basic but $119 per year (or

$12.99 per month) for Prime service. Note that the qualitative results hold under the model

with xed fees, as shown in the Appendix(B). Such one-time xed fee structure can also be

considered as a variation of per-transaction fee by considering the xed fee as continuous:

if Amazon Prime members make hundred transactions per year on average, the average

per-transaction cost is $1.19 (i.e., pb

l = 0 and pb

h = $1.19).

The sellers' side is not aected by quality; therefore, there is no quality component. We

assume that bs

j represents seller j's heterogeneity with respect to the per-
usage benet, which is also distributed by a distribution function F s with support on [0,1]

j = Sαs

j, where αs

and density f s. For seller j, the utility function is given by the following:

U s
j = (bs
⇔ U s
j = (Sαs

j − ps)N b
j − ps)N b.

(1.2)

j −
The sellers' utility is the net benet from each interaction with the other side, i.e., Sαs
ps, multiplied by the number of interactions, which is denoted N b.2 All sellers are charged

ps per interaction, so the price discrimination is only on the buyers' sidefor example, an

individual seller on Amazon pays $0.99 for each sale. The total number of interactions is

N bN s.3

2In this model, we assume that the sellers' side is aected only by the total number
of buyers, not the type of buyer with which a seller interacts. Thus, the total number of
interactions for each seller is N b, and the total number of interactions by sellers is not aected
by the type of buyer with which they interact.

3Note that the qualitative results still hold under a generalized setup with any function

of N bN s.

7

Next, the cost of the two-sided monopoly rm depends on the quality provided. The total
cost of a transaction is given by c(ql) ≥ 0 for a transaction between a low-quality buyer and a
seller and c(qh) ≥ 0 for a transaction between a high-quality buyer and a seller. In Amazon
example, such cost dierentiation captures that two-day shipping for Prime members is

costlier than standard shipping for Basic members. We normalize the cost for sellers cs = 0.
The cost function is assumed to be increasing and convex in quality (c(cid:48)(q) > 0 , c(cid:48)(cid:48)(q) > 0).
We analyze the nontrivial case in which qh > ql.

The demand on the buyers' and sellers' sides is represented by Db and Ds, respectively.

In equilibrium, demand will be equal to the number of participants on each side, which

means Db

k = N b

k andDs = N s, where k ∈ {l, h}. Given the equilibrium demands, we turn

to the monopolistic platform's problem. The monopoly platform's problem can be written

as follows:

ˆ If one type of quality is oered:

Π = [pb + ps − c(q)]DbDs.

max

(ps,pb,q)

ˆ If two types of quality are oered:

max
,pb
h

(ps,pb
l

,ql,qh)

Π = [pb

l + ps − c(ql)]Db

l Ds + [pb

h + ps − c(qh)]Db

hDs.

(1.3)

(1.4)

Note that if the monopolist serves only one side of the market, say the buyers' side, its

prot function is given by the following:

Πone-sided monopolist = [pb − c(q)]Db,

max
(pb,q)

(1.5)

in the case of one quality. Throughout the paper, we make the following assumptions.

Assumption 1. The cost is increasing and convex in quality: c(cid:48)(q) > 0 , c(cid:48)(cid:48)(q) > 0.

This suggests that it becomes increasingly costly to provide higher-quality service, which

is a standard assumption.

8

Assumption 2. The distribution functions for buyers and sellers are increasing in type:
(f b)(cid:48) ≥ 0 and (f s)(cid:48) ≥ 0, which implies that f b(1) > 0 and the inverse hazard rate is non-

increasing in user type:

∂

≤ 0, k = {b, s}.

1−F k(θ)
f k(θ)
∂θ

This implies that we consider the case with a positive mass of consumers. Additionally,

it guarantees that as users value the per-usage benet more, there are more platform users

than nonusers.

Assumption 3.

∂U b(αb
i ,pb,q)
∂pb

< 0,

∂U b(αb
i ,pb,q)
∂q

> 0,

Assumption 4. The single crossing property holds:

∂U s(αs
∂ps

i ,ps)

< 0.
∂2U b(αi,q(αi))

∂αi∂q

> 0.

This means that we can always distinguish high-type buyers from low-type buyers based

on their αi.

1.3 Model

1.3.1 Model with one quality case

As a benchmark, we begin by considering a model that omits the practice of quality dier-

entiation and then modify the model to allow for its practice in Section 1.3.2. The two-sided

monopolist oers a single quality of access in this case. Buyers have the following utility:

U b
i = (Bαb

i q − pb)N s,

where q ∈ [0, 1] denotes the quality index. The seller has the following utility:

U s
j = (Sαs

j − ps)N b.

(1.6)

(1.7)

We rst analyze the user side (buyers and sellers) to identify the equilibrium demand.

The equilibrium demand functions are derived from the participation constraint:

(cid:16)
(cid:16)

Db = P rob

Ds = P rob

i ≥ 0
U b

j ≥ 0
U s

(cid:17) ⇔ Db = 1 − F b
(cid:17) ⇔ Ds = 1 − F s

(cid:32)
(cid:18) ps

pb
Bq

(cid:33)
(cid:19)

.

S

.

(1.8)

9

The monopoly problem can be written as follows:

Π = [pb + ps − c(q)]DbDs,

max

(ps,pb,q)

(1.9)

where we have normalized the marginal cost on the seller's side to zero, i.e., cs = 0. We can

solve for the optimal solutions for the buyers' side and sellers' side as follows:

pb − c(q) + ps

pb

=

1
εb

;

ps − c(q) + pb

ps

=

1
εs .

(1.10)

Equation (1.10) is similar to the standard Lerner pricing formula, which states that the

markup on price is equal to the inverse of the price elasticity of demand. The price elasticity

of demand for buyers (or sellers) is represented by εb (or εs). The added term in the case of a

two-sided rm is the extra opportunity cost of increasing the price on the buyers' (or sellers')
side, which is the marginal loss on the sellers' (or buyers') side, equal to ps (or pb − c(q)).

Finally, the optimal condition for quality is given as follows:

c(cid:48)(q) =

[pb − c(q) + ps]

Db

∂Db
∂q

.

(1.11)

The optimal quality equates the marginal cost to the marginal revenue of increasing

quality. The marginal revenue is the change in buyers' demand,4 which is represented by
∂Db
∂q

times the per-transaction prot. From the conditions given above, the equilibrium

price-quality structure is given by Theorem 1.3.1.

Theorem 1.3.1. The equilibrium price and quality variables are given by the following equa-

tion:

qc(cid:48)(q)
νb

=

pb
εb

=

ps
εs ,

(1.12)

where νb is the quality elasticity of demand on the buyers' side, and εb or εs is the price

elasticity of buyer or seller side, respectively.

4In the optimal quality equation, the term for the number of sellers (Ds) is canceled out,

as it is present on both sides of the equation.

10

Equation (1.12) is similar to the equilibrium of two-sided market with quality decision by

the platform as in Rochet and Tirole (2003). However, our equilibrium condition still diers

from that in Rochet and Tirole (2003) insofar as we focus on a three-way trade-o which

includes the quality variable as well, instead of a trade o between prices on the two sides.

By placing a main focus on price variables only, Rochet and Tirole (2003) nd that price on

the buyers' side would be lower if sellers are more price elastic because the platform wants

to balance the sizes of two sides. Theorem 1.3.1 further says that the higher quality the

platform oers, the higher price it charges to buyers, while such upward pressure on prices

diminishes as buyers becomes less quality sensitive.

Given that many platforms consider their quality of service as another important decision

variable, our nding broadens the necessary considerations for the platform: it needs to set

optimal prices not only by considering the price structures in terms of the ratio of price

elasticities, as pointed out in Rochet and Tirole (2003), but also by taking quality elasticity

into account, as we additionally nd. For instance, if buyers on Amazon become more

elastic to quality increase, Amazon is able to increase the buyers' side demand substantially

by improving its quality at a minimal level. Accordingly, if Amazon changes its shipping

policy for Prime members to three-day shipping, instead of two-day shipping, and lowers the

fee charged to Prime members (i.e., pb is lower than $119 per year, which is currently set for

two-day shipping benets), this makes Amazon better o because more Basic members will

sign up for Prime members: the demand increasing eect arising from quality improvement

outweighs price decreasing eect due to large quality elasticity.

Allowing the platform to consider how high or low quality its service is oered, or how

quality tiers it provides are dierentiated, opens more doors for optimal business strategies,

insofar as quality choice gives another level of exibility in terms of prot maximization to

the platform. Indeed, as we will show, the platform's optimal pricing decisions depend on

its quality choice.

11

1.3.2 Model with two qualities case

We start by analyzing the users' side (buyers and sellers) to identify the equilibrium demand.

First, the buyers have two choices for accessing the platform. They can join the platform

through either low-quality access or high-quality access. Given the two types of quality, high

and low, the number of participants joining with low-quality access is determined by the

number of buyers who satisfy the following two conditions:

1. (IR constraint) The buyers' utility from low-quality access is greater than zero: P r(U b

l ≥

0).

2. (IC constraint) Buyers for whom the utility derived from low-quality access exceeds that

from high-quality access: P r(U b

l ≥ U b
h).

The two conditions jointly determine the proportion of low-type buyers.

(cid:18) pb
Db
l = Pr
l ≡ Db(pb

h − pb
B(qh − ql)
h, pb

l

(cid:19)

(cid:19)

(cid:18) pb

h − pb
B(qh − ql)

l

(cid:19)

,

(cid:18) pb

l
Bql

− F b

≥ αb

i ≥ pb
l
Bql

= F b

(1.13)

where Db

l , qh, ql). Similarly, the number of participants joining the high-quality

service is given by the number of buyers who satisfy the following two conditions:

1. (IR constraint) The buyers' utility from the high-quality good is greater than zero: P r(U b

h ≥

0).

2. (IC constraint) Buyers for whom the utility derived from the high-quality good exceeds

that from the low-quality good: P r(U b

h ≥ U b
l ).

The IR condition is satised when the IC constraint of the high type and IR constraint

of the low type holds.5 Thus, the proportion of high-type buyers is given by:

Db

h = Pr(U b

⇔ Db

h = Pr

(cid:18)

h ≥ U b
l )
h − pb
i ≥ pb
αb
B(qh − ql)

l

(cid:19)

= 1 − F b

(cid:18) pb

h − pb
B(qh − ql)

l

(cid:19)

,

(1.14)

5We maintain the standard single crossing condition, which implies that higher types
have greater willingness to pay (WTP) for quality at any price or that consumers may be
ordered by their type.

12

where Db

h ≡ Db(pb

h, pb

l , qh, ql). Given the utility function for buyers, the total number of

buyers joining the platform is given by the following:

Db = Pr(U b
⇔ Db = Pr(Bαb

l ≥ 0) = Pr(bb
i ql ≥ pb

l ) = Pr(αb

l ≥ pb
l )
i ≥ pb
l
Bql

(cid:19)

,

(cid:18) pb

l
Bql

) = 1 − F b

(1.15)

where Db ≡ D(pb

l , ql). Equation (1.15) shows us how the number of participants on the

buyers' side depends only on the price and quality of the low-quality good. Although there

are network externalities in the total utility derived from the platform or the gross transaction

utility, the per-unit transaction demand is not dependent on the participation rate on the

other side.6 This is because the participation constraint (IR constraint) for the high-quality

buyers is slack. This means that the participation of low-quality buyers guarantees the

participation of high-type buyers. In other words, the buyers on the margin of joining the

platform are low-quality buyers.

Next, the total number of sellers who join the platform is given by the following:

Ds = Pr(U s ≥ 0) = 1 − F S

,

(1.16)

where Ds ≡ Ds(ps). Given the total number of buyers and sellers, the equilibrium level of

(cid:18) ps

(cid:19)

S

participation is the following:

Db = D(pb

Db

l = F b

(cid:19)
(cid:18) pb
(cid:18) pb
(cid:19)
(cid:18) pb
l
Bql
(cid:19)
l , qh, ql) = 1 − F b

(cid:18) pb
(cid:19)
l , ql) = 1 − F b
(cid:18)ps

h − pb
B(qh − ql)
h, pb

l
Bql
− F b

,

l

.

S

Db

h = Db(pb
Ds = Ds(ps) = 1 − F s

(cid:19)

h − pb
B(qh − ql)

l

Given quality dierentiation, the monopoly problem can be written as follows:

max
,pb
h

(ps,pb
l

,ql,qh)

Π = [pb

l + ps − c(ql)]Db

l Ds + [pb

h + ps − c(qh)]Db

hDs.

6This setup has one restriction that we need to impose, which is that the proportion of

low-type buyers has to be nonnegative: Db

l ≥ 0.

13

(1.17)

(1.18)

The following is the breakdown of the equilibrium prices and quality for buyers and

sellers:7

1.3.2.1 Price of low-quality access on the buyer side

We rst examine the price of low-quality access on the buyer side as follows.

l − c(ql) + ps
pb

pb
l

=

1
εb

, after using equilibrium value of pb
h,

(1.19)

where the price elasticity of demand for low-quality access is represented by εb. Note that

the equilibrium conditions for the price elasticity with respect to the lower price is denoted

as those for the full demand: that is why we have εb, not εb
l .

1.3.2.2 Price of high-quality access on the buyers' side

The price of high-quality access on the buyers' side can be obtained as follows:

pb
h = pb

l +

[c(qh) − c(ql)] +
(cid:124)

(cid:123)(cid:122)

pb
h
εb
h

(cid:125)

additional cost plus extra market power

,

(1.20)

where the price elasticity of demand for high-quality access is represented by εb

h. The optimal

price for high-quality access is equal to the price for low-quality access and the additional
cost, i.e., c(qh) − c(ql), plus an additional markup, i.e.,

.

pb
h
εb
h

1.3.2.3 Price for sellers

We now turn our attention to the price for sellers.
ps

l + ps − c(ql) =
pb

εs − pb

h
εb
h

Db
h
Db

.

(1.21)

Again, Equation (1.21) is similar to the standard Lerner pricing formula, which states

that the markup on price is equal to the inverse of the price elasticity of demand. The added

term in the case of a two-sided rm is the extra opportunity cost of increasing the price on

7The details are in the Appendix.

14

the sellers' side, which is the marginal loss on the buyers' side, and is equal to the average

per-interaction prot on the buyers' side.8

1.3.2.4 Low-quality service for buyers

Given prices, the monopolistic platform solves the prot maximization problem separately

for the low- and high-quality services for buyers. First, for the low-quality service, the rst

order condition can be derived as follows:

l + ps − c(ql) =
pb

l c(cid:48)(ql) + Db
Db
Db

hc(cid:48)(qh)

,

ql
νb

(1.22)

where νb denotes the quality elasticity of demand for low-quality access. The cost of low

quality service equates the marginal cost to the marginal revenue of increasing quality.

1.3.2.5 High-quality service for buyers

Here, the rst order condition for the high-quality service for buyers is given by the following:

c(cid:48)(qh)

=

qh
νb
h

pb
h
εb
h

,

(1.23)

where νb
h denotes the quality elasticity of demand for high-quality access. The marginal cost
c(cid:48)(qh) should be equal to the marginal revenue, which is the product of increased high-quality

, and the extra markup generated from the increase in high-quality buyers,

νb
h
qh

buyers, i.e.,

i.e.,

pb
h
εb
h

.

1.4 Equilibrium results

We derive several important implications from the model. Before we examine the diverse

eects of quality dierentiation on the platform's strategies, we rst address that the mo-

nopolistic rm provides higher quality to buyers for each dollar that they pay when it serves

more sides of the market. As the monopolist opens more sides to serve, say from a one-sided

8Note that we have normalized the cost on the seller's side to zero, so cs = 0.

15

rm serving buyers only to a two-sided rm as a platform serving both buyers and sellers,

such openness increases the quality per dollar oered to buyers. Mathematically, the quality
per dollar is denoted as q

pb . This nding is summarized in Proposition 1.4.1.

Proposition 1.4.1. As a rm serves more sides of the market, it provides higher quality

per dollar oered to buyers:

One-sided rm ≤ q
pb

q
pb

Two-sided rm.

Intuitively, the monopolist serving multiple sides has more incentive to oer a better

quality price ratio to buyers because it now obtains more prot from the seller's side. If the

two-sided rm oers a better quality price menu to buyers, it attracts more buyers. When

it serves the sellers' side at the same time, more demand from the buyers' side makes sellers

on the other side earn more revenue. The platform can extract those additional revenues

on the sellers' side, which incentivizes the platform to oer a better quality price ratio to

buyers.

In other words, the openness of the platforms from serving one side of users only to serving

both sides increases the quality per dollar, which ultimately attracts more buyers than a

one-sided rm. Both traditional one-sided rm and two-sided platforms oer dierentiated

quality tiers for buyers. When those two types of rms engage in quality dierentiation on

buyers' side, we show that the platform is more willing to oer a better deal to low type

members by giving a high quality per dollar in the basic level than a one-sided rm. For

example, the average quality of services provided by taxi companies, as traditional one-sided

rms, is known to be lower than that provided by ride sharing platforms, such as Uber

and Lyft. As Liu et al. (2019) shows, taxi drivers are more likely to detour with non-local

customers, which results in longer travel time. Such empirical evidence supports our nding

that the platform's basic quality provision is better than a one-sided rm's. The reason

the platform provides a higher quality for basic service is because it is able to exploit such

quality improvement in one side to encourage more participation from the other side, thereby

raising its prots. As in the ride sharing platforms example, when such platforms provide

higher basic quality for riders, which attracts more riders, it ultimately gives a stronger

16

incentive for drivers to join the platforms, thereby permitting them to extract more rents

from drivers: the underlying incentives for the platforms to provide higher service provision

than a one-sided rm arise from this cross-subsidization motive. This nding is summarized

in Corollary 1.4.2.

Corollary 1.4.2. The platform in two- or multi-sided market is more likely to oer higher

quality of basic service or product than a one-sided rm.

Now, we will show how the quality provision decided by the platform aects its opti-

mal use of the interaction between two sides, such as cross-subsidization, in the following

propositions below. Returning to the multi-sided platform case with two qualities provision,

we rst nd that quality dierentiation reduces the other side's price level. The Appendix

contains a proof of this result.

Proposition 1.4.3. Quality dierentiation on the buyers' side decreases the price charged

on the sellers' side relative to the price charged by the platform that oers one quality.

The eect of oering low- and high-quality access to the buyers makes the buyers more

price inelastic because the platform can extract additional surplus from high-quality buyers

without deterring buyers' participation. Now, recall that for multi-sided rms, the optimal

pricing scheme is to subsidize the more elastic side of the market and extract rents from the

other, more inelastic side. As the buyers' side becomes more inelastic, it creates an incentive

for the platform to extract higher rent from the buyers' side and subsidize the sellers' side

by lowering the price charged to sellers. This can be explained by comparing the equilibrium

pricing structures of the two cases:

one-quality case:

two-quality case:

ps
εs =
ps
εs =

pb
εb
pb
l
εb

=

+

qc(cid:48)(ql)
νb
pb
h
εb
h

Db
h
Db

.

l c(cid:48)(ql) + Db
Db
Db

hc(cid:48)(qh)

=

ql
νb

hc(cid:48)(qh)
Db
Db

.

+

qh
νb
h

(1.24)

Similar to the single-quality case, the platform faces a trade-o of whether to charge a

higher price on the buyers' or sellers' side in cases with two quality types. After quality dif-

ferentiation, the trade-o features an additional markup benet on the buyers' side, namely,

17

the extra margin from high-quality buyers. Thus, the monopolist becomes more ecient in

extracting rent from the buyers' side. Given this, the platform has a higher incentive to

increase the size of seller demand by lowering the price on the sellers' side.

We also nd that quality dierentiation leads to greater prot for the platform, as in

Corollary 1.4.4. The detailed proof is in the Appendix.

Corollary 1.4.4. The platform strictly prefers to price discriminate by quality on the buyers'

side

Corollary 1.4.4 implies that a platform that provides only one type of quality is able

to obtain more prot if it slightly dierentiates product quality. Even a minor quality

improvement with a small price increase can increase the platform's prot as long as it

continues to provide dierentiated products, such as low- and high-quality products. Thus,

quality dierentiation permits the platform to earn more prot by implementing premium

service in addition to basic service, which not only expands the total buyer market size, but

also extracts more rents from relatively high-quality type of buyers.

As for the the platform's optimal quality provision, we nd that the high quality provision

is independent of the sellers' side equilibrium whereas the low quality provision is related

to the sellers' side equilibrium. By comparing Equations (1.22) and (1.23), we derive the

following proposition.

Proposition 1.4.5. The platform's optimal quality level for the high-quality service does not

depend on the sellers' side equilibrium, whereas that for low-quality service increases in the

marginal revenue from the sellers' side.

Proposition 1.4.5 states that the platform has an incentive to increase the quality level of

the basic service (low-quality) because of the positive network eect coming from the sellers'

side, whereas it does not consider the network eect when determining the optimal quality

level of the premium (high-quality) service. The intuition behind this nding relates to total

buyer demand. As in Equation (1.15), the participation constraint for high-quality buyers is

18

slack, which means that the eect of increasing the quality level of the premium service does

not increase the total buyer demand, although it increases the share of high-quality buyers.

The platform will be able to increase the total buyer demand, Db, only by attracting more

low-quality buyers, and one way of doing so is to increase the quality level of the basic (low-

quality) service. More total buyer demand arising from increasing ql boosts the marginal

revenue from the sellers' side due to the positive network eect on the platform. Thus, the

optimal condition for ql is a function of the marginal revenue on the sellers' side.

Moreover, we nd that the additional markup from quality dierentiation is increasing in

the quality gap. Thus, if the platform suciently dierentiates its product line with respect

to quality, it can earn a higher markup. Proposition 1.4.6 summarizes this nding.

Proposition 1.4.6. The platform's incentive to raise the fee charged to high-quality buyers

is increasing in the dierence in quality, as shown in

∂

(cid:17)

(cid:16)
pb
h/εb
h
∂(qh−ql) > 0.

Proposition 1.4.6 implies an interesting resultthe platform is more likely to charge a

higher fee to high-quality buyers if it either provides much better service (e.g., one-day rather

than two-day shipping for Amazon Prime members) or maintains the high-quality service at

the same level while reducing the quality of the basic service (e.g., increasing the minimum

order qualied for free shipping for Amazon Basic members). Section 1.5.2 discusses this

point in depth.

In addition, we examine the strategic relationships between the platform's choice variables

to derive further implications. We rst examine whether the platform's decision variables

are strategic complements or substitutes in the game of the one-quality case.

Proposition 1.4.7. The prices on the buyers' side (pb) and the sellers' side (ps) are strategic

substitutes. Whether the price variable (buyer or seller side) and quality variable are strategic

substitutes or complements is ambiguous.

From Proposition 1.4.7, reducing pb is the prot-maximizing response to increasing ps,

and vice versa. This means that the platform does not maximize its prots if it increases

19

both prices. Unlike this case, the strategic relationship between price and quality variables

is ambiguous. The price for the buyer and quality are strategic substitutes if
pb

Bq ) − 1

Bq2 [pb + ps − c(q)]f(cid:48)( pb

Bq )} + c(cid:48)(q) 1
Bq2{Dsf b( pb
the seller and quality are strategic substitutes if ∂2Π
If F b and F s both have a uniform distribution, ∂2Π
∂pb∂q
whereas ∂2Π

∂ps∂q is negative if c(cid:48)(q) > S(S − ps) pb

Bq f b( pb
∂ps∂q = Ds pb

Bq ) < 0. Similarly, the price for
Bq2 f b( pb

S ) < 0.
is always positive (because f(cid:48) = 0),

Bq )−c(cid:48)(q) 1

S2 f s( ps

Bq2 . This parametric example suggests that
if the platform increases quality, it charges buyers a higher price but sellers a lower price

∂2Π
∂pb∂q

=

(provided that the marginal cost of increasing quality is above a certain threshold).

Next, we derive results from the two-qualities case. For simplicity, we assume that F b

and F s both have a uniform distribution, which implies that the prot in the two-qualities

case is given as follows.

Π =

1 − ps
S

h − q2
pb

(cid:18)

(cid:19)(cid:16)

h + ps(cid:17)(cid:34)

(cid:35)

(cid:32)

+ 1

+

(cid:33)(cid:16)

1 − pb
l
Bql

l − pb
pb
B (qh − ql)

h

l + ps(cid:17) .

l − q2
pb

By the rst order conditions derived in 1.3.2, we nd the following.

(cid:1) + ps(cid:105)

(cid:104)

pb
h + qh

(cid:0)qh − 2ql
2(cid:0)qh − ql
(cid:1) 2
 .

+ 2ql

.

(1.25)

(1.26)

∂pb

∂2Π
l ∂pb
h
∂2Π
∂pb
l ∂ql
∂2Π
∂pb
l ∂ps
∂2Π
∂pb
h∂ql

=

2(qh − ql)

;

ql

B +

qh

=

1
2

∂2Π
∂pb
l ∂qh
h − q2
pb

(cid:16)
(cid:0)qh − ql

= − ql
h + ps(cid:17)
(cid:1)2

=

qh

2(qh − ql)

− 1;

= − B
2

;

∂2Π
h∂ps

∂pb

∂2Π
h∂qh

∂pb
= − 1
2

.

=

B
2

+ qh.

From Equation (1.26), we identify whether two choice variables are strategic substitutes

or complements for the platform. The following proposition summarizes the ndings.

Proposition 1.4.8. The price for high-quality access for buyers (pb

ment for the price for low-quality access for buyers (pb

h) is a strategic comple-
l ) and high-quality service (qh), whereas

20

it is a strategic substitute for the price for sellers (ps) and low-quality service (ql). Whether

the price for low-quality access for buyers is a strategic substitute or complement for quality

measures and the price for the seller is ambiguous.

Note that if the high-quality service is much better than the low-quality service,9 pb

l is
a strategic substitute for qh but a strategic complement for ps. This implies that if the

platform improves the high-quality service (qh increases), the prot-maximizing response is

to increase the price for high-quality access for buyers while decreasing that for low-quality

access. In addition, the best response to an increase in the price for high-quality access for

buyers is to decrease the price for sellers. However, if the platform increases the price for

low-quality access for buyers, the optimal response is to increase the price for sellers provided

that the quality dierence is large enough.

Finally, we also conduct comparative statistics to determine how changes in the exogenous

parameters aect the equilibrium outcomes. In particular, we are interested in how B, which

represents the basic benet from the quality dimension for every buyer, aects consumer

demand in the two qualities case. Proposition 1.4.9 summarizes the result.

Proposition 1.4.9. Consumer demand for the high-quality service always increases in the

basic benet from better quality (B). Whether consumer demand for low-quality service

increases in B is ambiguous.

In other words,

∂Db
∂B is always positive (where Db
h

∂Db
∂B is positive only if a certain condition is met (where Db
l
l
h−pb
pb
B(qh−ql)

∂Db
l
∂B is positive if

Specically,

h−pb
pb
qh−ql

l

f b

pb
l
ql

f b

pb
l
Bql

>

(cid:32)

(cid:33)

h is given by Equation (1.14)), whereas

(cid:32)

(cid:33)

is given by Equation (1.13)).

l

and negative otherwise.

That is, when the basic benet from the quality dimension increases, it can reduce the

buyers' demand for low-quality access if the price-quality ratio for the quality dierence

(between high- and low-quality) is greater than that for low-quality service. As in Equation

9We can guarantee that

∂2Π
∂pb
∂qh
l

< 0 and ∂2Π

∂pb
l

∂ps > 0 if qh > 2ql.

21

(1.13), buyers in the middle range of willingness to pay (i.e., who are willing to pay for low-

quality service but not for higher priced high-quality service) demand low-quality service

access. As B increases, we observe two simultaneous outcomes: (1) more buyers who were

(cid:32)

(cid:33)

pb
l
ql

f b

pb
l
Bql

(cid:32)

(cid:33)

not in the market join the low-quality service (measured by

), and (2) more

buyers who used to use the low-quality service switch to high-quality service (measured by
h−pb
pb
qh−ql
buyers for the low-quality service. Per Propositions 1.4.7, 1.4.8, and 1.4.9, we can see that

). If the latter eect is larger than the rst, a greater B leads to fewer

f b

h−pb
pb
B(qh−ql)

l

l

considering quality dierentiation for the platform aects its strategic choices on the price

and demand structure. If the platform overlooks such dynamic relationship between quality

choice and optimal pricing, it could lose a potential opportunity for better business strategies

using three-way interaction among quality, buyers', and sellers' side.

1.5 Discussion

Quality dierentiation is one example of product dierentiation, which makes buyers'

demand less elastic. In other words, the platform can strategically use quality dierentiation

to maximize its prot. In Section 1.5, we discuss several business implications based on our

theoretical predictions.

1.5.1 Quality dierentiation and optimal pricing strategy

As in the model, if the platform provides dierent quality choices to buyers, it faces more

inelastic demand from them, which allows the platform to charge a lower price to users on

the other side, namely sellers. Specically, the platform can extract a higher margin from

buyers by providing multiple dierent qualities, which makes their demand inelastic. Given

more inelastic demand from buyers, the platform nds it optimal to increase the number of

sellers, as this increases the utility of buyers from interactions through the platform. The

platform can increase the number of sellers by decreasing the price on the sellers' side, which

is one way of subsidizing sellers.

22

There are several instances in which the platform might nd it protable to subsidize

sellers by exploiting buyers' inelastic demand (arising from quality dierentiation). One

such example is a ride sharing service that connects riders and drivers such as Uber. The

model ndings predict that if Uber provides two or multiple dierent quality of services, for

example a premium service with a higher usage fee and a basic service with a lower usage

fee, which makes consumers' demand inelastic (due to quality dierentiation), the platform

(Uber) is able to maximize its prot by charging a lower driver's pay rate (a price charged to

drivers). In particular, if there is competitive pressure in attracting drivers, the platform can

strategically exploit the quality dierentiation on the riders' side to subsidize the drivers'

side, which helps it overcome intense competition on the drivers' side. Suppose that the

competition for drivers is so intense, after Lyft and other competitors start operating, that

it is dicult for the company to have sucient number of drivers during the peak time. The

platform wants to attract more drivers because widespread availability of drivers is crucial

for expanding its business. Here, if the Uber charges much lower fees for drivers, more drivers

will be willing to work for the platform. Our theory predicts that the platform will oer

lower fees in equilibrium by dierentiating on product quality on the riders' side, which leads

to a higher driver participation rate.

1.5.2 Quality dierentiation and extra markup

The model predicts that the platform will earn more extra markup if it widens the quality

gap. This suggests that the platform can adopt either of two strategies: it can improve the

high-quality product while maintaining the low-quality product at the same level, or it can

reduce the quality of the basic product while maintaining the high-quality product at the

same level. Both strategies lead to more quality dierentiation, which results in more extra

markup being charged to the high-quality buyers per Proposition 1.4.6.

Most incumbent platforms can use their pre-existing resources to develop a much higher

quality product, thereby generating more quality dierentiation (higher qh). However, be-

23

cause entrants or small platforms lack substantial resources, they might not be able to make

large investments to produce better-quality products. What those platforms can do is to

provide a very basic quality product at a lower price (or zero price) and a slightly higher

quality product at a higher price (lower ql). In other words, by lowering the basic product

quality at an almost zero price (or free of charge), the platforms can enjoy more extra markup

even without having very high product quality. For example, there are two ways for Amazon

to widen the quality gap. It could make its high-quality service more attractive by providing

one-day shipping for Prime members. Alternatively, it could oer more dierentiated ser-

vices by maintaining the two-day shipping policy for Prime members while reducing some

of the benets for basic members, for example, increasing the order minimum to qualify for

free shipping from $25 to $30.

1.6 Conclusion

This paper analyzes a generalized version of quality dierentiation by a monopolist in

a multi-sided market. The main focus of this paper's analysis is the eect of buyers' side

quality dierentiation on the optimal pricing strategy for the platform. We rst showed

that quality dierentiation on the buyers' side will decrease the price charged to sellers.

To understand the intuition behind this result, recall that the pricing structure for multi-

sided rms depends on the relative elasticity of the two sides. Quality dierentiation on the

buyers' side can increase the surplus extracted from buyers, which means that the buyers'

side becomes relatively inelastic. The platform can exploit this inelastic demand among

buyers to extract more prot from that side while discounting the sellers' side by decreasing

the price charged to them. This nding suggests how a platform can subsidize the more

elastic side by introducing quality dierentiation on the other side.

We also found that quality dierentiation, which leads to a lower price on the sellers'

side, ultimately increases the platform's prot. Thus, the platform can strategically use

quality dierentiation to raise its prots. Another strategic variable that the platform can

24

use is the extent to which the two qualities dierthe platform can earn extra markup from

relatively high-valuation buyers by widening the quality gap. Given that the driving force of

this greater markup is the quality gap, rather than how high the quality of the better-quality

product should be, we derive relevant business implications, especially for small platforms or

entrants without substantial resources: if they are unable to make a higher quality product

due to their limited resources, they can lower their basic product quality, which would lead

to similar consequences in terms of the quality gap.

Overall, our ndings suggest one plausible business strategy for the platform: how quality

dierentiation implemented by the platform can be used as an optimal business strategy. It

would be interesting for future research to investigate how competition in the platform market

alters our results. In this regard, a model with an asymmetric setup in the competitive market

structure faced by the platform could determine the extent to which such asymmetry aects

the platform's optimal business strategy.

25

CHAPTER 2

DYNAMIC GAME WITH MULTIDIMENSIONAL TYPE: THE CASE OF

CARBON-CREDIT MARKET†

2.1

Introduction

One of the most popular market-based solutions for limiting greenhouse gas emissions

(GHG) is to use Cap-and-Trade schemes. Under the scheme, rms use emission credits to

pay for GHG emissions. The scheme's governing body begins by setting a cap on allowable

emissions. It then distributes or auctions o emissions allowances that total the cap. The

rms that do not have enough allowances to cover their emissions must either make reductions

or buy another rm's spare credits. Members with extra allowances can sell them or bank

them for future use.

A successful cap-and-trade scheme relies on a strict but feasible cap that decreases emis-

sions over time. If the cap is set too high, an excess of emissions will enter the atmosphere

and the scheme will have no eect on the environment. A high cap can also drive down the

value of allowances, causing losses in rms that have reduced their emissions and banked

credits. If the cap is set too low, allowances are scarce and overpriced. The previous liter-

ature has looked at the optimal rate of decrease in supply for the carbon credit market by

accommodating the eect on carbon credits being optimally valued.

In this paper, we extend this analysis and look at the optimal per period supply when

there is an uncertainty of future demand in the market. We nd that in the dynamic setting

introduction of demand uncertainty changes the optimal supply rate. In particular, we nd

that the expectation about future supply and demand changes the equilibrium price and

contributes to price uctuation in the market.

Several papers have shown evidence of price uncertainty in the carbon permits market.
†This work is joint with Thomas D.Jeitschko and is unpublished.

26

The demand of carbon permits is uncertain and uctuates due to multiple reasons such

as weather conditions, high correlation with electric power generation, nancial trading in

carbon permits. For example, in the EU emissions trading system (EU ETS) 1 a dry summer

in July 2005 in Southwestern Europe led to under-utilization of hydroelectric plants and a

lack of cooling water for nuclear power plants, which therefore increased the demand for

carbon permits. Thus, it is integral to accommodate the uncertainty in the demand in the

model so as to make it more realistic.

The results show that a decrease in future supply increases the current price. This is

because increasing the future supply makes it easier for the rm to buy the carbon credit

in the future which makes them less willing to pay a high price in the current period. On

the other hand, we nd that an increase in expected future demand leads to a decrease in

the current price. The intuition behind a negative eect of an increase in expected future

demand on the current price is that shift in future demand curve makes the rm demand

more in the current period as the carbon credits can be stored and used in future periods.

The outward shift of the demand curve consequently increases the equilibrium price. Using

these results the paper suggests that the future supply should be a function of expected

future demand. In particular, the government should decrease the supply every time the

expected future demand decreases and visa-versa. We show that such a policy can decrease

the price uctuation in the market.

The cap and trade scheme uses uniform price auction to distribute the carbon credits.

The allowance is auctioned over multiple periods. To study this market, we look at a dynamic

repeated uniform price auction setting with stochastic supply and demand. The dynamic

setting in the single good case can be of two kind. The rst keeps the set of buyers xed and

have their types change over a time as a function of allocations selected in earlier periods (for

example Athey and Segal (2007), Eso and Szentes (2007) and Akan et al. (2009). The second

is where a nite number of goods are sold to buyers arriving over time. This paper looks

1as noted by Thomson Rueters Point Carbon (2006)

27

at the second type of dynamic setting which we refer to as the changing buyer case2. The

focus here is on the sale of greenhouse gas emission, as used in the European Union, the US

(RGGI, NOx, California Cap and Trade), Switzerland and other countries. The auctioned

goods are close substitutes (assumed to be homogeneous) with the bidder having dierent

degrees of urgency to get the permits. This is modeled in the paper as bidders having a

dierent number of periods of active demand. To accommodate the dierent degrees of

urgency among the buyers, the model allows the buyer's type to dier in terms of their

demand duration. Thus, buyers have multi-dimensional private information, namely about

their valuation and demand duration. The buyers have single-unit demand 3

In this setting, we derive the equilibrium bid and show that the bid is truthful and ex-

post incentive-compatible. The optimal bidding strategy indicates that the buyers take their

future period payos into consideration when deciding the value of winning in the current

period. Thus, the outside option value is endogenously determined through the expected

payo of auctions in future periods. Apart from the carbon credit auction, this model can

be applied to any market where the bidders dier in terms of the value of the object as well

as the urgency for getting good. This includes markets such as the sale of spectrum (used

for a wireless network), auction of house or electricity markets with dierent delivery dates.

This paper is related to the literature on price and supply restriction imposed in the

cap and trade auction. The early work on this was done by Robert & Spence (1976) and

Weitzman (1978) . They considered price ceiling and oor under demand and supply un-

certainty in the static model. In the dynamic setting papers such as Philibert (2008) and

Burtraw et al (2010) look at price control with quantity regulation. Webster et al. (2010)

compare price ceiling to a policy that allocates allowance on emission targets. This paper

2The term changing buyer type is taken from Dynamic Mechanism design literature review

by Rakesh V. Vohra

3The objective of this paper is to focus on the question of auction periodicity, hence we
abstracting away from multi-unit demand. Another way of thinking of this is the simplica-
tion of each bidder having the homogenous number of units demands, thus the item is sold
is as a bundle of a specic amount.

28

contributes to this literature by looking at how instead of a xed supply rate or price ceiling,

we can implement a dynamic control for price uctuation by changing the supply rate with

the change in demand uncertainty and thereby aecting the equilibrium price.

This paper is also related to the literature on dynamic mechanism design with multidi-

mensional private information. It extends this literature to look at the optimal auction for

an auctioneer with an unknown number of buyers and sellers in each period. The literature

on dynamic mechanism design is vast(see the survey by Bergemann and Said for details).

The most relevant papers for current work are Pai and Vohra (2013), where they look at the

optimal auction for a single seller selling multiple units to stochastically arriving bidders.

These authors also allow for private information about the arrival time. The main dierence

in this paper is that we are looking at auctioneer's problem of ecient mechanism with

stochastically arriving sellers. Also Pai and Vohra paper assumes perfectly patient bidders

with a focus on optimal auction for maximizing seller revenue. Another related paper is

Mierendor, K., (2014):, where the author looks at a revenue-maximizing mechanism for a

seller selling a single good in a dynamic environment with buyers having multidimensional

private information. The main dierence with current work is that we are looking at an e-

cient mechanism in a dynamic environment with multiple and stochastically arriving sellers.

This paper is also related to the literature on Ecient Sequential Auction with Impatient

Buyers. The most relevant paper is Gershkov and Moldovanu (2010). They examine the

allocation of a set of durable goods to the dynamic buyer population. In their setting, ob-

jects are durable whereas in this paper objects are non-durable and the total supply in every

period is stochastic.

In the current model, we are analyzing sequential auctions with stochastic supply and

demand. The early work on stochastic auctions includes Mcafee, R. P., and McMillan, J.

(1987), Konrad, M.(2013), looks at an ecient dynamic allocation of a single object when

bidder arrival is stochastic. On the supply side, Thomas.J (1999) looks at stochastic supply

in a sequential auction.

29

The remainder of the paper is structured as follows : Section(2.2) and section(2.3) de-

scribe the generalized model setup and derive the equilibrium bid. Section(2.4) applies the

model to emission trade market and section(2.5) concludes.

2.2 Model setup

Consider a sequential auction in innite, discrete time period model, t 
 {−∞.., 0, ..∞}.

In each period multiple units of a homogeneous good are auctioned. In the case of a spectrum

market, we look at the trading auction where the secondary users bid to buy spectrum units,

sold by primary users. Buyers with single unit demand arrive over time. Buyer i has a

valuation vi, for one unit of the good, which is an i.i.d random draw from the distribution

F (v) on [v, ¯v]. The demand for each buyer lasts for multiple periods. In particular, each

buyer has an arrival time ai and a demand duration ki. This means that the demand
lasts for all t 
 {ai, ....(ai + ki)}. Thus apart from heterogeneous valuation, a buyer also
dier in terms of their demand lifetime. The type of a buyer is a triplet consisting of his

valuation, arrival time and demand duration, x = (vi, ai, ki); and the type space is given as
X = [v, ¯v] × [a, ¯a] × [1, ¯k]. Buyer's type is an i.i.d random draw from a commonly known
Fi = Fv × Fa × Fk over X. We assume that the three components of

distribution (cid:81)

i={v,a,k}

the type space, i.e. valuation, arrival time and demand duration are independent.

In our model, in period t, an agent of type xi = (vi, ai, ki) and makes a payment zt derives

the following instantaneous utility:

(vi − zt),

0,

Ui,t(vi, ki) =

if he wins the auction

otherwise

The buyers arrival rate is stochastic; In any period t, nt new buyers arrive. The arrival rate,
nt, is an i.i.d random draw from the distribution F n on {1, ...., ¯n}. The distribution of arrival
rate of buyers in each period is common knowledge, however the exact number of per period

new buyers is unknown. Apart from this uncertainty in the market leads to uncertainty of

the current bidders' likelihood of surviving in the future. To capture this, we dene Ï„ as

30

the probability of surviving in the next period for each active buyer. The total number of
potential buyers is given by N 
 IN such that N ≥ ¯n¯k.

Sellers, with single period supply, arrive over time. Seller j has a per unit value vj ,
which is assumed to be the same for all sellers and is normalized to zero, vj = 0 ∀ j 
 S4.

We allow the sellers to have more than one unit to sell but assume that each sale request is

sent to the auctioneer independently5.

Similar to the buyers, the sellers also arrive stochastically. However unlike the buyers,

sellers are active only for one period. The units auctioned by the sellers are identical, and

these units remain valid only for one period. Each unit is considered for sale independent

of their provider, as sellers oer homogeneous goods.

In any period t, mt new units are
available in the market. It is assumed that for each tth period, mt is an i.i.d random draw
from distribution F m on [m, ¯m]. The total number of potential seller is given by M 
 IN
such that M ≥ ¯m. The distribution of units available in each period and seller's valuation
is common knowledge however the exact per period supply is unknown ex ante. 6.

Information Structure: The distribution of buyer's type space, the distribution of avail-

able per period units, and seller's valuation for the object are assumed to be common knowl-

edge. The buyer has private knowledge about his own type, composed of his valuation and

demand lifetime. He does not have knowledge of exact number of other buyers and sellers,

their types and reports , or previous allocation decision by the auction. The arrival rate of

buyers and the number of items in each period are stochastic. Thus the exact per period

demand and supply is unknown for future periods.

The timeline of the game is as follows. In each period, t, the active buyers report a bid

for a single unit to the auctioneer. The strategy set of the buyers in period t compromises of

4This assumption has been made so that we can concentrate on the buyers side in this

paper

5Thus this is equivalent to each seller selling single unit item
6In this model we consider the case of multiple sellers. The role of a seller is limited upto
to reporting the available unit, and thereby accepting to sell at a non negative price as the
auctioneer knows seller's valuation.

31

their bid in period t, i.e. bt(vi, ri), where vi is the value and ri is the numebr of active periods
left at tth period. The active buyers comprises of new buyers arriving in the current period

and the existing buyers which are still active and have unfullled demand for the item. The

active sellers report the items available for sale. After receiving bids from the active buyers

and an estimate of number of items to be sold from the active sellers, the auctioneer holds

an auction to decide the number of items to be traded, denoted as St and the clearing price,

denoted as zt.

We now give a detail description of the auction mechanism. The auctioneer holds a series

of static uniform price auctions. Bidders simultaneously submit sealed bids for the item and

sellers report the units available for sale. The auctioneer calculates the total number of items

to be traded, St, by equating the demand and supply in the current period. If the number of

items traded in the market are equal to the available units i.e. St = mt, auctioneer accepts

the sale request of all the active sellers. On the other hand if the number of items traded

is less than available units i.e. St < mt, auctioneer accepts the sale request of randomly

selected St number of sellers. The buyers are ranked in ascending order of their bids and

St highest bids are accepted to allocate the item. Each winning bidder gets one unit of the

item and pays a price equal to the highest losing bid.

To formally determine the clearing price, we denote the order statistic for bid as b(l),

which represents the lth highest order statistic of the bidding values. Note that St highest

bids are selected in period t to trade. So the bid of a buyer is accepted for trade if bt(vi, ri) 

{b(1), b(2)............b(St)}. Every winning bidder pays the bid of the highest losing bidder, i.e.
zt = b(St+1). The price paid by all buyer in every period is equal to the (St + 1)th highest

order statistic of that period. All buyers who bid above zt win the item at price zt and each

accepted sale request yields a payment equal to zt for sellers.

We solve the repeated period problem using Subgame Perfect Bayesian Nash equilibrium

as the solution concept. In each period the buyers reports a bid for single unit of the item

32

to the auctioneer. The equilibrium denes a set of strategy and beliefs, such that given the

opponents' strategies, the expected payo of every buyer is maximized in each period.

Observation 2.2.1. Notice that, although the arrival time ai is private knowledge, the buyer

does not have any incentive to lie about the arrival period. This is due to the independence

of buyer's payo function and the arrival time ai. Thus the relevant private information of

buyer i is (vi, ki).

2.3 Symmetric equilibrium

A bidding strategy for a bidder i consists of a set of bid functions dened as bi =
{b1(vi, ri), b2(vi, ri), ....b∞(vi, ri)} , where bt(vi, ri) denotes the bid in the tth period given
that the bidder's value is vi and demand will last for ri periods after period t.7 Note that

the bidders arrive and leave at dierent time periods , thus the subscript on period tri, i.e
ri, denotes the number of active periods for bidder i in period tri.

As this is a dynamic setting, we start by dening the state variables. Let σt = {mt, nt}
denotes the auction "state" consisting of the number of bidder i at time period t, and it is

represented with a k-dimensional matrix n = [n¯k, ..., n1] and m represents the number of

sale units available in that period. Here, nx denotes the number of bidders with x periods

of active demand. Let N (k, n) =

nx denote the set of active buyers in current period.

¯k(cid:80)

x=0

Let us now consider the maximizing objective function for the buyer which is the total

lifetime payo after realization of demand and supply , denoted by V (vi, ri|σ)

(cid:26)

(cid:18)

P r

b(vi, ri) > b

(mt)
j(cid:54)=i

E

vi − b(mt)(vi, ri)

V (vi, ri|σt) ≡

(cid:18)

+ P r

b(vi, ri) > b

(mt)
j(cid:54)=i

(cid:90)

(cid:19)

(cid:12)(cid:12)(cid:12)(cid:12)σt

Ï„

σt+1

(cid:20)

(cid:19)

(cid:12)(cid:12)(cid:12)(cid:12)σt

V (vi, ri − 1|σt+1)

(cid:12)(cid:12)(cid:12)(cid:12)b(vi, ri) > b

(mt)
j(cid:54)=i

(cid:21)

(2.1)

(cid:27)

The rst term represents the expected payo from auction in the rst period and the second

term is the future period payo integrated over possible arrival rate σt+1. The future payo

7All this assumes, of course, that he particular bidder has not already won an object so

is still active in period t

33

is equal to the total payo for value vi and ri − 1 pd left. Now we dene the total payo
e-ante, i.e., before the realization of the state variable 'σt'

(cid:20)
vi − b(mt)(vi, ri)

E

(cid:12)(cid:12)(cid:12)(cid:12)b(vi, ri) > b

(cid:21)

(mt)
j(cid:54)=i

(2.2)

(cid:90)

(cid:26)

W (vi, ri) ≡
(cid:18)

σtri

+ P r

b(vi, ri) > b

(mt)
j(cid:54)=i

Ï„

P r

b(vi, ri) > b

(cid:12)(cid:12)(cid:12)(cid:12)σtri
(cid:19)
(cid:27)

(mt)
j(cid:54)=i

(cid:19)
W (vi, ri − 1)

(cid:18)
(cid:12)(cid:12)(cid:12)(cid:12)σtri +1
(cid:26)
(cid:18)

Using the total payo ex-ante, we can rewrite the ex-post per period payo in eqn(2.1) as

) ≡

(cid:20)
V (vi, ri|σtri
(mt)
j(cid:54)=i
b(vi, ri) > b
vi − W (vi, ri − 1) − b(mt)(vi, ri)
E

P r

(cid:21)

(cid:27)
+ W (vi, ri − 1)

(2.3)

(mt)
j(cid:54)=i

(cid:12)(cid:12)(cid:12)(cid:12)σtri
(cid:19)
(cid:12)(cid:12)(cid:12)(cid:12)b(vi, ri) > b

Pseudo type for each period:

Observe that we have the probability of winning in each period dened in terms of the bid,

in order to dene that in term of the bidder's type, we will dene a per period pseudo type

for each period t and bidder i as ηi,t. Let Gt(.) be the distribution for ηt,i. The pseudo type

is dened as follows :

(cid:82)

vi − ki(cid:80)

0,

l=t+1

ηi,t =

(cid:18)
ηi,l − E[(η
(ηi,l|σl)

τ l−tG

(ml)
l

σl

(cid:19)

(ml)
j,l

)j(cid:54)=i|ηi,l > η

(ml)
j,l

]

,

if t
{ai, ki}

otherwise

The pseudo type helps simplify the payo function as well as the bid. Following lemma

shows that relation between pseudo type and the payo function

Lemma 2.3.1. The equilibrium bid is increasing in pseudo type and the total payo in period

t can be rewritten as follows :

(cid:90)

(cid:18)
(cid:18)
(ηi,t|σt)
ηi,t − E[(η
(ηi,t|σt)

ηi,t − E[(η

(mt)
j,t

(mt)
Ï„ G
t

W (ηi,t) =

σt
(mt)
V (ηi,t) = G
t

(mt)
j,t

(cid:19)
)j(cid:54)=i|ηi,t > η

(mt)
j,t

)j(cid:54)=i|ηi,t > η

(mt)
j,t

(cid:19)

]

+ W (ηi,t+1)

(2.4)

]

+ W (ηi,t+1)

(2.5)

We can use this equation in order to determine equilibrium bid functions, as demonstrated

in the following result. We focus on symmetric Bayesian Nash equilibrium.

34

Theorem 2.3.2. If auction in every period is vickery auction then the equilibrium bidding

strategy in the dynamic auction game is given as:

bi(ηi,t) = vi − W (ηi,t+1)

or

bi(ηi,t) = ηi,t

35

2.4 Applications and comparative statics : emission market

Here we look at the case of xed decreasing supply with an uncertainty of demand in

each period. In the emission auction markets, the goal is to reduce the supply of emission

credits, thereby reducing the total emission. This is usually done by deciding in advance the

decreasing rate of supply of emission credits. The general model, introduced in the previous

section, is modied in terms of supply rate to t the market better.

Instead of having

stochastic supply, for this section we have the supply decreasing at a constant rate.8 Let

the rate at which supply decreases be denoted by λ 
 [0, 1]. This changes the state variable

σt = (λmt, nt). Additionally, the probability of active demand τ will aect the future as well

as the current value for the object. This is because any change in demand for credit in the

future aects current demand as well. Everything else is the same. In this section, we look

at comparative statics in terms of how λ and τ . This will give insight into how the supply

rate and the demand uncertainty aect bidder behavior. The rst two propositions look at

how the supply rate, i.e. λ aects the market variables. This is done to understand how the

supply rate can be strategically used to stabilize the price.

Proposition 2.4.1. The bidder's expected payo is increasing with increase in the future

supply rate.

d(V (ηi,t|σt))

d(λ)

≥ 0

(2.6)

The above proposition shows that the expected payo in each period t is positively

correlated with the future periods' supply rate. The intuition behind the result is that as

the supply in the future increases, the chances of acquiring credits in the future increase,

thereby increasing the total expected payo from current and future periods. However, our

purpose is to understand how the supply rate can be used to control the price. In the next

8To focus on the eect of supply and demand dynamics we will be abstracting away from

the multi-unit demand nature of this market

36

proposition, we shift our focus to see how the supply rate aects the bid as well as the

equilibrium price.

Proposition 2.4.2. The bid and price are decreasing with increase in the future supply rate.

d(b(ηi,t))

≤ 0

d(λ)
dE(Pt)
d(λ)

≤ 0

The price and the bid in the current period are negatively aected by an increase in the

supply rate. Thus, even though the total payo is increasing for the bidder, they will still

decrease the price in the current period. This is because increasing the supply rate increases

the payo in the future periods, which also increases the opportunity cost of winning in

the current period (tth period). Therefore, bid and thereby price is negatively correlated

to supply rate. We have now established the eect of the supply rate on market variables.

However, in order to see how the supply rate can stabilize the eect of demand uncertainty

on the price we need to look at the eect of demand uncertainty as well. We now look at

how do market variables react to demand uncertainty.

Proposition 2.4.3. The bidder's expected payo is decreasing in the uncertainty of demand.

d(V (ηi,t|σt))
d(1 − τ )

≤ 0

(2.7)

Recall that Ï„ represents the probability that bidders will have demand for the credits in
the next period.9 Thus, 1 − τ represents the probability of demand reduction in the next
period. For this study, we take 1 − τ as a proxy for expectations about future demand

uncertainty. The proposition(2.4.3) shows that the payo is negatively aected when the

demand uncertainty increases in the market.

9this is assuming bidder has active demand next period and is between his entry and

deadline period.

37

Proposition 2.4.4. The current bid and price increase with decrease in expected demand

uncertainty.

d(b(ηi,t))
d(1 − τ )
dE(Pt)
d(1 − τ )

≤ 0

≤ 0

This shows that increase(decrease) in expected demand increases(decrease) the price.

Now that we have established the individual eects of supply rate and uncertainty on price,

we will look at how to utilize it to stabilize the price path. From propositions 2.4.2 and 2.4.4

we see that λ and τ have an opposite eect on the price. Thus, an optimal strategy will

negatively correlate the future supply rate and expected demand. Let the proposed supply

rate be dened as follows :

λnew = f (τ )
f(cid:48)(τ ) ≥ 0

(2.8)

(2.9)

The new supply rate changes with the change in demand. The next proposition proves that

the change in price due to change in demand uncertainty would be less in case of the new

supply rate.

Proposition 2.4.5. If the demand in the future changes by x then, the change in price would

be lower in case of the new supply rate.

dE(Pt|λnew)

d(Ï„ )

dE(Pt|λ)

d(Ï„ )

<

2.4.1 Comparison with price control strategies

The literature provides a xed price ceiling and reserve price as a solution to control the price

uctuation. However, even after the price caps, there can be high variance in price within

the bounded prices (as seen in gure(C.1). In this paper, we instead present a more exible

strategy, where the supply rate would be linked to future uncertainties and thereby adjust

38

higher for high-level uncertainty and low for low-level uncertainty. Let's take an example of

the RGGI carbon credit market. Figure(C.2) shows the price path with major events during

the timeline. We can see that price uctuates with changes in the demand such as in 2106 we

see a big fall in price as the demand uncertainty increased as in 2016 supreme court halted

the Environmental Protection Agency's Clean Power Plan. In our model, the supply rate

would have temporarily adjusted to decrease the fall.

This work shows that linking the supply rate to changing market factors will stabilize

the price. Further, empirical analysis is required to understand the implementation of such

a policy.

39

2.5 Conclusion

This paper analyzes a dynamic auction setting with the stochastic arrival of bidders and

multidimensional bidder's type. We derive the BNE bid in the repeated game. We apply

this setting to the Cap and Trade scheme for the auction of carbon credits. The setup is

used to understand the uctuation of price in this market. Price uncertainty is a major

concern in the Cap and Trade market. The reason for that is that for rms to change to

more renewable energy they would need a more stable short term supply of carbon credits.

The paper identies two factors aecting price uctuation, namely the rate of supply and

uncertainty in future demand. One of them is not in control of the auctioneer (or the

government in this case), that is the future uncertainty in demand. However, the rate of

supply is decided by the government. The paper shows that the eect of the rate of supply

on price is opposite to the eect of uncertainty in future demand. Thus, one policy suggested

in this paper is that the government should correlate the supply rate with the uncertainty

in the market. Specically, they should decrease the future supply rate when the future

demand uncertainty in the market increases. The results show that this policy would lead

to a more stable price over time. The paper also analyzes the general model setup, which

can be applied to other markets as well. One key feature of the paper is that we look at the

multi-dimensional type of bidders. Thus, this model can t markets where the bidders dier

in more ways than just the value for the object. Future extensions of this paper can look

at extending this setting to multi-unit demand and looking at double auction setting which

can further generalize the auction design.

This work shows that linking the supply rate to changing market factors will stabilize

the price. Further, empirical analysis is required to understand the implementation of such

a policy.

40

CHAPTER 3

REVENUE-MAXIMIZING NUMBER OF ADS PER PAGE IN THE

PRESENCE OF MARKET EXTERNALITIES†

3.1

Introduction

Online advertising is a new but rapidly growing market. Back in 1998, when Google was

a small startup company, there were on average 10,000 search queries made per day; fast-

forward to 2019, Google recorded an average of 5.5 billion searches per day.1 Furthermore,

this rapid growth is accompanied by new and evolving ad features. One such example is the

pay per click feature, wherein the advertiser pays for the click on the ad link and not for

the ad display.2 In such a dynamic environment, even a feature as simple as the number

of ads per page can have signicant implications. This paper focuses on the implications

of the number of search ads per page on the search engine's ad revenue. Search ads are

paid search links that appear above generic3 search results on major search engines such as

Google, Yahoo! and Bing. Figure E.1 gives an example of the Yahoo! result page.

The motivation for looking at the number of ads per page is twofold. First, analyzing

this feature can help us derive the revenue-maximizing number of ads per page, which can

provide suggestions on how to improve the current practices. Second, the empirical literature

on online advertising does not address how the number of ads impacts the ad price and,

thereby, the search engine's revenue. This paper lls this gap by quantifying the revenue

impact of the number of ads per page.

†This work is unpublished.
1https://martechseries.com/mts-insights/guest-authors/googles-seo-strategy-is-

constantly-changing-four-ways-small-businesses-can-keep-up/

2This is true for most of the online advertising platforms such as Google, Yahoo! Face-

book, Amazon, and eBay.

3Generic search results are non-sponsored links.

41

The search engine faces a trade-o while deciding the number of ads per page. The

addition of one more ad leads to an increase in the quantity of ads sold; however, it also

leads to a decrease in the ad price. Thus, the revenue-maximizing number of ads is an

empirical question that is derived after quantifying the change in price due to a change in

the number of ads. Note that the price for each ad is decided through an auction mechanism.

The change in equilibrium price is broadly due to the auction design, as well as due to the

externality exerted from other ads on the page. The externality is dened as a side eect of

the presence of other competing ads on an advertiser's benet from the ad. I will rst talk

about the externality in the market and then give details of the auction design.

Let us look at an example to understand the consequences of externality in this market.

Consider Walmart as an advertiser that has an ad appearing in two consumer search queries.

In the rst case, the ad appears adjacent to one from Amazon (as seen in gure E.1), and

in the other, it appears as an exclusive ad. In this example, the consumer who sees only

Walmart's ad is more likely to buy from them, compared to the consumer who sees both

Amazon and Walmart's ad. The presence of Amazon's ad exerts an externality on Walmart's

benet from the ad, which translates into Walmart having a higher willingness to pay for the

exclusive display. Notice that the externality from the other ad is dependent on the number

as well as the quality of the ads, where the quality measures the consumers' preference for an

advertiser. For instance, an adjacent ad from a high-quality advertiser, say Amazon, exerts

a higher externality than an ad from a low-quality advertiser. Thus, I create an externality

index that captures the quality as well as the number of other ads on the page.

Although the externality estimates are interesting by themselves, this paper aims to

compute the revenue-maximizing number of ads for which we also need to accommodate other

components that aect the equilibrium price. The selection and pricing of the ads is done

through an auction referred to as Generalized Second Price (GSP) auction.4 Additionally,

the advertisers pay per click and not for the ad's display; thus, the advertiser submits a per

4A new auction is held for consumer search.

42

click bid. The winning ads are decided using the weighted bid, where the weight captures

an ad's click probability. Note that a single auction is used to allot all the ad positions on a

given page. The positions are assigned in order of the weighted bids, meaning an ad with a

higher weighted bid is allotted a higher position. The equilibrium condition shows that the

ad price depends on the advertiser's willingness to pay, the consumer's click probability, and

the information available to the advertiser.

To evaluate this empirically, I use a data set provided by the Yahoo! research lab. It covers

all ads5 displayed on Yahoo! search result page, over four months, for ve major categories:

laptop, TV cable, cruise travel, collectible coins, and car insurance. I have information about

the number of displays, the number of clicks, ad description, and the ad position. The data

also provides the bids for each ad. Additionally, I can measure the number of advertisers per

day and the number of ads per page.6 Notice that the data does not provide the quality of

an ad, I solve this limitation by estimating the quality of an ad in terms of the advertiser's

eect on consumer's click probability.

For estimation, I use a discrete choice method to model consumers' click decisions and a

partial identication method to bound the advertisers' willingness to pay. The estimation is

performed in three steps. In the rst step, I estimate the parameters that aect a consumer's

click decision using a weighted logit model.7 In the second step, I set up a hedonic regression

to estimate the eect of the externality on an advertiser's bid. The nal step estimates

bounds on the distribution of the advertiser's unobserved willingness to pay for which I

follow the Haile and Tamer (2003) methodology for partial identication of distribution.

The ndings show that externality has a negative and non-linear eect on the advertiser's

5The data excludes ads that appear for the search of brand names.
6the number of ads on the rst page is assumed to be seven ads unless observed less than
7 ad positions. This is a common assumption made for papers using this data set from yahoo
such s Agarwal and Mukhopadhyan (2016) Agarwal & Mukhopadhyay (2016)

7The reason for using a binary logit model instead of a multinomial logit is for two reasons.
First, the choice set of the displayed ads varies depending on the consumers' preferences.
Thus, the choice set is endogenous. Second, the choice set does not have a xed number of
choices.

43

willingness to pay. For a one-percent increase in externality leads to 0.34, 0.6, 1.3 and 0.14

percent decrease in the advertiser's willingness to pay for categories car insurance, laptop,

cable tv and coins respectively.8 The eect of including one more ad is dependent on the

quality of the additional ad as well the number of ads already on the page. In the laptop

category following the Walmart example earlier, this would imply that addition of a second

ad decreases willingness to pay by twenty ve percent if the new ad is from Amazon, but

only by two percent if it is from a local retailer.9

These estimated primitives and equilibrium price condition are used in the Monte Carlo

simulation to derive and measure gains from implementing the revenue-maximizing number of

ads. To derive the revenue-maximizing number I calculate the expected revenue for dierent

values of the number of ads per page and then select the one that has the highest expected

revenue. The results show that the revenue-maximizing number is 5 ads per page, on average.

For three out of ve categories the revenue-maximizing number of ads are dierent than the

currently display quantity of ads per page (i.e. seven ads).

Implementing the suggested

number of ads per page would lead to, on average, a 4.5 percent gain in revenue, which

translates into 5.2 billion dollars in revenue.10 One of the reason for a dierence in the

result in this paper and current practices is that the paper suggests optimizing number of

ads separately for each category, however the search engines currently optimize the number

of ads jointly for all categories.

These results provide evidence on how search engines can increase revenue by changing

the design of the ad space. Furthermore, these suggestions extend the recent changes in

the online advertising market; for example, Microsoft has introduced a service (RAIS) that

provides advertisers with an option of an exclusive ad display.

This paper contributes to several dierent strands of literature.11 It contributes to the

8Note that cruise did not show a negative or signicant eect of externality
9assuming local retailer is of low quality and amazon is of high quality
10calculated using google's advertising revenue in the second quarter of 2019 - see here for

details https://www.statista.com/statistics/266249/advertising-revenue-of-google/

11Please refer to the next section for a full literature review.

44

studies that look at the eect of externality in the online advertising market. To the best of

my knowledge, this is the rst paper that estimates the eect of externality on advertiser's

willingness to pay. Additionally, this paper also contributes to the studies on equilibrium

price in auction design, where recent papers have looked at solving the equilibrium price un-

der a more realistic assumption on the information available to the advertisers (for example,

Athey and Nekipelov (2010) look at entry uncertainty). In this paper, I extend this further

by looking at the incomplete information case and provide for equilibrium conditions that

can be estimated empirically.12 Lastly, this paper contributes to the relatively new literature

on ad display design; the closest related paper is Jerath and Sayedi (2015). They look at

introducing exclusive ad display options, whereas this paper looks at the more general case

of the revenue-maximizing number of ads, in which an exclusive ad is a special case.

3.2 Literature review

This research is related to a few dierent strands of literature. It contributes to the lit-

erature on externality in the online advertising market. The empirical studies on externality

have focused on the eect of externality on the consumer's decision to click on an ad, such

as Jeziorski and Segal (2015) and Narayanan and Kalyanam (2015).13 Despite the growth

of literature on online ad externality, little eort has been made to empirically estimate the

indirect eect of externality on an advertiser's behavior. This paper focuses on these previ-

ously unexplored issues: the eect of online ad externality on an advertiser's willingness to

pay for an ad and, consequently, on ad platform revenue.

This paper is also related to the work on estimating the unobserved advertisers' will-

12The closest paper to this analysis is Gomes (2014), which solves for the incomplete
information case in the GSP auction. Here, I do a nontrivial extension of their work by
solving the incomplete information case in the weighted auction. Furthermore, I contribute
to this literature by providing equilibrium bounds that can be estimated empirically.

13For instance, Jeziorski and Segal (2015) Jerath & Sayedi (2015) show that consumers
click on multiple ads and that the click probability is aected by the presence of other ads.
Narayanan and Kalyanam (2015)Narayanan & Kalyanam (2015) show that, for large rms,
higher ad positions lead to smaller click probability improvements.

45

ingness to pay using the equilibrium bid. In the theory literature, Edelman et al. (2007)

(referred to as EOS) and Varian (2007) were among the rst to derive the equilibrium bid.

Although online ad auctions have received great attention in the theoretical literature, em-

pirical research remains sparse. Borgers et al.

(2013) analyze Yahoo! data to estimate

position-dependent value, and Yang et al. (2013) structurally estimate EOS's model. Athey

and Nekipelov (2010) propose and estimate a structural model tailored to features of spon-

sored search auctions run by US search engines (such as Google or Microsoft).14 A key

contribution of this paper is that it looks at the equilibrium behavior under weaker infor-

mation assumptions. The empirical literature in sponsored search auctions has looked at

variants of full information, with few looking at uncertainty in the market. This paper

relaxes the full information assumption and examines the optimal bidding behavior under

incomplete information. Gomes and Sweeney (2014) solve for the incomplete information

case in a non-weighted Generalized Second Price (GSP) auction. This paper extends their

work by looking at the incomplete information case in weighted GSP auction. The extension

is nontrivial as the weight introduces a multidimensional type of the bidder. Additionally,

the equilibrium bid does not have a closed-form. Thus, the paper further contributes to

this literature by providing closed-form bounds on the equilibrium bids that give us partial

estimates for the advertiser's willingness to pay. To the best of my knowledge, this is the rst

paper that proposes how to estimate the willingness to pay under incomplete information.

This paper is also related to the literature exploring multi-ad display settings in sponsored

search ads. For instance, few papers look at giving the advertisers the option of bidding

for both multi-ad and exclusive-ad option, such as Jerath and Sayedi, (2015), Deng and

Pekec (2013), and Ghosh and Sayedi (2010). The change in the auction design makes the

advertisers strategically change their bid, which has led to advocacy for changing the auction

design to VickreyClarkeGroves (VCG) auction, for example, in Sayedi, Kinshuk, Baghaie

14Specically, they accommodate uncertainty in bidders' perceptions (due to randomness
in a bidder's quality score over time, as well as in the set of competitor bidding in the auction
at any time).

46

(2018). In this paper, the counterfactual suggestion is on showing a xed number of ads

that dier across the ad product category. The advantage of the suggested xed number of

ads is that it does not require a change of setup for the advertisers. Thus, it is easier to

execute. Another contribution of this paper is that, unlike the previous papers that look at

this question from a theoretical point of view, this paper estimates the market parameters

in the empirical section. Thus, the simulations provide a more realistic magnitude of gain

through the proposed new method.

Lastly, this paper is related to econometric theory papers on partial identication meth-

ods. The methodology in this paper closely follows a method rst proposed in Haile and

Tamer (2003). Their paper shows how to estimate bounds on the distribution of object value

in an English auction. I extend it and show how to apply the method in an online auction,

i.e., a Generalized Second-Price auction.

3.3 Market environment and theoretical Model

3.3.1 Overview of the search advertising market

In this section, I discuss the search ad market from the advertiser's point of view. Sponsored

search ads are paid search links that appear alongside search results (as shown in g(E.1)).

These ad links are purchased by advertisers in order to have their website appear higher in

the search results page. Multiple ad position slots are allotted for each search result page

through an auction. The ad display process has three stages, as shown in the timeline (in

g(E.2)).

Stage 3.3.1. Advertisers select their bid and keywords.

In the rst stage, the advertiser has to decide the bid per click as well as the ad-related

words (referred to as keywords). Following the earlier example, this means Walmart needs

to decide the bid as well as a set of keywords for an ad on a gaming laptop. The advertisers

can specify multiple keywords for an ad. For instance, in this example, Walmart species

47

keywords `gaming laptop' and `gaming laptop cheap'. The multiple keywords help in reaching

consumers with diverse search queries.

Stage 3.3.2. Auction is held, and winners are decided.

In the second stage, for every search query, Yahoo! collects all related ads, which is done

by matching the search query words to the ad's keywords. The matched ads enter an auction

to decide the winning ads that will be displayed to the consumers. Yahoo!, similar to other

search engines such as Google, uses a special auction for deciding on the winning ad called

the Generalized Second Price (GSP henceforth) auction.

Stage 3.3.3. Yahoo! sends feedback on ad's performance and ad price to the advertisers.

The third and nal stage compromises of a feedback report that goes to the advertiser

about the ad performance. gure E.3 shows a snapshot of an advertiser's account on Ya-

hoo!. The variables in the data set are similar to the feedback information available to the

advertiser. The advertiser gets detailed feedback on the ad, which is aggregated for each

specied keyword. Following the earlier example, this means for Walmart's ad on `cheap

gaming laptop', Walmart gets periodical information15 on the two keywords, namely `gam-

ing laptop' and `cheap gaming laptop'. For each keyword, they get the display and click

frequency in each ad position. Apart from the consumer response, they also get information

on the price paid per click for each winning position. For example, feedback for Walmart's

ad shows that the search queries that matched keyword `cheap gaming laptop' had their ad

display 100 times in the 1st position, and that translated into ve clicks, with 0.2 cents as

the price per click. The data set used in this paper contains similar information, where,

on the consumer side, it reports the display and click frequency for each position won by

keyword-ad observation,16 and on the advertisers' side, it reports the advertiser's bid and
15I assume that the advertiser uses the day as a given period to change/revise their bid.
Note that the information provided to the advertiser can be more detailed than the daily
aggregation that I assume here. However, previous papers have noted that the change in a
bid does not change much within a day; see Borger (2013)Börgers et al. (2013).

16aggregated on a daily basis

48

winning positions.

3.3.2 Theoretical model

In this section, I present a model of the advertiser's equilibrium bid and the consumer's click

decision using features of weighted Generalized Second Price auction (GSP w) and discrete

choice model. The reason for modeling the consumer side is to get an estimate of relative

click rate of dierent positions and each advertiser's quality score.

In the section below,

I specify the click behavior using a discrete choice model. In the next section, I present a

model of advertiser's equilibrium bid, in which the advertisers choose the bid that maximizes

their prot from advertising.

3.3.3 Consumers side

Each consumer i enters the market with a unit demand for a product/service and conse-

quently starts the search by putting a query on an online search engine. Once the result

page displays all links related to the query, the consumer clicks on all relevant links and pur-

chases a good or service from one of the clicked links. In this section, I model the consumer's

click decision.

The online environment motivates several considerations. Firstly, the consumer antici-

pates the derived click benet by visible characteristics of the ad. Along with the visible ad

characteristics, the consumer also uses the belief that ads at a higher position are of higher

quality and relevance. This belief stems from the fact that the search engine's algorithm

assigns a higher position to ads with higher quality score, ceteris paribus. Thus, I also add

the position as a variable that predicts ad benet. Another consideration is that in an online

space, each click requires the consumer to spend a considerable amount of time on it, which

can be thought of as a search cost or time cost.

49

The expected utility of consumer i receives from clicking in ad j in market m is given as:

Ui,j,m = U (xj, kj, xi; ηj, ηi) + 
i,j,m

(3.1)

Where {ηj, ηi} are coecients that reect how intensely the cost and benet variables aect
the utility. The variables {xj, xkj
} capture the benet from a click on ad j at position kj;
this includes advertiser specic and position-specic xed eects, along with ad's popularity
measure17. Apart from these variables, {xi} are consumer specic variables that help capture
heterogeneous search cost; this includes variables such as how detailed is the search (captured

by the length of search query18). The term 
i,j is the idiosyncratic shock to the consumer's

benet from clicking on the link; it represents a part of the utility which is observed by

consumer i, but not by the researcher.

I assume 
i,j,m is independently and identically

distributed according to type 1 extreme value distribution. Additionally, if the consumer

does not click on the ad, she uses her time for an outside good, leading to a normalized
utility of Ui,0,m ≡ 0. Given the utility function in the above equation, I now dene the
equilibrium click behavior of the consumers.

Proposition 3.3.4. consumers in equilibrium may click on multiple ads per page.

Essentially in the equilibrium, consumers click on all ad links where the benet of a click

is more than the search cost.19 Let y∗
equilibrium click decision for ad j , with y∗

i,j denote the binary variable capturing consumer i's

i,j = 1 if consumer decides to click on the ad.

17measured as the proportion of times the ad appeared in the search result page relative

to total search queries in the category

18This is measured as the number of words in the matched keyword, since I do not have

the queries

19although most of the literature assume single click per page, this is more real-
istic situation in this market, as can be seen by a new move by Bing to give an
option of opening a new tab every time you click on a link. Here is the link to
the article: https://searchengineland.com/bing-is-testing-an-open-in-new-window-icon-in-
the-search-results-301922

50

Then the click decision can be written as follows:

1

0

y∗
i,j =

if U (xj, kj, xi; ηj, ηi) + 
i,j,m > 0

otherwise

(3.2)

The above equation is used in the empirical section to estimate the probability of click

aggregated over all consumers. The estimation gives us the predicted probability of a click

for an ad j in position k, represented by ctrj,k. Assuming that the ad and position eects

are separable20 the click probability can be rewritten as:

ctrj,k = sjck

∀ j 
J & k 
 {1, 2, ...K}

(3.3)

where

sj: The eect of advertisement j on probability of a click.

ck: The eect of ad position k on probability of a click.

The click probability in equation(3.3) is used in advertiser's maximizing problem as described

in the next section.

3.3.4 Advertising model

3.3.4.1 Model without externality

In this section, I rst specify the auction design. I then model the advertiser's maximization

problem and derive the equilibrium bid. In the end, I look at the case of added externality

to the per-click ad value.

Auction Setup

For each consumer query, a single auction is held to sell multiple ads on the result page. Let
there be K ads on sale and N potential advertisers denoted by j 
 J := {1, ...J}. Each

advertiser submits a single bid bj, which can be interpreted as per click payment.

20This is a similar assumption adopted by various papers in the literature for identication

of the quality of advertiser

51

The K positions are allotted through a weighted Generalized Second Price auction (re-

ferred to as GSP w henceforth). Each advertiser is assigned a quality score, sj, which mea-
sures the ad's impact on the consumer's click probability.21 The advertisers are then ranked

in terms of their weighted bids denoted as bw

j , i.e.,
j = bj × sj
bw

The auction assigns position in decreasing order of weighted bids, essentially allotting

kth position to advertiser with kth highest weighted bid. For example, the top position goes

to advertiser with the highest weighted bid, second position goes to second highest and so

on. The price paid is equal to the bid of advertiser in the next slot weighted by their relative

score:22

Ad position k alloted to j if bw

j = b

[k]
w

Per click price is equal to pk =

b

[k+1]
w
s[k]

Here b

[k]
w is the kth highest weighted bid and s[k] denotes the score of advertiser with kth
highest weighted bid. Thus, the kth highest position goes to the advertiser with kth highest

weighted bid, and he pays the price of the bid below him weighted by their relative score,

which is equivalent to the weighted bid of the advertiser below him divided by his score.

Advertisers maximization problem

Each advertiser j has a per click ad value of vj. The advertiser's gain from winning position

k is given as

πk(vj) = ctrk,j(vj − pk)

(3.4)

21The score can also be thought of as the quality of the ad, as higher consumer relevance

is an indication that the consumer perceived it to be of a higher quality.

22I assume no reserve price for simplicity.

52

where vj denotes the per click value to the advertiser and pk is the per click price for position

j. The term ctrk,j denotes the probability of a consumer click for ad j in position k. The

probability of a click can be further broken down as

ctrk,j = sjck

(3.5)

here sj is the advertiser's aect on click probability and ck is the position aect on click

rate. These variables are estimated on the consumers side.23

Note that the advertiser is uncertain as to which position he wins. Thus, the expected

prot is given as the prot from each position times the probability of winning that position.
[k]−j,w

Before we write the expected prot, we dene the order statistic among bids.

let b

denoted the kth highest weighted bid among all other advertisers except j.

Advertiser j wins position k if the weighted bid bw
j

is less than (k − 1)th weighted bid

and more than kth weighted bid, i.e. b

[k]−j,w ≤ bw

j ≤ b

[k−1]−j,w . As shown below:

K(cid:88)

k=1

Π(bj; vj, sj) =

P rob(b

[k]−i,w ≤ bw

j ≤ b

[k−1]−i,w ) ∗ ctrk,j

3.4

Equilibrium bid analysis

(cid:20)

(cid:18)
vj − E

(cid:12)(cid:12)(cid:12)(cid:12)bw

pk

j = b[k]

(cid:19)(cid:21)

(3.6)

Model Assumptions  This model looks at the incomplete information case. Each adver-

tiser does not know the bid or value of other advertisers but knows the primitive distributions;

namely the distribution of value Fv, the distribution of score Fs as well as the the distri-
bution of a variable referred as the weighted value, denoted as ωj ≡ sj × vj), ω ∼ Fw(.).
The weighted value is the product of the per click value and the click rate of the advertiser.

Apart from this, the number of advertisers and ads per page are common knowledge. For the

23Note, that as I assume one ad per advertiser for each auction, I have used subscript j

interchangeably for advertiser as well as an ad.

53

estimate of the externality we also need the additional assumption that the average quality

of ads in each position is known to each advertiser24.

Given the setup, the equilibrium bid maximizes the following objective function:

K(cid:88)

k=1

K(cid:88)

k=1

(cid:20)
vj − E

(cid:18) b

(cid:12)(cid:12)(cid:12)(cid:12)b

[k+1]
w
sj

(cid:19)(cid:21)

ˆb

[k]
w = sj

(cid:18) b

(cid:12)(cid:12)(cid:12)(cid:12)b

[k+1]
w
sj

(cid:19)(cid:21)

ˆb

[k]
w = sj

[k−1]−j,w )ctrj,k
(cid:20)

[k−1]−j,w )ck

b(vj, sj) = Arg max

ˆb

P rob(b

[k]−j,w ≤ ˆbsj ≤ b

Using ctrj,k = cksj we get,

→b(vj, sj) = Arg max
ˆb

P rob(b

[k]−j,w ≤ ˆbsj ≤ b

vj − E

In order for the advertisers to solve for the equilibrium bid they need to know the distri-

bution of other bids, however we assume that they only know the distribution of the value

and do not have information about other bids (i.e.

incomplete information case). In the

standard auction this is solved by inverting bid and using the value distribution. However,

in this case the weighted bid bw(sj, vj)) is is multi-dimensional as it depends on the value

vj as well as the score sj.

Due to this limitation most of the papers in the literature have concentrated on non-

weighted auction in the incomplete information case. This paper over comes the problem of

bid by showing equivalence between the weighted GSP and another auction which I refer as

the modied GSP auction (GSPM henceforth). In the GSPM auction, instead of a per click
bid the advertisers bid Ëœb for sj clicks. The value for sj click then becomes wj, which recall

is the weighted value wj = sjvj. Thus, the bid in GSPM serves a similar purpose as the

weighted bid in GSP auction. The dierence being that in GSPM the bid can be written as

a single dimension function given as follows:

bGSP M
w

: (ωj) → R+, where ωj = sj × vj

bGSP M (ωj). In the next lemma, I formally prove the equivalence between the weighted bid

in weighted GSp to the bid in GSPM.

24The assumption of average quality of the ad in each position is only needed for exter-
nality, the BNE equilibrium in incomplete information case does not need this assumption.

54

Lemma 3.4.1. The weighted GSP auction equilibrium bid function bGSP w

(vj, sj) → R+ is

equivalent to the bid in GSPM auction divided by the quality score sj

bGSP M (ωj)

sj

= b(vj, sj),

→bGSP M (ωj) = b(vj, sj) ∗ sj = bw

j (vj, sj)

where ωj = sj × vj

(3.7)

The lemma shows that the weighted bidding function is equivalent to a function that

is dependent only on one-dimensional advertiser's type ωj. Additionally, it shows that at

equilibrium we can rewrite the weighted bid sjbj as a function of weighted value , i.e. bw(ωj).

This simplication comes in handy for proof of bounds and equilibrium as now inverse of

bid function is one dimension.

Proposition 3.4.2. The unique symmetric Bayesian Nash equilibrium of the weighted GSP

auction is given by the following bidding strategy:

b∗(ω) = ω − Γ(ω) −

Mn(ω, t)φ(t)dt

∀ω ∼ Fw(.)

(3.8)

(cid:90) ω

∞(cid:88)

n=1

0

where

Γ(ω) =

ck

ck

k=1

N−2

k−1 (1 − F (ω))k−2(cid:82) ω
K(cid:80)
K(cid:80)
K(cid:80)
K(cid:80)
(cid:90) ω

0 F N−k(x)dx
N−2
k−1 (1 − F (ω))k−1F N−k−1(ω)
N−2
k−1 (1 − F (ω))k−2F N−k−1(t)
N−2
k−1 (1 − F (ω))k−1F N−k−1(ω)

ck

ck

k=1

k=1

M1(ω, t) =

k=1

Mn(ω, t) =

M1(ω, 
)Mn−1(ω, 
)d


0

∀n ≥ 2

The above proposition shows the equilibrium bid25. The equilibrium bid in equation

(3.8) has some issues regarding empirical identication. First, the structural elements can

25Once the lemma(3.4.1) is used to make the objective function depend on weighted value
only , the subsequent proof of the equilibrium is similar to BNE derived in Gomes & Sweeney
(2014)

55

not be identied using observed parameters in the data; specically, the equation uses the

unknown latent distribution F (.). Secondly, it does not have a closed-form solution. In order

to derive identication of equilibrium bid empirically, I derive bounds on the bid as shown

in the next section.

3.4.1 Bounds on exclusive ad value

As the equilibrium bid does not have a closed-form, I will instead use bounds on the equilib-

rium bid to derive bounds on the exclusive ad value. The next proposition bounds the bid in

the Generalized Second Price auction in between bid from two more well know auctions that

have a closed and easily tractable equilibrium bid. Specically, I use VickreyClarkeGroves

auction (VCG) auction and a Weighted Generalized First Price auction (GFP). The next

proposition bounds the bid shading in these three auction designs. Bid shading is the amount
by which the advertisers shade their bid below their ad value  (vj − bj).

Proposition 3.4.3. The bid shading in GSP w auction can be bounded between the bid in

analog VCG and generalized rst price (GFP) auctions.26

(cid:125)
(vj − bj)VCG ≤ (vj − bj)GSP w

(cid:123)(cid:122)

(cid:124)

price less than bid

(cid:124)
(cid:125)
≤ (vj − bj)GF P w

(cid:123)(cid:122)

price equal to bid

∀j
×’

(3.9)

Shows that the bid shading is more than the truthful bidding in VCG; however, it is less

than that of the rst-price auction. This is because even though the GSP auction bid aects

price, the eect on price is still less than that of a rst-price auction. To understand this,

recall that in GSP, your price is equal to the bid below your bid, whereas, in the analog

rst-price auction, you pay your bid. Using the above, I can bound the value as follows:

Proposition 3.4.4. If the proposition(3.4.3) holds, advertiser's value can be bounded in

26proof of proposition (4) and (5) are given in appendix(G.1)

56

terms of observed variables27:

bj ≤ vj ≤ bj + Φ(fw(.), ck, bj)

∀j
×’

(3.10)

Here Φ(fw(.), ck, bj) is the bid shading amount, which shows that advertisers would bid

below their value. The term can be expanded in terms as shown below

Φ(fw(.), ck, bj) =

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1)(cid:20)

K(cid:80)

k=1

ck

sj

f (ωj )
(cid:48)
b
(ωj )

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1) (1 − F (ωj))k−1(F (ωj))N−k

K(cid:80)

k=1

ck

(N − k)(1 − F (ωj))k−1F (ωj)N−k−1 + (k − 1)(1 − F (ωj))k−2F (ωj)N−k

(cid:21)

The numerator is the probability of winning any position in the auction and the denomi-

nator the dierentiation of that probability. Notice that the function Φ(fw(.), ck, bj) has an

unobserved distribution fw i.e., distribution of weighted value. However, we can substitute

that with the bid distribution as the weighted bid is monotonic.

I will use the following

equality conditions :

Thus, the function

Φ(gb(.), ck, bj) =

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1)(cid:20)

K(cid:80)

k=1

ck

sjg(bw)

G(bw) = F (ω|N )
f (ω|N )
(ω)
b

g(bw) =

(cid:48)

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1) (1 − G(bw))k−1(G(bw))N−k

K(cid:80)

k=1

ck

(N − k)(1 − G(bw))k−1G(bw)N−k−1 + (k − 1)(1 − G(bw))k−2G(bw)N−k

(cid:21)

(3.11)

The lower bound is a well known observation in the auction literature that a rational

advertiser will not bid more than the value. The upper bound is the bid plus the bid shade

amount in case of the GFP auction.

27proof in appendix(G.1)

57

3.4.1.1 Model with externality

Now we look at the Advertiser's model with externality. The aim of this subsection is to

show how we can separate the value with and without externality.

The per-click value to the advertiser is compromised of two-part, (i) an advertiser-specic

ad value and (ii) a negative value from the number of other ads on the page  externality

component. To have a simple and tractable model we assume that the two-component are

separable. Altogether the per click value for buyer j is given as:

Vj = vj(EXTj)β1

(3.12)

where vj corresponds to the externality free part as analyzed in the previous section. The

second part captures the externality which depends on other ads EXTj is a function of

Kj, which denotes the set of ads present next to ad j. Note β1 captures the intensity

of externality's eect on ad value.

In the empirical section I well estimate β1 ( refer to

step(3.7.2) of the estimation section for more details).

Deriving externality eect on the bid: The goal of this step is to recover the

externality impact on the bid and in turn, on the advertiser's ad value. Using eqn(3.12),

I can derive the relation between externality and the advertisers' bid; the next proposition

formally states the result.

Proposition 3.4.5. The additive separability of externality and individual eect on valuation

leads to additive separable bid parameter (after controlling for various factors).28

(cid:124)

(cid:123)(cid:122)

(cid:125)

(cid:124)

(cid:123)(cid:122)

(cid:125)

(cid:124)

(cid:123)(cid:122)

(cid:125)

Log(b(vj, sj; αK,n, Extj)

) = Log( b(vj, sj; αK,n)

) +

β1Log(Extj)

(3.13)

observed bid

externality free bid

externality eect on bid

Where the bid b(vj, sj; αK,n, Extj) gives the bid in the presence of externality, which is

dependent on advertiser specic ad value (vj) and score (sj) as well as the auction parameters

αK,n, where K denotes the number of ads and n denotes the number of advertisers. The

28proof in the appendix(G.1)

58

proposition shows that the log of bid in the presence of externality is separable in externality

eect β1Log(Extj,Kj
the market Log(b(vj, sj; αK,n)).

) and the unobserved hypothetical bid if there was no externality in

The above proposition will help to estimate the externality in the empirical section,

where I estimate β1 that captures the intensity of externality's eect on ad value. Another

insight from this proposition is that once we know the β1Log(Extj) we can estimate the

externality-free bid, i.e. b(vj, sj; n). In the next section, I look at the equilibrium bid in case

of no externality. The next section helps derive the externality free ad value, i.e. vj, which

can also be thought of as the exclusive ad value.

3.5 Data

3.5.1 Data details

The data set is provided by Yahoo! as part of the Yahoo! Research Alliance Webscope pro-

gram.29 It is a four-month period of data covering search queries from January 2008 to April

2008. The sample covers all search ads in 5 categories, namely Laptop, TV Cable, Cruise,

Collectible Coins and Car Insurance.30 Each category is treated as a separate data set, and

the results are obtained separately for each of them. The advantage of data from multiple

industries is that after the estimation, we can compare the results across industries to see

whether the results are sensitive to industry characteristics. The data set has two parts. The

rst part has consumer side information, and the second part has advertiser bid and auction

outcome information. For this the analysis, I limit my sample to ads on the rst page of the

search result.31 This is mainly done because 90% of the clicks in the data are from rst page

ads, as can be seen by gure E. This nding is also consistent with the observed pattern in

29The data set I analyzed was part of the Advertising & Markets Data and, more specif-
ically A3. Yahoo! Search Marketing Advertiser Bid-Impression-Click data on competing
Keywords

30Search of specic brands names are removed from the data.
31A similar restriction was followed in Athey and Nekipelov (2010)Athey & Nekipelov

(2010), who use Bing data

59

the industry, which shows that the consumers do not go beyond the rst page.32 For more

information on data cleaning refer to appendix(J.0.1).

Consumers side data: On the consumer side, I have information about ad display and

consumers' click response for each position-advertiser-keyword combination. Continuing the

Walmart example, the data will report that Walmart's keyword `cheap gaming laptop' got

100 displays in the 1st position, and that translated into ve clicks. Table(F.1) gives the

list of variables used and table(F.3) gives the summary statistics. Notice that this is similar

to feedback given to an advertiser in gure E.3. Thus, this data is useful in analyzing how

advertisers decide their equilibrium prot-maximizing bid.

Apart from the clicks and display information, a few other important measures can be

obtained from the data. First, we can deduce the click rate of each ad,33 which is measured

as the ratio of the number of clicks over the number of displays. The summary statistic show

an average of 1% click rate, implying that about 1% of the ads get clicked. Additionally,

the keyword (matched words between ad and search) gives an approximation on the type of

search. Therefore, the number of words in the keyword referred to as keylength can be used

as an approximation for the length of the search query. Previous papers in the literature34

have noted that longer search queries are typically associated with a more focused search

intent and can thus be more valuable for the advertisers. The maximum number of words

is 10, with an average keylength of 3 words. Another variable used is the popularity of the

keyword, measured by the relative number of searches. This controls for the possible eect

of the popularity of the search.

Advertisers side: On the advertisers' side, the data is likewise aggregated on a day level.

32Various articles show that, apart from Yahoo!

consumers on Google and Bing so
not go beyond page 1: https://www.conversionguru.co.za/2017/05/29/90-people-dont-go-
past-page-1-google-search-results-searching/, https://www.theleverageway.com/blog/how-
far-down-the-search-engine-results-page-will-most-people-go/

33ad is dened as the set of keywords for which the advertiser had the same bid on a given

day

34for instance, Ramaboa, Kutlwano KKM, and Fish, Peter (2018) look at dierences in

consumers with dierent search length

60

For each ad,35 I have information on the bid for the ad, the number of times the ad won

an auction, the winning ad position and the total number of advertisers shown in a day.36

Table F.2 lists the variables and table F.4 provides the summary. The bid is measured in

terms of cents. To mask the actual amount, Yahoo! scaled all bids by an unknown amount.

I subtract the bid with the lowest value, Thus, the bid can be taken as the lower bound

on the actual bid. The average bid is 0.6 cents. I limit my analysis to the ads on the rst

page considering the top 7 ads.37 These variables help in identifying the auction outcome

for each advertiser. Through the data, I can measure how many times an advertiser had a

winning ad in the auction, which position he won and what was his corresponding bid.38

Apart from the given variables, I can also measure the ad specicity in terms of the number

of keywords specied for an ad. This gives me an approximation of whether the ad was

made for a broader search or a specic search. Additionally, I also use the popularity of the

keywords measure by the display frequency.

A note on grouping ads: As the data set has no information on consumer queries, it

is hard to know which ads enter the same auction. Nonetheless, the rule through which

Yahoo! decides which ads enter an auction can provide useful insights on how ads were

matched together. Recall that here, each consumer query is a separate auction. For each

query, Yahoo! pulls out relevant ads by matching the ads' keywords with the consumer query.

In eect, keywords related to each other enter the same auction. Thus, the paper creates

markets that are sub-groups of keywords that are related to each other. I assume the sub-

35I dene ad as the set of keywords-advertiser combination in a day for which advertiser

had the same bid

36I assume that the total number of potential ads is equal to the total number of ads that

won at least once in a day

37On average, seven ads were shown on the page. I assume the number of are seven ads

unless the number of positions observed was less than seven.

38The real identity of keywords and advertisers are kept condential by de-identifying the
data. This is done to avoid revealing any proprietary information. Also, all the bids are
scaled by an unknown amount in order to avoid revealing information about the total revenue
of the platform. Even though the data is de-identied, I can still track the same keywords
as the same de-identied number is used for all observations.

61

groups are created such that only the ones within a market compete with each other.39 I

assume that the same set of advertisers enter all auctions within a market; this way, the

markets can be treated as a proxy for auctions.

Dierences across ad product category: Table(F.5) shows mean values for dierent vari-

ables across categories.40 The relative popularity of these categories compared to the total

daily search can be seen in gure(E.5); laptop has a high popularity for consumer search

with value of 55% meaning it is more than half as popular as the peak popular search topic

measured as 100%. The car-insurance category stands out with a high bid level, with an

average 4.36 cents. It also has a relatively concentrated market with 20 advertisers per day.

The high bid level makes this an important market to analyze from Yahoo!'s perspective.

Apart from car insurance, the laptop market is also important to analyze from Yahoo!'s

perspective as it is the most popular search category with an average 540.7 search per day.

It also seems to have a high level of competition as there are, on average, 45 advertisers per

day. Lastly, the TV cable category has the highest high click rate and the second highest

per click bid making it yet another protable market for Yahoo!. Thus, the data provides

categories that have dierentiating characters and can, therefore, help us check how the

results vary across the category.

3.5.2 Characterizing features of the data

This section provides evidence on how the assumptions of the current model t the observed

data. I also look at the variation in the data that might be helpful to identify the parameters

of interest.

1. Winning bid statistics: A distinct feature of this auction is that each auction has

39I give more details on the process of making markets in the estimation section.
40Note that the data was masked, so the actual keywords were converted into random
I know the name ve dierent categories, which I match to the
numbers and alphabet.
masked categories using characteristics of the market. Please refer to the appendix(J.0.2)
for more details

62

more than one winner. Thus, unlike standard auction designs, where the researcher

can only use a single winning bid for each auction, I can use multiple winning bids for

each auction. This is especially useful in the last step of the analysis, where I have to

use bids to estimate the distribution of advertisers' willingness to pay. Figure(E) shows

the mean bids for dierent winning positions in the ve categories41. It seems that in

some categories, such as laptops, the bidders are willing to bid substantially higher to

get the rst position. However, in other categories, such as cable, advertisers are not

particularly willing to pay a higher price for a better rank. This dierence might be

due to the varying sensitivity of consumers to the position of the ad. Note that as the

auction mechanism decides the allocation of the ad position according to the weighted

bid, it is not necessary for a higher bid to get a higher position.42

2. Variation in attributes of the ad:

To better understand the determinant of how advertisers and consumers value each

other. I look at how consumers interact with the ad. One of the attributes of ads is the

position of the ad. In general, consumers tend to focus on higher positioned ads than

the ones below. To see whether I can disentangle the eect of an ad's characteristics

from the eect of an ad position on the consumer's behavior, I need variation in the

position allotted to an ad. I observe many ads in the data which are placed at dierent

positions on dierent days. Using this, in gure E.10, I plot the relative click of the

same ad in dierent positions. To compare this across ads, I measure the clicks for

each ad relative to the clicks the ad received in the rst position. The measure of clicks

used here is click-through rate, which is the probability of an ad getting a click. The

click-through rate is calculated as the ratio of clicks to impressions. In the estimation

section, this is derived from the consumers' choice model.

41To consistently graph all the categories in one graph, I have scaled the bid in car insurance

category to match the bid range of other categories (only for this graph)
42if there are two advertisers such that b1 > b2, advertiser 2 might get a higher position if
he has a higher weighted bid, i.e. bs ∗ s2 > b1 ∗ s2.

63

3. Externality: An important observation from the data, is the preliminary evidence

of externality. The externality is evident by examining the dependence of bid for a

given advertisement on the relevance of other ads displayed in the keyword category.

For example, gure E.11 shows the linear relation between the average bid and the

percentage of high-quality ads in the market.43 This shows how markets with high-

quality ads have a net negative eect on bids. This result gives preliminary evidence

that the advertiser chooses to bid less when other high-quality ads appear in the search

result page, indicating they take into account the eect of externality on consumer's

response to their ad.44

3.6

Identication

In this section, I provide intuition for the identication of the advertiser's externality-free

value distribution and the parameters for externality. I also characterize the machine learning

algorithm used for creating markets. Note that for the theoretical model I suppressed the

market subscript. However for next few sections, I add the subscript m, which represents a

market. Note, market is the ad-group and day combination.

3.6.1 Advertisers value distribution

The approach followed to derive upper and lower bounds on advertiser's value distribution

uses a combination of two standard method in the auction literature, as discussed in paper

(Guerre, Perrigne, Voung, 2000) and (Haile and Tamer 2003). The inequalities derived at

the equilibrium bid (Proposition (3.10) imply for each advertiser i, we have the following

43the the result is obtained regressing bid on the dummy variable for high-quality ads,

after controlling for position, category, popularity, keyword eects.

44The quality is measured as the ratio of clicks to impressions. In the model, it will be

formally derived from the consumer side.

64

bounds:

j,m ≤ vj,m ≤ ˆbext
ˆbext

j,m + Φ(ˆg(.|ˆb), ˆck,m, ˆbext

j,m, ˆsj,m)

∀ j, m

(3.14)

This gives an upper and lower bound for each advertiser in the sample. Thus, the distribution

of advertisers' valuation, Fv(.) can be recovered if I know (1) the estimates of reduced(i.e.
externality free) bids (i.e. ˆbext

j,m); and (2) the bid shading amount, Φ(ˆg(.|ˆb), ˆck,m, ˆbext

j,m, ˆsj,m).

These parameters are estimated in the initial steps of the estimation process and are then

used to derive the distribution bounds in the last step. For now lets assume we can estimate

them.

From the bounds on value in equation(3.14), I derive bounds on its distribution by using
stochastic dominance, which recall implies that if x ≤ y ∀ x y, then Fx() ≥ Fy(). Let Hb()
be the distribution of ˆbext
j,m, ˆsj,m).

j,m and Hφ(.) be the distribution of ˆbext

j,m + Φ(ˆg(.|ˆb), ˆck,m, ˆbext

Using stochastic dominance in equation(3.14) gives the following result:

Hφ(.) ≤ Fv(.) ≤ Hb(.)

(3.15)

Consistent and asymptotically normal estimates of the pointwise upper and lower bounds

can be obtained by taking the idealized sample analogs of these endpoints. This is a standard
case of nonparametric estimation of a CDF using kernel estimation, which gives us ˆHφ(.)
and ˆHb(.). Further details are given in the estimation section.

Now getting back to the estimates used above, i.e. (ˆck,m, ˆsj,m, ˆbext

j,m, ˆg(.|b)). These are
discussed in the next two subsections. The rst two (ˆck,m, ˆsj,m) are estimated using con-
j,m, ˆg(.|b)) are estimated
sumer's click data in a discrete choice model. The other two (ˆbext

advertisers bid data.

3.6.2 Consumers click behavior

I use the utility function of consumers in equation (3.2) to estimate the predicted probabilities

of a consumer clicking on the advertisement. The weighted logit model is used to separately

65

estimate the eect of ad characteristic (i.e. ˆsj,m) as well as the position (i.e. ˆck,m). The data

identies the position and ad characteristic for each ad click by the consumer. I also observe

the impressions, which signify the number of times an ad was displayed per period. The

variables, impressions, and clicks together help identify the number of clicks and no-click

observations per day. Further detail is given in the method section.

3.6.3 Externality estimation

(cid:113)(cid:80)

Externality is dened as the quality weighted sum of number of ads per page, which can be
k(cid:54)=K ˆs2−j,m, where ˆs is the average quality of an ad in position k for
all ads except ad j.45 The quality estimate, ˆs, is derived from the consumer side analysis46.

written as Extj,m =

The quality is denoted on 0 to 1 range with 1 being the highest quality. Fig(E.18) shows

the distribution of externality variable across dierent categories. I use variation in average

quality of ads across markets and periods to identify the externality co-ecient.47 The
estimates are then used to calculate the externality-free bid, bext−f ree
= bj,m,t(Extj,m)−β1.

j,m,t

There is a concern that externality might be endogenous. Even though the quality of rival's
ads does not directly impact the advertiser j(cid:48)s bid, there is possibly an indirect eect as

the relative quality aects the winning probability. Thus, the variable externality is treated

endogenous, and the externality in other markets are used as instruments. The instrument

variable is independent of any supply-side eect from the advertisers, and at the same time,

it correlates with the demand side i.e. consumer behavior. Thus, it is correlated to the

externality but is independent of any eect from the bid decision.48

45this term is weighted by dierent positions the advertiser gets in a day
46This is under the assumption that the quality of an ad can be captured by the ad
dependent aect on consumer's click probability. Note that this measure is widely used as
quality measure by search engines such as google and yahoo.

47The number of ads in most cases is 7 ads for rst page
48This is similar to the standard practice of using prices in other markets as an instrument

for price in IO literature.

66

3.6.4 Creating market using unsupervised machine learning

Each advertiser species a set of keywords that describe his ad. As mentioned earlier, Yahoo!

matches these keywords with consumer's query in order to pull out relevant ads. In eect,

keywords related to each other enter the same auction. Thus, the paper creates markets that

are sub-groups of ads such that only the ones within a market compete with each other. In

this section, I give details of how the markets are created.

Fig(E.14) shows the visualization of the distance between keywords for the ve main

categories. The distance measure used is cosine similarity. A key insight that will help

increase precision for estimating markets is to use the fact we know the main categories. We

will use them to see what is the best method to cluster the markets. Specically, we will

focus on two aspects that are needed for the algorithm, namely the attributes that capture

the similarity between ads and the distance matrix used.

The rst step of grouping keywords is to nd a way to calculate the similarity between

dierent keywords. A keyword is composed of multiple words. These words are used as

attributes that take positive value for keywords that contain the word. The similarity mea-

sure then assigns a positive score for each matched word and a negative score for each

non-matched word. Additionally, the score can be improved by putting more weight on a

less frequent word being matched, under the assumption that such words are more valuable

signal for grouping similar keywords than words that frequently appear across all keywords.

In order to do this, I use tf-idf (term frequency inverse document frequency)49 as a weighting

factor. The weight increases proportionally to the number of times a word was used for an

ad, and is oset by the overall frequency of the word, which helps to adjust for the fact that

some words appear more frequently in general.50. Apart from using words as attributes for

the ad, I also need to specify the distance metric used between keywords. There are several

49tf-idf is a numerical statistic that is intended to reect how important a word is to a

document in a collection or corpus.

50tfidf is one of the most popular term-weighting schemes today; 83% of text-based

recommender systems in digital libraries use tfid.

67

distance measures, such as euclidean distance and cosine similarity. I use dierent distance

measures to sort the keywords in the ve main categories and see which one works the best.

For details, see g(E.14), the graph plots the distance between keywords for various distance

measures51. It turns out cosine similarity measure works the best, coincidentally this is also

one the most commonly used distance measure to match text documents in the machine

learning literature. Thus, cosine similarity will be the selected choice.

The advantage of using unsupervised machine learning is that except the similarity mea-

sure and features(words in this case), no other variable needs to be specied. Furthermore,

we don't need a measure of actual markets to get a prediction. Remember that here we

are creating subgroups(or markets) within a base category, for example, one of the base

categories is Laptop. Thus the algorithm might have a tendency to group all of them in

one big group as `laptop' will be a common word for all of them. To solve this, we delete

the single word `laptop' as a matching feature. This means two keywords `Business Laptop,'

and `Student Laptop' will have zero similarity score as the only word common is `laptop',

which is disregarded in case of making markets. The rest of this section gives details of the

k-means algorithm.

After the keywords are processed and vectorized, the markets are dened using k-means

clustering. Given a set of keywords X = {x1, x2, ...xNm} and an exogenously determined
number of group, i.e. M , the algorithm assigns each keyword x 
 X to one of the m groups.

For each group has a centroid, which is one of the elements from X. A keyword xl is in
group m if and only if the similarity measure is the highest for other x(cid:48)s in m than to those
in other groups. Let λl,m denote the allocation variable such that:

1,

0, otherwise

λl,m =

if xl is in cluster m

(3.16)

Let θm be the chosen centroid of group m. The cluster algorithm decides the allocations

(λ) and centroids(θ) by maximizing the mean squared distance between points within the

51compressed in two dimensional space

68

group, as shown below:

(cid:18)
1 − m(cid:88)

m=1

min
θ,λ

(cid:19)

λl,m

X.Θm

||X||||Θm||

(3.17)

The k-means algortihm used in this paper uses cosine distance to calculate similarity between

points52. Equation(3.17) is solved recursively. It is a two steps process which is repeated till

stable groups are reached. In the rst step it optimally selects λl,m for each keyword i given
θ = {θ1, ...θM} and in second step optimal θ is picked given λ. The algorithm is given as:

(cid:18)
1 − M(cid:88)

m=1

(cid:19)

λl,m

X.Θm

||X||||Θm||

Step:1 min

λ

Nm(cid:88)

Step:2

λl,m(xl − θm) = 0

∀i

∀m

l=1

The steps are repeated until convergence of λ and θ. The optimal number of clusters

(i.e. markets). The optimal number of clusters m is determined by repeating the algorithm

across a dierent number of clusters and then using the silhouette score, which provides an

average measure of how well each keyword matches with the allotted market, compared to

how it matches with other markets.

3.7 Econometric Method

In this section, I describe tmhe estimation method. The estimation steps are as follows:

ˆ Step 1: Estimate consumers click probability.

ˆ Step 2: Estimate the externality eect on advertisers bid.

ˆ Step 3: Estimate lower and upper bounds on the advertisers exclusive ad value distri-

bution.

52There are several other distance measures that can be used in k-means algorithm

69

3.7.1 Step 1: Estimate consumer click probability

In this step, I model the consumers click choice. The main aim of this step is to derive

ad position and advertisers' eect on the click probabilities. The ad position eect on click

probability are used as a measure for click rate for each position.53 The advertisers' partial

eect on click probability is used to create the measure for ad quality. To estimate these two

eect I consider a click/no-click binary choice setting using a weighted logit model,54 where

the weights are on the frequency of clicks and no click. As shown in the theory section the

consumers i's click choice on ad j is given as follows:

1

0

yi,j =

consumer i clicks on ad j if Ui,j > 0
otherwise Ui,j ≤ 0

The above equation shows that the click decision is captured by the binary variable yi,j = 0, 1,

where y = 1 is consumer decides to click on the ad. It also shows that consumer click on the

ad whenever the utility from the click, represented by Ui,j is greater than zero. We can use

this variable to set up a logit model. The utility from a click can be further elaborated to

depend on observable as follows:

Ui,j,m = φ0 + Φ1Xposition dummy + Φ2Xadvertiser dummy + Φ2Xcontrols + 
i,j,m

(3.18)

where the position dummy captures the ad position eect and advertiser dummy captures

the ad eect. Apart from this the control variables include consumer specic variables such

as search popularity measure55 as well as the keylength which captures how detailed is the

search. Lastly the term 
i,j is the idiosyncratic shock which is independently and identically

distributed according to type 1 extreme value distribution. The logit model gives us the

53click rate is the expected percentage of clicks received in each position
54similar set up is considered in Athey & Nekipelov (2010)
55measured as the proportion of times the keyword appeared in the search result page

relative to total search queries in the category

70

probability that consumer i chooses to click ad j in market m is:

ˆP (yi,j,m = 1|x) =

exp(Φxi,j,m)

1 + exp(Φxi,j,m)

where yi,j,m is a binary variable, which equals to 1 if consumer j chooses to click on ad i in

market m, and xi,m denotes the set of variables considered in equation(3.18).

Parameters estimated in step 1:

ˆ Click rate of position k in market m (ˆck,m): this is measured as the predicted proba-

bility of a click in position k in market m.

ˆ Quality measure (ˆsj,m): The quality measure used the predicted probability of a click

for advertiser j in market m, denoted by si,m. This measure is then scaled to be

between [0, 1] by dividing it by the highest value.56

ˆ Externality measure: Once we have the quality measure, we can derive the externality

measure. Externality for ad j is equal to the weighted sum of the number of other

ads, where the weight is equal to the square of the average quality of other ads in each
position for market m. Thus, externality in market m for ad j is equal to ˆExtj,m =
57, where ˆs is the average quality of an ad in position k for all ads except

(cid:114) (cid:80)

ˆs2−j,m

k(cid:54)=Kj

ad j in market m.

3.7.2 Step 2: Estimate the externality eect on the advertiser's bid

The goal of this step is to recover the externality impact on the bid. Proposition (3.4.5)

in the theoretical model provides the equation showing the relationship between externality

and equilibrium bid. Using this, I now analyze the relationship empirically. I use a hedonic

regression approach suggested by Haile et al. (2003) for english auction (this paper shows

56Note the top 0.01% of the values are considered the highest quality, thus are given value

1 in the 0-1 scale

57note that here the subscript kj is suppressed for simplicity, and the subscript j captures

the dependence on ad j

71

how to apply for GSP auction setting). It presents equilibrium bid (denoted as bj,m) as a

function of externality (denoted as Extm,j), the number of bidders, quality of the ad and a

vector of observable market characteristics. Thus, using the bid data, the underlying bid for

advertiser j in market m can be written as:

log(bm,j) = β0 + β1log(Extm,j) + Zmβ2 + β3ˆsj + δN,K + um,j

(3.19)

ˆExtm,j = estimated externality in the market

Zm = Market characteristics

δN,K = Dummy variables for number of advertisers, ads and ad-position

ˆsj = estimated ad quality

In above equation, β1 measures the eect of externality on the advertiser's bid, interpreted

as percentage change in bid for 1 more additional ad on the page.

I control for market

characteristics such as popularity of the keywords of the ads, the keylength as well as the

specicity of the ad(measure whether the ad is made for a specic or broad category58).

Lastly, I control for number of advertisers and number of ads eect by using dummy variables

for each one of them.

As noted in the identication section, even though quality of rival's ads does not directly
impact the advertiser j(cid:48)s bid, there is possibly an indirect aect as the relative quality aects

the winning probability. The resulting correlation between externality and of competitor's

weighted bid induces a positive bias in the OLS estimate of β1. Therefore I estimate ex-

ternality via instrumental variables, focusing on correlation between externality in dierent

markets for a given period, which gives potential exogenous variation by capturing the de-

mand side variation but being independent of the supply side. My rst stage regression in

the 2SLS methods is:

Extm,j = γ1Extm(cid:48),j + Γ2Zm + γ2ˆsj + δN,K + µj,m

(3.20)

Parameters estimated
58measure by the number of keywords specied for an ad

72

ˆ β1: This measures the impact of externality on bid. As externality oncreases by 1%,

bid will decrease by β1 percent.

ˆ Externality free bid - the externality-free bid is residual when the externality eect is

removed from the observed bid bext−f ree

.

j,m

ˆ The distribution of externality free bid: I can also calculate the distribution of the

weighted externality free bid, as follows:

(cid:88)

(cid:88)

j

m

ˆg(b) =

1
δg

1{ˆb

[w]ext−f ree
j,m

≤ b}K

(cid:18)ˆb

[w]ext−f ree
j,m

(cid:19)

− b

δb

(3.21)

3.7.3 Step 3: Estimate lower and upper bounds on advertiser's externality-free

value distribution

This step involves estimating the distribution of advertisers value, Fv(.). Note, that this

step uses a nonparametric estimation method since in this step the goal is to estimate a

distribution and not a parameter. Additionally, since the distribution is partially identied,

meaning that the only the upper and lower bound on the distribution is identied, I would

estimate a lower and upper distribution that bound Fv

This step used equation(3.10) from the theory section,as reproduced below:
ˆbext−f ree

+ Φ(ˆg(.), ˆck, ˆbext−f ree

≤ vj ≤ ˆbext−f ree


 {1, 2, ....nm,t}

∀ j

, ˆsj)

j;m,t

j;m,t

j

(3.22)

From the bounds on value in equation(3.14), I derive bounds on its distribution by using
stochastic dominance, which recall implies that if x ≤ y ∀ x y, then Fx() ≥ Fy(). Let Hb()
be the distribution of ˆbext
j,m, ˆsj,m).

j,m and Hφ(.) be the distribution of ˆbext

j,m + Φ(ˆg(.|ˆb), ˆck,m, ˆbext

Using stochastic dominance in equation(3.14) gives the following result:

I use kernel estimation to estimate the cdf, as shown below:

Hφ(.) ≤ Fv(.) ≤ Hb(.)
(cid:88)
(cid:88)

1{ˆbj,m ≤ h}K

(cid:18)ˆbj,m − h

δh

(cid:19)

(3.23)

(3.24)

ˆHb(h) =

1
δh

j

m

73

Similar equation is used for the upper bound, giving the nal estimate as:

ˆHφ ≤ Fv ≤ ˆHb

(3.25)

3.8 Results

In this section, I discuss the results that are reported in gure(E.15-E.23) and tables

(F.6-F.8). The discussion on results is presented separately for each estimation step: step(1)

consumer side - click behavior step(2) Externality eect on advertiser's bid (3) Deriving of

Advertisers' parameters - advertiser's value for an ad and bid markdown.

3.8.1 Consumers side

On the consumer side, I derive consumer's click probability using a weighted logit model

with keylength and popularity of search as controls. The main parameters of interest are

the eect of position and ad on click probability. To capture the eect of each position and

ad I include a dummy variable for position and advertiser.59

Position eect on click probability: Table(F.8) shows results of average partial eect(APE).

Fig(E.15) provides the predicted click probability (referred to as CTR) for dierent ad posi-

tions. As expected, the results show that higher positions have a higher probability of a click.

Categories cable, car insurance, and coins see a higher probability of click with an average

click rate of around 3%. In graph(E.16), I plot the ratio of predicted click probabilities (or

CTR) for adjacent positions, i.e.

predicted clicks at position k
predicted clicks at position k+1. This ratio helps in under-
standing the proportional increase in a click when you switch to one position above your

current one. It shows that the eect of a switch to the position above you is heterogeneous

and dependent on which position you are switching to. For category Car Insurance, it seems

the biggest gain is in being in the top 5, as the jump to the 5th position has the highest

59I include a xed eect for the market as well

74

gain. For laptop top 4 positions have the highest gain, whereas for Cable and Cruise rst

position holds the most importance. This heterogeneity gain across position is important as

it impacts advertisers' bid behavior; an advertiser will be willing to pay more for a higher

position if there is a large enough increase in the click rate.

Ad Quality: Measured as the eect of the ad on click probability:- The ad's quality is

identied as the predicted click probability for dierent advertisers. This is obtained by using

the predicted click probability for each market and advertiser combination. To compare the

quality across advertisers I normalize it to a 0-1 range, with 1 being the highest quality

ad.60 As shown in graph(E.17), the quality estimates dier across product categories, where

some categories are more skewed towards low quality than others. Car insurance seems to

have the most skewed quality distribution with the mean of only 0.05, which means that the

average ad quality is 5% of the magnitude of highest quality ad. On the other hand, cable

and laptop seem to have relatively well distributed ad quality, with an average of 0.3 and

0.2 respectively.

Externality Index: As stated earlier externality variable is the quality weighted sum of the

number of other ads on the page. I dene the externality index to give it similar properties

to the HHI index. Thus, the externality index is calculated using weights equal to the square

of quality. This intuitively has an advantage over the linear index as in the current index

a single high-quality ad would have a higher eect than two average quality ads. Fig(E.18)

shows the distribution of externality variable across dierent categories.

3.8.2 Externality eect

Table(F.6) shows results of the impact of externality on advertiser's bid using Eqn(3.19).

The model is estimated to look at non-linear eects by looking at the log of externality

eect on the log of the bid. Fig(E.19) plots the estimated β1 co-ecient that captures the

percentage change in bid when externality is increased by 1% . The results show that 1%

60The top 0.01% are given a score of 1

75

increase in externality leads to a decrease of 0.39%, 0.59%, 1.37%, 0.08% in categories car

insurance, laptop, cable and coins respectively. The cruise does not show any signicant

aect of externality. The result in percentage term is dicult to interpret. Thus I will now

look at increase in externality in terms of addition of an ad next to an advertiser's own ad.

For example, including one more high quality ad when 7 ads are already present on the page

decreases bid by 0.9% percent for car insurance, 1.5% in laptop, 3.56% in cable, 0.2% in

coins. I nd evidence that the externality has a non-linear eect on bid as it depends on

the quality of the ad as well as the number of ads already present on the page. The next

two paragraphs elaborate on it further. In appendix(I.0.1) I look at alternative denition of

externality and other robust checks.

3.8.3 Non-linear eect of externality

ˆ Eect of quality of the ad: The externality imposed on advertisers' willingness to pay

by the addition of one more ad on the page is inuenced by the quality of the additional

ad. Graph(E.20) shows the percentage decrease in the bid when the display goes from

an exclusive to two-ad display.61 The graph shows how the aect of the additional

ad depends on its quality.62 The graph is plotted for the laptop category. A similar

pattern is observed in all the other categories as well. Following our earlier example

this means, when an ad is included next to Walmart's ad, Walmart decreases their bid

by 25% if its a high quality ad from Amazon's, and only 1% if it is a low quality ad.

ˆ Eect of the number of ads included on the page: The eect of externality is diminishing

in the number of ads added to the page. This means that the addition of the rst ad

has the highest negative eect. This eect decreases as more ads are included next to

an ad. This diminishing eect can be thought of as saturation of the market, where

61Note that the theoretical setup proves that the percentage decrease in advertisers will-
ingness to pay due externality is same as the percentage decrease in bid. Thus, here I can
talk about this interchangeably

62I assume the base externality without any ads on the page is one.

76

after a certain number, more ads by competitors do not impact the advertiser. The

graph(E.21) plots the decrease in advertisers' willingness to pay due to the addition of

an ad for laptop category. For example, the eect of the second ad decrease advertisers

willingness to pay by 25%, however, the eect of the seventh ad decrease the advertisers'

willingness to pay by only 2%. Thus, this shows that the eect of an additional ad is

more when there are fewer ads present on the page.

3.8.4 Advertiser willingness to pay for an ad and prot margin

In this section, I analyze the advertiser's benet from an ad. I deduct the externality eect

on the bid from stage 2 results and use the residual of step 2 as the externality-free bid for

the analysis in this section. This step derives the distribution for advertisers exclusive ad

value.

Advertiser's ad value: Using equation(3.22), I get the bounds on the advertiser's

maximum willingness to pay for an ad or ad value. The distribution bounds are estimated

for each category, as shown in the graph(E.23). The bounds are tight for three out of 5

categories, implying that inequality is sucient for inference. The graph(E.22) plots for all

product categories, the upper bound estimates for the cumulative distribution function(cdf)

of the ad value.

It seems that the ad value follows a log-normal distribution, with the

variance varying across categories.63

An interesting nding in stage 3 results is that the decision of whether to use GSP (Gen-

eralized Second-Price auction) or GFP(Generalized First Price auction) does not matter

much when the number of bidders is very high. This is usually the case with online markets.

This is important as the choice of the auction is discussed intensively in the academic liter-

ature as well as the industry. For example, Google switched to GSP from GFP auction, and

facebook uses VCG instead of GSP. In this paper, I show I can bound the GSP bid between

63The estimated distributions use a boundary condition, which is that the value have to

be less than the highest observed bid

77

the VCG bid and the GFP bid. The results show that the bounds are very close to each

other, implying the three auctions might give a similar bid. In this case, one might favor the

rst-price auction as you are paying your bid, thus increasing revenue. I further explore the

design of auction by looking at which one gives higher payo when we include a prior stage

of selecting the optimal number of ads.

3.9 Counterfactual analysis: revenue-maximizing number of ads

In this section, I examine a method to calculate the revenue-maximizing number of

ads.

I allow the search engine, Yahoo!, to vary the number of ads per page, with the

range being from one to seven ads per page.64 For each case of the number of ads page,

I derive the equilibrium bid and thus, the expected revenue for Yahoo!.65 The revenue-

maximizing number of ads is selected as the one that has the highest expected revenue. This

counterfactual is done separately for each product category so the selected number of ads

can vary across category. This helps us see whether it is a good strategy to set the number

of ads dierent for each category.

The steps below give details of the algorithm used to determine the revenue-maximizing

number of ads. For each simulation round, the following steps are executed:

1. Draw N independent values from the empirical distribution:

vj ∼ ˆHU ( ˆφ)

2. Solve for equilibrium bid using the empirical estimates of average quality (¯s), average

click rate (ˆck) and externality co-ecient ( ˆβ1).

64The upper bound of the range is selected to be seven as the data showed seven ads
per page. Thus, this counterfactual is trying to determine whether seven was optimal or a
smaller number of ads was better.

65Note, as the equilibrium bid does not have a closed-form I use the upper bound on the bid,
which is given by the bid for generalized rst-price auction as shown in proposition(3.4.3).
Additionally these simulations are done assuming everyone has average quality, however this
can be extended to look at advertisers with varying score quality. The externality is assumed
to be one for base case of exclusive ad.

78

3. Calculate the revenue (i.e. TR) for each case of number of ads per page:

T R(K)

∀K = {1, 2...7}

4. Pick the revenue maximizing number of ads (K∗)

K∗ = Argmax

K

M ean[T R(K)]

These steps are repeated for 1000 iterations. At the end of the iterations, I calculate the

mean revenue from each quantity of ads per page. The revenue-maximizing number of ads

is the one that has the highest average revenue K∗ = ArgmaxK

. The

(cid:80)1000

it=1 T Rit(K)

1000

percentage increase in revenue is calculated by taking the dierence in the revenue between

the selected optimal one and the current number of ads (i.e. seven ads).

3.9.1 Results

The results from the counterfactual simulation are presented in table(F.9). The table shows

that for three out of the ve categories, the number of ads suggested by this algorithm is less

than the current number of ads displayed (i.e. less than seven). I also calculate the potential

gain in revenue by comparing the revenue from the number of ads suggested by this method

to the currently used number of ads (i.e. seven ads). The results show that the largest gain

is for the cable TV category of about [15.6%, 22.7%] increase in revenue, with the selected

number being two-three ads per page. It seems that the categories that had a high externality

co-ecient had the highest gain. However, apart from the externality eect, the gains also

depend on the mean quality of the ads in the category. For example, laptop category, which

has a medium level of externality eect and a medium level of average quality, show a higher

gain of about [1.014%,2.985%] compared to the car insurance category that had medium

externality eect but low average quality and showed a gain of around [0.6942%, 1.698%].

The dierence in the revenue-maximizing number of ads across ad product categories

show that the features of the ad market might inuence the choice of the search engine.

79

Features that determine the bid as well as the externality index play a key role in determining

the number of ads per page. This paper suggests that the markets that have a high average

quality and more homogeneous products should show lesser number of ads per page compared

to other categories.

3.10 Conclusion

This research looks at the externality generated by the multi-ad display setting on search

engines such as Google, Yahoo!, and Bing. The externality in this market is dened as

the external cost on an advertiser's willingness to pay for an ad due to the presence of

competitors ads on the same page. In particular, I estimate the impact of the number of

ads per page on the ad price and then use the estimate to simulate the revenue-maximizing

number of ads.

I begin by developing a theoretical model to derive the equilibrium ad

price in the market. The equilibrium conditions show that the ad price is dependent on the

externality eect and the auction design The primary empirical contribution is twofold. The

rst contribution is the estimation of the impact of externality on the ad price. The ndings

show that the advertiser's willingness to pay decreases by an average of 18.48% when the

display changes from an exclusive to a two-ad display, where the average is across dierent

product categories.66 This decrease is more if a high-quality ad is displayed compared to a

low-quality one. Following the Walmart example from the introduction, this means that the

Walmart's willingness to pay decreases by 25% when the display changes from an exclusive

to a two-ad display, where the new ad is by Amazon. Furthermore, the decrease is only 2%

if the ad next to Walmart is by a low-quality advertiser rather than Amazon. Additionally,

the eect on advertisers' willingness to pay is more for the rst few ads added next to their

ad, implying that the eect of an additional ad becomes minimal when there are already ve

to seven ads on the page.

The second empirical contribution of this paper is that it estimates the advertiser's

66next to a high-quality ad

80

externality-free willingness to pay (also referred as exclusive ad value). Using the equi-

librium conditions, I can estimate bounds on the distribution of the exclusive ad value. This

result is essential as it helps to simulate how the advertiser's payment behavior changes with

change in the market environment. Unlike the consumer side for which the search engine

can do a randomized controlled trail to test the changes, a similar approach is tough on the

advertisers' side. This is because the advertisers' reaction to changing market factors such

as pricing mechanism is usually slower. Additionally, frequent changes in the environment

can make advertisers leave the ad platform due to increase in diculties. Thus, companies

such as Microsoft and Google often estimate the advertiser's unobserved parameters such

as ad value and then simulate their best response to changes in the environment. Thus,

the estimation of bounds on the distribution holds importance in this market and can be

used to simulate revenue implications of changes in the market. I nd that the estimated

distribution is close to the log-normal distribution.

These results are further used to evaluate the expected revenue for dierent quantities of

ads per page and derive the revenue-maximizing number of ads. The counterfactual analysis

shows that the revenue-maximizing number of ads will dier across ad product categories

according to the market concentration and the product dierentiation. I nd that three out

of the ve categories provided in the data show sub-optimal number of ads. Furthermore,

using the suggested number of ads leads to, on average, a 4.5 percent increase in revenue.,

which translates into a revenue gain of 5.2 billion dollars in revenue.67

These counterfactual results can be further combined with other design improvements to

increase the expected gain. For example, the restriction on the number of ads can be imple-

mented with an increase in the ad size. Additionally, this research has broader implications

as these results can be applied to any online advertising platform, which shows multiple ads

on the same ad space or to the same consumer. A few examples are Amazon and Facebook

67calculated using 2018 Google's ad revenue of 116.3 billion US dollars.

- see here for

details https://www.statista.com/statistics/266249/advertising-revenue-of-google/

81

that show multiple ads to the consumer.68

While this paper provides a possible method for determining the optimal number of ads

for the search engine, I believe the dierentiating features of the ad product category are the

key to further analyzing a more intricate revenue-maximizing number of ads per page.

68Note that the application is limited to the case of the adjacent ads being from the same

ad product category.

82

APPENDICES

83

APPENDIX A

Figures for Chapter 1

Figure A.1: Two-sided rm with quality dierentiation

84

APPENDIX B

Proofs for Chapter 1

Details of the equilibrium price and quality equations: The monopoly problem as in

Equation (1.4) can be rewritten as follows:

max
,pb
h

(ps,pb
l

,ql,qh)

Π = [pb

l + ps − c(ql)]DbDs + [(pb

h − c(qh)) − (pb

l − c(ql))]Db

hDs.

(B.1)

Using Equation (B.1), the rst order conditions for choice variables can be simplied as

follows.

ˆ Price for low-quality access on the buyer side: Equation (1.19) can be obtained

by the following steps.
(Db − Db

h)Ds + [pb

l + ps − c(ql)](Db)(cid:48)
pb
l
+ [(pb

l + ps − c(ql)](Db)(cid:48)
pb
l

⇔ (Db

l ) + [pb
k)(cid:48)
where (Db
pb
k

means that

h − c(qh)) − (pb
k)(cid:48)
and (Db
pb
j

means that

h)(cid:48)
l − c(ql))](Db
pb
l
∂Db
k
∂pb
j

, where j (cid:54)= k.

= 0,

∂Db
k
∂pb
k

Ds + [(pb

h − c(qh)) − (pb

h)(cid:48)
l − c(ql))](Db
pb
l

Ds = 0.

Using equilibrium condition for pb

h from Equation (1.20),

Db

l + [pb

l + ps − c(ql)](Db)(cid:48)
pb
l

+

− Db

h

h)(cid:48)
(Db
pb
h

 (Db

h)(cid:48)
pb
l

= 0.

h)(cid:48)
Using (Db
pb
l

h)(cid:48)
= −(Db
pb
h

, Db

l + [pb

l + ps − c(ql)](Db)(cid:48)
pb
l

+

⇔ Db

l + [pb

l + ps − c(ql)](Db)(cid:48)
pb
l

+ Db

h = 0.

 Db

h

h)(cid:48)
(−Db
pb
h

 (−Db

h)(cid:48)
pb
h

= 0.

⇔ [pb

l + ps − c(ql)] =

=

pb
l
εb

.

Db
(Db)(cid:48)
pb
l

ˆ Price for high-quality access on the buyers' side: Equation (1.20) can be ob-

tained by the following steps.

85

{[pb

h − c(qh)] − [pb
h − c(qh)] − [pb

⇔ {[pb

⇔ {[pb

h − c(qh)] − [pb

Ds + Db

hDs = 0.

h)(cid:48)
l − c(ql)]}(Db
pb
h
h)(cid:48)
l − c(ql)]}(Db
pb
h
Db
h
h)(cid:48)
(−Db
pb
h

l − c(ql)]} =

+ Db

h = 0.

=

pb
h
εb
h

.

ˆ Price for sellers: Equation (1.21) can be obtained by the following steps.

l − c(ql)]}Db

ps + DbDs = 0.

l + ps − c(ql)]Db + {[pb
{[pb
l + ps − c(ql) =

⇔ pb

h − c(qh)] − [pb
− {[pb

Ds
(−Ds)(cid:48)
ps
l + ps − c(ql) =

h − c(qh)] − [pb

Using Equation (1.20), pb

.

h}(Ds)(cid:48)
l − c(ql)]}Db
(cid:34)
(cid:35)
h
Db
Db
(cid:34)
h
Db
pb
h
εb
h

ps
εs −

pb
h
εb
h

−

,

(cid:35)

Db
h
Db

.

Ds
(−Ds)(cid:48)
ps
l + ps − c(ql) =

which can be further simplied as pb

ˆ Low-quality service for buyers: Equation (1.22) can be obtained by the following

steps.

Ds+

(Db − Db

h)c(cid:48)(ql)Ds + [pb

h − c(qh)) − (pb
[(pb
⇔ (Db − Db
+ {[pb

h − c(qh)] − [pb

h)c(cid:48)(ql) + [pb

h)(cid:48)
l − c(ql))](Db
ql

l + ps − c(ql)](Db)(cid:48)
ql
Ds = 0.
l + ps − c(ql)](Db)(cid:48)
ql

h)(cid:48)
l − c(ql)]}(Db
ql

= 0.

Using Eqn (1.20), − Db

l c(cid:48)(ql) + [pb

l + ps − c(ql)](Db)(cid:48)
ql

Using Eqn (1.23), Db

l c(cid:48)(ql) + [pb
h)(cid:48)
, − (Db
= −(Db
qh

l + ps − c(ql)](Db)(cid:48)
ql
l )c(cid:48)(ql) + [pb

h)(cid:48)
Using (Db
ql

− Db

h

 (Db

h)(cid:48)
ql

= 0.

+

h)(cid:48)
(Db
pb
h
Db
l )(cid:48)
+ [c(cid:48)(qh)
](Db
h
h)(cid:48)
ql
(Db
qh
− c(cid:48)(qh)Db
l + ps − c(ql)](Db)(cid:48)
ql

= 0.

h = 0,

which is simplied as,

l + ps − c(ql)] =
[pb

Db
(Db)(cid:48)
ql

l c(cid:48)(ql) + Db
Db
Db

hc(cid:48)(qh)

l c(cid:48)(ql) + Db
Db
Db

hc(cid:48)(qh)

,

=

ql
νb

86

k)(cid:48)
where (Db
qk

means that

∂Db
k
∂qk

k)(cid:48)
and (Db
qj

means that

∂Db
k
∂qj

, where j (cid:54)= k.

ˆ High-quality service for buyers: Equation (1.23) can be obtained by the following

h − c(qh)] − [pb

steps.
{[pb
Using Eqn (1.20), c(cid:48)(qh)

h)(cid:48)
l − c(ql)]}(Db
qh
Db
h
h)(cid:48)
(Db
qh

=

hc(cid:48)(qh) = 0.
, which can be simplied as, c(cid:48)(qh)

− Db
pb
h
εb
h

=

qh
νb
h

pb
h
εb
h

.

Proof of Proposition 1.4.1. It shows the platform oers a better price-quality ratio in

the case of one quality oering. This basically implies

pb

q(cid:124)(cid:123)(cid:122)(cid:125)

Platform (two-sided)

≤

pb

q(cid:124)(cid:123)(cid:122)(cid:125)

One-sided

.

(B.2)

We start by comparing the prot functions for two dierent cases. For simplicity, we nor-

malize cs to zero.

Πone-sided = [pb − c(q)]Db ≡ Ψ(pb, q).
Πplatform = [pb + ps − c(q)]DbDs ≡ Ψ(pb, q)Ds + psDbDs.

(cid:16) ¯pb, ¯q
(cid:17)

The one-sided monopolist's prot maximization problem is given in Equation (1.5). Let

be the optimal solution for the one-sided monopoly problem and(cid:101)x =

¯x =
for the two-sided platform. Given that the monopolist optimal value for ps (cid:54)= 0,

(B.3)

(cid:19)

(cid:18)(cid:101)pb,(cid:101)q,(cid:101)ps

(B.5)

(cid:4)
(cid:4)

As ( ¯pb, ¯q) is the optimal solution Πone-sided; this implies that Ψ( ¯pb, ¯q) ≥ Ψ((cid:101)pb,(cid:101)q) ≥
Ψ((cid:101)pb,(cid:101)q)(cid:102)Ds, so Equation (B.4) holds only if

(B.4)

Ψ((cid:101)pb,(cid:101)q)(cid:102)Ds + (cid:101)ps(cid:102)Db(cid:102)Ds ≥ Ψ( ¯pb, ¯q).

(cid:102)Ds(cid:101)ps(Db)at(cid:101)x > (cid:102)Ds(cid:101)ps(Db)at ¯x.
q(cid:124)(cid:123)(cid:122)(cid:125)
⇔ pb

q(cid:124)(cid:123)(cid:122)(cid:125)

pb

<

.

platform

one-sided

Hence proved.

Proof of Corollary 1.4.2. It is guaranteed by Proposition 1.4.1.

87

Proof of Proposition 1.4.3. We use proof by contradiction. Let us suppose that (ps)1Q ≤
(ps)2Q where the subscripts 1Q and 2Q denote the model with one quality and with two

qualities, respectively. This implies

As ps

εs is a decreasing function of ps, we derive the following:

(B.6)

(B.7)

(B.8)

(Ds)1Q ≥ (Ds)2Q.
(cid:19)
(cid:19)

(cid:18) ps

≥

1Q

εs

.

2Q

(cid:18)ps
(cid:33)
(cid:32)

εs

pb
εb

≥ pb
l
εb

+

Db
h
Db

pb
h
εb
h

.

1Q

Using Equation (1.24), we obtain the following:

Using rst order condition for pb in the model with one quality and those for pb

l and pb
h

in the model with two qualities, we obtain the following:

(cid:124)

(cid:123)(cid:122)

(cid:125)

(cid:124)

[pb + ps − c(q)]

≥ [pb

l + ps − c(ql)] +

average prot for 1Q

Db
h
Db

{[pb

(cid:123)(cid:122)
h − c(qh)] − [pb

average prot for 2Q

Given Equation (B.9), the rm would provide two qualities only if (DsDb)

.

(cid:125)
l − c(ql)]}
(cid:124) (cid:123)(cid:122) (cid:125)

1Q

(B.9)

< (DsDb)

(cid:124) (cid:123)(cid:122) (cid:125)

2Q

holds. This condition along with equation(B.6) imply:

By Equation (B.8), we have

(cid:19)

(cid:18)

pb
εb

< (Db)

2Q
pb

(cid:124)(cid:123)(cid:122)(cid:125)
q(cid:124)(cid:123)(cid:122)(cid:125)
(cid:33)

2Q

.

(Db)

1Q
pb
l

(cid:124)(cid:123)(cid:122)(cid:125)
ql(cid:124)(cid:123)(cid:122)(cid:125)
(cid:32)

1Q

≥

>

pb
l
εb

1Q

l(cid:124)(cid:123)(cid:122)(cid:125)

pb

1Q

2Q

≥ pb(cid:124)(cid:123)(cid:122)(cid:125)

2Q

(B.10)

(B.11)

(B.12)

, which yields

Furthermore from Equation (B.8), we also have

88

(cid:32)

(cid:32)

≥

(cid:33)

1Q

qc(cid:48)(q)
νb

l c(cid:48)(ql) + Db
Db
Db

hc(cid:48)(qh)

ql
νb

(cid:33)

2Q

Now, from the equilibrium conditions for 1Q we have
qc(cid:48)(q)
pb
νb
εb
1 − F (p/q)
f (p/q) 1
q
→ c(cid:48)(q)q = p

1 − F (p/q)
f (p/q) p
q2

→ c(cid:48)(q)

=

=

Similarly using 1.12, for 2Q case we get

substituting eqn(B.14) and eqn(B.15) in eqn(B.13), we get

ql

(cid:32)

l c(cid:48)(ql) + Db
Db
Db
(cid:33)
(cid:33)

pb
l
νb

2Q

1 − F (p/q)
f (p/q) p
q

p

≥

1Q

(cid:19)
(cid:18) p
(cid:32)

νb

→

≥

1Q

hc(cid:48)(qh)

= pb
l

pb

l



2Q

1 − F (pb

f (pb

l /ql)

l /ql)
pb
l
ql

(B.13)

(B.14)

(B.15)

using eqn(B.12), we get

pb
l

ql(cid:124)(cid:123)(cid:122)(cid:125)

1Q

.

q(cid:124)(cid:123)(cid:122)(cid:125)
≤ pb

2Q

This contradicts Equation (B.11). Hence (ps)1Q > (ps)2Q

(cid:4)

Proof of Corollary 1.4.4. Let (¯pb, ¯q, ¯ps) be the prot maximization variable for the

single-quality case. We prove whether the platform wants to set a nonzero demand for high-

quality products at this price and quality level. The demand for high-quality products will

be zero if

h − pb
pb
B(qh − ql)

l

= 1. ⇔ pb

h − pb

l = B(qh − ql).

(B.16)

89

We choose ((pb

whether the rst order condition on (pb

h)∗, (qh)∗) such that Equation (B.16) is satised and then determine
h, qh) shows that the platform will attempt to increase

demand for the high-quality product above zero. The rst order condition with respect to
pb
h at (¯pb, ¯q, ¯ps, (pb

.

as

h − ¯pb
pb
B(qh − ¯q)

= 1.

(B.17)

Φpb

h = Ds

{[(pb

h)∗ − c(q∗

h)∗, (qh)∗) is given as follows:
(cid:40)
h)(cid:48)
h)] − [¯pb − c(¯q)]}(Db
(cid:26)(cid:110)
(cid:111)
pb
h
= Ds(cid:110)(cid:8)B(q∗
h)] − [¯pb − c(¯q)]

(cid:111)
h) − c(¯q)](cid:9) (−f b(1))

h)∗ − c(q∗
h − ¯q) − [c(q∗

(−f b(1))

= Ds

[(pb

+ Db
h

(cid:27)

.

(cid:41)

≤ 0

if f b(1) (cid:54)= 0 and c(cid:48)(¯q) < B.

In a similar manner, we can prove that at q∗

h, the rst order condition is greater than zero.
h (cid:54)= 0. Therefore, we see that
Thus, the platform will decrease pb
the prot increases when oering two product qualities as long as f b(1) (cid:54)= 0 and c(cid:48)(¯q) < B.
c(cid:48)(¯q) < B is true, as c(cid:48)(¯q) < B implies that ¯p
(cid:4)

h and increase qh such that Db

B ¯q < 1, which holds for nonzero demand.

(1.23)

Proof of Proposition 1.4.5.

Proof of Proposition 1.4.6. The proof is in the paper

It is trivial to prove from checking Equation (1.22) and
(cid:4).
(cid:4)
(cid:4)
Proof of Proposition 1.4.7. The proof is in the paper.
Proof of Proposition 1.4.8. The proof is in the paper, as shown in Equation (1.26). (cid:4)
(cid:4)

Proof of Proposition 1.4.9. The proof is in the paper.

Proof of equivalence of this model with xed fee case:

Proof. Suppose that on one of the side the platform also charges a xed fee. For example in

case of Amazon they charge a xed fee, i.e. Prime membership on the buyers side. The key to

the equivalence is that adding xed fee doesn't change the model as long as there are no xed

benets for the users. This case ts the Amazon example as even though Amazon charges

xed fee, the buyers only benet through transactions and do not have a non-transaction

benet from Amazon. Fixed fee Case WLOG, let us assume buyers side is also charged

90

a xed fee Buyers have the following utility:

i = (Bαb
U b

i q − pb)N s − P b,

Here Pb is the xed fee charged to the buyers. The seller has the following utility:

j = (Sαs
U s

j − ps)N b.

(B.18)

(B.19)

We rst analyze the user side (buyers and sellers) to identify the equilibrium demand.

The equilibrium demand functions are derived from the participation constraint:

(cid:16)
(cid:16)

Db = P rob

Ds = P rob

i ≥ 0
U b

j ≥ 0
U s

(cid:17) ⇔ Db = 1 − F b
(cid:17) ⇔ Ds = 1 − F s

 .

pb + P b
(cid:19)
(cid:18) ps

Bq

N s

.

S

(B.20)

The monopoly problem can be written as follows:

Π = [pb + ps − c(q)]DbDs + P bDb,

(B.21)

max

(ps,pb,q)

Modied xed fee case: Now we modify the above case to show the equivalence. Let

new = pb + P b
pb
the model parameters are as follows:

N s be the per transaction fee on the buyers side and let xed fee be zero. Then

Buyers have the following utility:

U b
i = (Bαb

= (Bαb

i q − pb)N s − P b
i q − pb − P b

N s )N s = (Bαb

i q − pb

new)N s

(B.22)

Thus, this shows the utility is the same in the case of (1) usage fee pb & xed fee - P b (2)

usage fee - pb

new

The seller has the following utility:

U s
j = (Sαs

j − ps)N b.

(B.23)

91

We rst analyze the user side (buyers and sellers) to identify the equilibrium demand.

The equilibrium demand functions are derived from the participation constraint:

(cid:16)
(cid:16)

Db = P rob

Ds = P rob

i ≥ 0
U b

j ≥ 0
U s

(cid:17) ⇔ Db = 1 − F b
(cid:17) ⇔ Ds = 1 − F s

(cid:33)

(cid:32)
(cid:18) ps

pb
new
Bq

(cid:19)

.

S

The monopoly problem can be written as follows:

Π = [pb + ps − c(q)]DbDs + P bDb

max

(ps,pb,q)

= [pb + ps − c(q) +

P b
Ds ]DbDs

= [pb

new + ps − c(q)]DbDs

.

(B.24)

(B.25)

(B.26)

(B.27)

Thus, as shown above the prot function for the platform and the users utilities are the same
(cid:4)

in these two case.

92

APPENDIX C

Figures for Chapter 2

Figure C.1: Decrease in uctuation due to price ceiling and oor

Figure C.2: Price path for carbon credits for RGGI auction

93

APPENDIX D

Proofs for Chapter 2

Proof of Lemma(2.3.1) Recall the denition of η is as follows:

(cid:18)
ηi,l − E[(η
(ηi,l|σl)

τ l−tG

(mt)
l

σl

(mt)
j,l

)j(cid:54)=i|ηi,l > η

(mt)
j,l

(cid:82)

vi − ki(cid:80)

0,

l=t+1

ηi,t =

(cid:19)

]

,

if t
{ai, ki}

otherwise

Through recursive addition and subtraction, it is easy to see that the above is equivalent to

the following :

Replacing probability of bid with probability of pseudo type we can rewrite the payo

(cid:19)

]

(mt)
j,t

)j(cid:54)=i|ηi,t > η
(cid:19)

functions as

(cid:90)

W (ηi,t) =

(mt)
Ï„ G
t

σt
(mt)
t

vi − E[(η

(mt)
j,t

+ (1 − G

(cid:18)
(ηi,t|σt)
(cid:18)
(ηi,t|σt))W (ηi,t+1)
vi − E[(η
(ηi,t|σt)
(mt)
V (ηi,t) = G
t
(cid:18)
vi − W (ηi,t+1) − E[(η
(ηi,t|σt)
(cid:18)
(ηi,t|σt)

vi − W (ηi,t+1) − E[(η

)j(cid:54)=i|ηi,t > η

(mt)
V (ηi,t) = G
t

(mt)
Ï„ G
t

W (ηi,t) =

(mt)
j,t

(cid:90)

σt

This can be rewritten as

(mt)
j,t

]

+ (1 − G

(mt)
t

(ηi,t|σt))W (ηi,t+1)
(cid:19)

]

+ W (ηi,t+1)

(D.1)

(mt)
j,t

(mt)
j,t

)j(cid:54)=i|ηi,t > η
(cid:19)

(mt)
j,t

)j(cid:54)=i|ηi,t > η

(mt)
j,t

]

+ W (ηi,t+1)

(D.2)

Now, we rewrite the pseudo type in terms of the payo function. Using addition and sub-

94

traction and using the denition of η we can rewrite the denition of η as :

(cid:90)
ηi,t =
vi −
ki(cid:88)

(cid:90)

σt+1

(mt)
Ï„ G
t

(cid:18) l−(t+1)(cid:89)

(cid:18)
(ηi,t|σl)
(cid:90)

(1 −

l=t+2

σl

q=1

, if t ≥ ai or t ≤ ki

σq

vi − E[(η

(mt)
j,t

)j(cid:54)=i|ηi,t > η

(cid:19)
τ l−tG

(ml)
l

mq
G
q

(ηi,q))

(cid:19)
(cid:18)
vi − E[(η
(ηi,l|σl)

(mt)
j,t

+

]

(cid:19)

]

)j(cid:54)=i|ηi,l > η

(ml)
j,l

(ml)
j,l

Note that the second term in the equation above is equal to W (ηi,t+1). Thus we have

vi − W (ηi,t+1),

0,

ηi,t =

if t ≥ ai or t ≤ ki

otherwise

Thus, equation(D.1) and (D.2) as

(cid:90)

(cid:18)
(cid:18)
ηi,t − E[(η
(ηi,t|σt)
(ηi,t|σt)

ηi,t − E[(η

(mt)
j,t

(mt)
Ï„ G
t

W (ηi,t) =

σt
(mt)
V (ηi,t) = G
t

(mt)
j,t

(cid:19)
)j(cid:54)=i|ηi,t > η

(mt)
j,t

)j(cid:54)=i|ηi,t > η

(mt)
j,t

(cid:19)

]

+ W (ηi,t+1)

(D.3)

]

+ W (ηi,t+1)

(D.4)

(cid:4)

Proof of theorem(3.8)

The symmetric Bayesian Nash equilibrium bid in period t maximizes the following payo of

bidder t:

V (ηi,t) =

(cid:26)

(mt)
G
l

(cid:20)
(ηi,t|σl)E

(cid:12)(cid:12)(cid:12)(cid:12)b(ni,t) > b

(mt)
j(cid:54)=i

ni,t − b(mt)(ni,t)

(cid:21)

(cid:27)

+ W (ηi,t+1)

Notice that W (ηi,t) in the above expression is merely an additive constant. we will use this

and backward induction to solve for the equilibrium bidding function.

First from the structure of V (ηi,t|σt) , it is clear that after the last active period ki, the
t = 0 ∀ t > ki. This is because the buyer
is only active till period ki and would earn a negative prot from winning if he is active after

buyer's equilibrium bid will be equal to zero, i.e. bi

95

the actual deadline. Thus we can rewrite the equilibrium bidding strategy as a set of nite
)}. Now we will show that in the last active round

bids given as bi = {b(ηi,1), b(ηi,2), ....b(ηi,ki
of bidder i's lifetime i.e. kth

i period, bidder bids their pseudo valuation, so b(ηi,ki
Note that in the last period pseudo type is equal to value of the bidder, i.e. ηi,ki

) = ηi,ki.
= vi

< vi, the current period discounted utility from winning is positive i.e (vi−ztki

ˆ If b(cid:48) < vi.
In cases where the price for the object is in-between b(vi, ki) and vi, i.e. b(vi, ki) <
ztki
0 but the buyer does not win. Thus this is not optimal
ˆ If b(cid:48) > vi.
In cases where the price for the object is in-between b(vi, ki) and vi, i.e. b(vi, ki) >
ztki
0. Thus this is not optimal.

> vi, the current period discounted utility from winning is negative i.e (vi−ztki

) >

) <

From above we get that any other bid than b(ηi,ki
payo. Thus b(vi, ki) = ηi,ki is an optimal bid in the last active period (kth
bidder i.

) = vi = ηi,ki would decreases buyers
i period) for

Next we prove reporting bid equal to b(ηi,t) is optimal in an arbitrary t during the active

demand period, i.e., ai < t ki , assuming it is optimal in all period after t. Recall that

equilibrium bid maximizes V (ηi,t)

V (ηi,t) =

(mt)
G
l

(cid:26)

(cid:20)
(ηi,t|σl)E

(cid:12)(cid:12)(cid:12)(cid:12)b(ni,t) > b

(mt)
j(cid:54)=i

(cid:21)

(cid:27)

+ W (ηi,t+1)

ni,t − b(mt)(ni,t)

Here the rst term represents the expected current period discounted utility and the second

term represents the expected utility from future periods if he loses the current period auction

. Notice that the second term is independent of the bid in period tr. Thus, this is equivalent

to the bid maximizing the rst term.
Note that ηi,t = vi − W (ηi,t+1) represents the adjusted value for bidder i in period t.We will
now show b(ηi,t) = ηi,t maximizes eqn(6). Consider any arbitrary b(cid:48) (cid:54)= b(ηi,t).

96

ˆ If b(cid:48) < b(ηi,t)
In cases where the price for the object is in-between b(cid:48) and b(ηi,t), i.e. b(cid:48) < zt < b(ηi,t),
the current period discounted utility from winning is positive i.e vi − W (ηi,t+1) − ztr
> 0 but the buyer does not win. Thus this is not optimal.
ˆ If b(cid:48) > b(ηi,t)
In cases where the price for the object is in-between b(cid:48) and b(ηi,t), i.e. b(cid:48) > zt > b(ηi,t),
the current period discounted utility from winning is negative i.e vi − W (ηi,t)− zt < 0.
Thus this is not optimal.

Which gives the optimal bidding strategy as, b(ηi,t) = vi − W (ηi,t+1).

(cid:4)

Proof for proposition(2.4.1) First we look at how the rate of future supply eects the

equilibrium payo of the bidder . The period t bid maximizes the following

+ (1 − Gmt(ˆη))W (ηi,t+1|λ)

(D.5)

b(ˆη)
 Arg max

ˆη

Gmt(ˆη)E

vi − b(mt)(ηj,t)j(cid:54)=i

(cid:20)

(cid:12)(cid:12)(cid:12)(cid:12)b(ˆη) > b(mt)(ηj,t)
(cid:21)

Note that the bid is made after the supply and demand realization, so the supply rate λ only

aects payo from future periods. Also, W (ηi,t+1) is dependent on the supply and demand

distributions as well as λ. Usually we suppress this dependence for easier notation Here we

reintroduce its dependence on λ as it is critical here. Using integral-form Envelop theorem

we get :

δ(V (ηi,t|σt))

δ(λ)

=

(cid:18)

1 − G

(mt)
t

(cid:19) δ(W (ηi,t+1|λ))

δ(λ)

[ηi,t|σt]

(D.6)

Now we use equation(8) and backward induction to derive the derivative

Let us derive this in the last period of active demand. Recall that the equilibrium bid in last

period will be bi(η(vi, ri)) = η(vi, 1) = vi and W (ηi(vi, 0) = 0, thus

δ(W (ηi(vi, 1)))

δ(λ)

≥ 0

97

Now let us assume for any arbitrary r(cid:48) period of active demand left, i.e. assume
, we show that this hold in r(cid:48) + 1 too. Rewriting equation (2.4) for t(cid:48)
δ(W (ηi(vi, t(cid:48)

r + 1

r + 1)))

δ(W (ηi,t(cid:48) )

δ(λ) ≥ 0

ηi,t(cid:48)

r+1 − E[(ηm
j,t(cid:48)
δλ

)j(cid:54)=i|ηi,t(cid:48)

r+1 > ηm
j,t(cid:48)

r+1

r+1

+ W (ηi,t(cid:48)

r+1)

(cid:19)

]

(cid:19)

]

(cid:4)

(D.7)

(D.8)

(D.9)

(cid:4)

δ(cid:82)

δ(λ)

σ

t(cid:48)
r+1

λm

Ï„ G

t(cid:48)
r+1(ηi,t(cid:48)

r+1)

=
Using envelop theorem and t(cid:48)
(cid:90)

δG

λm

t(cid:48)
r+1(ηi,t(cid:48)
δλ

r+1)

=

Ï„

σ

t(cid:48)
r+1

(cid:18)

(cid:18)

λm

− G

t(cid:48)
r+1(ηi,t(cid:48)

r+1)

using the assumption

≥ 0

Thus,

δ(λ) ≥ 0 ∀t
δ(W (ηi,t)

r + 1 maximization equation we get

ηi,t(cid:48)

r+1 − E[(ηm
j,t(cid:48)

r+1

r+1 > η1
j,t(cid:48)

r+1

)j(cid:54)=i|ηi,t(cid:48)
(cid:19)

δE[(ηm
j,t(cid:48)

r+1

)j(cid:54)=i|ηi,t(cid:48)

r+1 > ηm
j,t(cid:48)

r+1

δ(W (ηi,t(cid:48))

δ(λ)

δλ

> 0, we get

]

+

δW (ηi,t(cid:48)
δλ

r+1)

Proof for proposition(2.4.2) rst we show bid is decreasing in supply rate:

δ(b(ηi,t)

δ(λ)

=

δλ

δ(vi − W (ηi,t+1|λ))
= −δ(W (ηi,t+1|λ))
≤as a resutl of proposition(2.4.1)

δλ

Notice that this also implies

(cid:18)
δ(λ) ≤ 0 , thus we have
δ(ηi,t)

(cid:19)

E(Pt) = E

→ δE(Pt)

δ(λ)

=

η

(λ∗mt)
t
(λ∗mt)
δ(E[η
t
δ(λ ∗ mt)

]

mt +

δ(E[η
t

(λ∗mt)
δ(ηt)

]

δ(ηt)
δ(λ)

≤ 0

98

Proof for proposition(2.4.3) First we look at how the rate of future supply eects the

equilibrium payo of the bidder . The period t bid maximizes the following

(cid:20)

(cid:12)(cid:12)(cid:12)(cid:12)b(ˆη) > b(mt)(ηj,t)|τ

(cid:21)

b(ˆη)
 Arg max

ˆη

Gmt(ˆη)E

τ vi − b(mt)(ηj,t)j(cid:54)=i

+ (1 − Gmt(ˆη))W (ηi,t+1|τ )

(D.10)

Note that the bid is made after the supply and demand realization, so the supply rate Ï„ only

aects payo from future periods. Also, W (ηi,t+1) is dependent on the supply and demand

distributions as well as Ï„ . Usually we suppress this dependence for easier notation Here we

reintroduce its dependence on Ï„ as it is critical here. Using integral-form Envelop theorem

we get :

δ(V (ηi,t|σt))

δ(τ )

= V (ηi,t|σt) > 0

proof of proposition(2.4.4) rst we show bid is decreasing in uncertainty:

δ(b(ηi,t)

δ(τ )

=

δ(τ vi − W (ηi,t+1|τ ))

δτ

vi − δ(W (ηi,t+1|τ ))

δτ

≥ 0

Notice that this also implies

δ(τ ) ≥ 0 , thus we have
δ(ηi,t)
(cid:19)

(cid:18)

E(Pt) = E

(mt)
η
t
δ(E[η
(mt)
t

→ δE(Pt)

δ(τ )

=

]

δ(ηt)
δ(τ )

≥ 0

δ(ηt)

99

(D.11)

(cid:4)

(D.12)

(D.13)

(D.14)

(cid:4)

Proof of proposition(2.4.5)
dE(Pt|λnew)

d(Ï„ )

δE(Pt|λnew)

δ(λnew)

δ(λnew)

δτ

+

=

δE(Pt|λnew)

δ(τ )

as rst term is positive we have
δE(Pt|λnew)
δ(τ )
dE(Pt|λ)

>

>

d(Ï„ )

(cid:4)

100

APPENDIX E

Figures for Chapter 3

Figure E.1: Sample of Yahoo! search result page

Figure E.2: Timeline

The gure shows the stages within each period. The advertiser decides the bid and keywords
at the start of the period, and the bid enters all auctions held in the period. A separate
auction is held for each search query. Keywords are words specied by the advertiser that
describe the ad and are used by Yahoo! to match it to the search queries.

101

Figure E.3: Snapshot of an advertiser's account on Yahoo!

The gure shows a sample snapshot of information available to advertisers. The rst one
shows aggregated data for each keyword. The second one shows the details for each keyword.
Click through rate refers to the ratio of the number of clicks times the number of displays.
Refer to this link for more information.

102

Figure E.4: Percentage of clicks across pages

The graph plots the percentage of the clicks received across dierent pages. This also shows
why the paper restricts the analysis to rst page. As we need to model consumers click
behavior limiting the ads to rst position captures most of the click decision. The later
pages will show less variation in the consumer's click behavior

103

Figure E.5: The popularity of the product categories for google in the past ve years

The graph plots the popularity of the categories for google in the past ve
years. The y-axis numbers represent search interest relative to the highest
point on the chart for the given region and time. A value of 100 is the
peak popularity for the term. A value of 50 means that the term is half
as popular. A score of 0 means there was not enough data for this term.
The average popularity score across last ve years for laptop, cable, car
insurance, cruise, coins are 55, 30, 20, 40, 32 respectively. Source: Google
Search Analytics click here for details

Figure E.6: No. of keywords specied by advertisers across days

The graph shows a scatter plot of the number of
keywords specied per advertiser across days. The
red line tracks the change in number of keywords
specied by the same advertiser. This variation
shows that the advertiser is using keywords to cap-
ture dierence in ad environment across searches,
this variation is used to see how the advertiser bids
dierently across keywords to accommodate the ef-
fect of other ads on the page.

104

Figure E.7: Average click rate and bid across ad positions

Click rate is the ratio of number of clicks over the
number of displays. The car insurance bid is scaled
by 1/10th of original value for descriptive analysis
only.

Figure E.8: Revenue per ad across bid

The graph shows the revenue per bid, where the
size of the circle shows the click rate of the ad
(larger circle signifying higher click rate). This
graph motivates the decision of the search engine
to weight the bid by the advertiser's eect on click
rate. Note: the revenue per ad is equal to price per
click multiplied by the quality score. As the price is
not given, this graph plots the bid instead of price,
which gives the upper bound on the revenue. The
results are for cruise category.

105

Figure E.9: Mean of bids at dierent winning positions

The bid is measured in cents. Note that as
the auction mechanism decides the allocation
of the ad position according to the weighted
bid, it is not necessary for a higher bid to get a
higher position. Due to the large dierence in
bids for car-insurance and other categories, I
have scaled the bid in car-insurance to 1/10th
of a cent.
(This is only done for this graph
and not in the data)

Figure E.10: Mean click probability for each ad across position

The plot shows the relative click of a single ad in
dierent positions. The click probability is mea-
sured relative to the clicks the ad received in the
rst position.

106

Figure E.11: Relation between the advertiser's bid and percentage of other high-quality ads
on the page

The plot graphs linear regression of bid on the pres-
ence of other high-quality ads on the page. The
plot shows preliminary evidence that the bid de-
creases with the increase in other high quality ads
on the page. The regression includes controls for
auction and consumer heterogeneity. The quality
is measured as click probability, which is calculated
as the ratio of click to impressions (note in ac-
tual estimation this is estimated on consumer side
model)

107

Figure E.12: Eye tracking Pattern

This gure plot the results of a eye tracking re-
search. It shows the eye movement of the consumer
on the page. The red region is the on scanned the
most followed by yellow and then blue. The pic-
ture reconrms that consumers do a top to bottom
scan. Thus, making ads on higher position more
valuable.

Figure E.13: Example of sub category within the laptop category

The plot shows an example of what a sub-category would look
within a major category such as laptop. I use a machine learning
clustering algorithm is to create such sub-groups.

108

Figure E.14: Keywords for Cosine and Euclidean distance

The plot shows keywords in the ve main categories. It shows
the relative performance of using dierent distance measure. the
one on the left uses Euclidean distance and the one on the right
uses Cosine distance. For the analysis cosine distance is used.

Figure E.15: The predicted click probability across positions

The plot shows the predicted click probability across
positions. The click probability is the predicted value
from the weighted logit model in step 1 of the estimation
method. The values are shown in percentage.

109

Figure E.16: The aect of choosing higher position on click probability

The plot shows the jump in click probability when
the ad moves one position up i.e. from position k
to k − 1. for example, the value in position 1 is the
percentage increase in the click probability when
you move from 2nd position to 1st. The graph plots
the two highest jump for each category.

110

Figure E.17: Ad-Quality

The plot shows distribution of ad quality across the ve categories. The quality score is
measured as the advertiser's eect on click rate. It is estimated on the consumer side.

111

Figure E.18: Cumulative distribution of Externality Index

(a) Cable TV

(b) Cruise

(c) Car Insurance

(d) Coins

(e) Laptop

Each graph plots the predicted externality index for the ve ad categories. Ex-
ternality index is measured as a weighted sum of number of other ads where the
weight is a function of the quality score of the ad.

112

Figure E.19: Externality coecient across categories

In this graph, I plot the co-ecient from 2SLS log-log regression
of log of bid on log of externality. The coecient is interpreted
as the percentage increase in the bid when externality increases
by 1%.

Figure E.20: Eect of an additional ad on advertisers bid across dierent ad quality

Notes: In this graph, I plot the percentage decrease in a bid for
each additional ad. The x-axis shows the quality of the added ad.
The graph plots result in the laptop product category. Similar
results hold for others as well.

113

Figure E.21: Diminishing eect of an additional ad on advertisers bid

The graph plots results for laptop product category. Similar
result holds for others as well.

Figure E.22: Upper bound for the cumulative distribution function of the ad value

The plot shows the upper bound of the estimated distribution of
advertisers' ad value. The distribution of advertisers value for an
ad diers across product category. Thus, estiamting the distri-
bution empirically is critical for getting realistic counterfactual
results.

114

Figure E.23: Cumulative distribution of advertiser's ad value

(a) Cable TV

(b) Cruise

(c) Car Insurance

(d) Coins

(e) Laptop

Notes: This graph plots the upper and lower bound estimated for the ad-value
distribution. The x-axis plots the values and y-axis shows the corresponding cumu-
lative distribution at each point. Here ad value captures the advertisers' externality
free value that can be thought of as their value for an exclusive ad

115

Figure E.24: Gain in revenue from using the alternate method in appendix(H)

Figure E.25: Revenue-maximizing number of ads from alternate method suggested in ap-
pendix(H)

The plot shows the average number of ads that are
displayed in the new auction design that selects the
number of ads as well as the winning ads.

116

APPENDIX F

Tables for Chapter 3

Table F.1: List of variables available for consumers side data

Variable

Description

The day of the month.

Day
Advertiser ID The id for each advertiser.
Clicks

Ad Displays

Keyword

Keylength

Ad Position

The number of clicks received by a advertise-
ment.
The number of times an advertisement was
displayed.
The keyword gives
matched between search and the ad.
The number of words specied in the key-
word.
The winning position of the advertisement on
the search result page.

the specied words

Ad denition:
bid gives the advertisement

id-keywords combination for the same

117

Table F.2: List of variables available on advertisers side

Variable

Description

The day of the month.

Day
Advertiser ID The id for each advertiser.
Bid
Ad Displays

The bid used for an ad.
The number of times an advertisement was
displayed.
The keyword gives
matched between search and the ad.
The number of words specied in the key-
word.
The winning position of the advertisement on
the search result page.

the specied words

Keyword

Keylength

Ad Position

Ad denition:
bid gives the advertisement

id-keywords combination for the same

Table F.3: Summary statistics for consumers side data

Variable

Mean/Range Std. Dev/Max

Consumer's side variables:

Keywords (ad description & search common words)

3174 (count)

Keylength (no. of words in keyword)

CTR: Click Through Rate (click percentage)

# of Search per Day

Ad-position

3.06

.98%

1925.6

1-7

-

10(max)

9.86

996.3

-

Ad display frequency and number of ads are on per day level. Consumer side
data: Aggregated for each day-advertiser- keyword - ad position observation. Total
number of observations: 131524. Restricting data to ads on rst page

118

Table F.4: Summary statistics for advertisers side data

Variable

Mean/Range Std. Dev/Max

Advertiser's side variables:
Per Click Bid1
Number of ads per page

.632

6.95

Keywords (ad description & search common words)

3174 (count)

Keylength (no. of words in keyword)

Number of advertisers

Ad-position

3.06

26.4

1-7

2.0

.27

-

10(max)

10.04

-

[1] Bid measured in cents.
Advertiser side data:Aggregated for each day-ad position obser-
vation. Total number of observations: 21,599. Restricting data
to ads on rst page.

Table F.5: Features of dierent categories

Category

Click Rate

Bid Advertisers Searches/Day

Car Insurance

Laptop

TV Cable

Cruise

Collectible Coins

2.1%

1.6%

2.4%

1.1 %

1.7%

4.359

.233

.600

.371

.174

20

45

25

22

23

386.24

540.73

277.26

533.84

103.52

Table reports mean value of variables across the ve product
categories. The bid is measured in terms of cents

119

Table F.6: Externality co-ecient across categories

Car Ins

Laptop

Log Bid
Cable TV

Coins

Cruise

Log Externality

Quality

Ad Popularity

Keylength

Ad Specicity

-0.336
(0.133)

-1.9

(0.454)

-0.592
(0.211)

-0.618
(0.341)

0.0000725
(0.0000469)

0.000753
(0.00014)

0.0046342
(0.00142)

-0.064
(0.007)

0.006
(0.003)

-0.124
(0.026)

-1.365
(0.621)

1.5882
(0.4865)

0.0019
(0.0002)

0.00675
(0.0019)

-0.0836
(0.079)

1.071

(0.1967)

0.146

(0.0879)

-1.322
(0.0667)

0.0001

(0.00014)

-0.00004
(0.000019)

0.0103521
(0.0010219)

-0.076

(0.01145)

-0.0945421
(0.00537)

0.007206
(0.00043)

-0.0319
(0.00309)

No. of advertisers
Sub-category
No. of ads
N

X
X
X
729

X
X
X

X
X
X

X
X
X

X
X
X

6977

3219

3589

5041

Table F.7: Quality measure across product categories

Car-Insurance Laptop Cable Cruise Coins

Quality Score (0 − 1):
Mean

0.05

0.21

0.30

0.27

0.13

(0.01)

(0.04)

(0.06)

(0.06)

(0.02)

Quantiles

25%

50%

75%

90%

0.00

0.01

0.06

0.13

0.05

0.14

0.29

0.51

0.11

0.21

0.46

0.66

0.06

0.21

0.42

0.64

0.05

0.10

0.16

0.26

The table summaries statistics of the predicted quality
score.

120

Table F.8: Estimated average partial eect of position on click probability

Variable

Laptop

Car-insurance Cable

Cruise

Coins

2nd Position -0.00110
(0.0002)

3rd Position

4th Position

5th Position

6th Position

7th Position

-0.00180
(0.0002)

-0.00235
(0.0002)

-0.00288
(0.0002)

-0.00301
(0.0002)

-0.00300
(0.0002)

-0.0116
(0.0010)

-0.0112
(0.0011)

-0.0202
(0.0012)

-0.0214
(0.0012)

-0.0247
(0.0012)

-0.0248
(0.0012)

-0.0228
(0.0015)

-0.0288
(0.0015)

-0.0343
(0.0015)

-0.0390
(0.0015)

-0.0407
(0.0015)

-0.0422
(0.0015)

-0.00367
(0.0003)

-0.00399
(0.0003)

-0.00431
(0.0003)

-0.00459
(0.0003)

-0.00455
(0.0003)

-0.00493
(0.0003)

-0.00831
(0.0015)

-0.0176
(0.0014)

-0.0193
(0.0015)

-0.0233
(0.0015)

-0.0258
(0.0015)

-0.0249
(0.0015)

The table shows the average partial eect on click probability relative to
1st position as calculated in the step 1 of consumer's click choice model.
Fixed eects for market and advertiser included.

121

Table F.9: Results for the revenue-maximizing number of ads per page

Predicted no. of ads per page
lower bound
upper bound

Predicted Change in prot

Externality eect Avg Quality

lower bound

upper bound

0.6942 %

1.698%

(0.694%, .694%)

(1.697%, 1.699%)

Medium

Low

1.014 %

2.985 %

Medium

Medium

(1.014%, 1.015%)

(2.985%, 2.987%)

15.575 %

22.7 %

(15.574%, 15.577%)

(22.697%, 22.704%)

0

0

0

0

High

Low

Nill

1000

High

Low

Medium

1000

Car Insurance

Laptop

TV Cable

Coins

Cruise

5

5

3

7

7

3

4

2

7

7

Simulation

1000

1000

1000

1000

Please refer to section(3.9) for more details. Note: The table shows the results from the counterfactual analysis of
deriving the revenue-maximizing number of ads. The results are calculated separately for each category and within each
category for each upper and lower bound of the ad-value distribution. The table also shows the percentage increase
in revenue from using the suggested number of ads as compared to the current number of ads, which is seven. The
externality estimate and quality variables are labeled low, medium and high in order to make it simpler to compare
categories. The top level among the ve categories is given the label high, the next two are given medium and the next
two are given low index.

122

Table F.10: Identifying dierent categories

Variable

Description

Clicks Bid No. of adv.

search

Car Insurance High price per click & highly con-
`Car Insur-

2.1%

4.359

20

386.24

1.6%

.233

2.4%

.600

1.1 % .371

1.7%

.174

45

25

22

23

540.73

277.26

533.84

103.52

across

Laptop

Cable

Cruise

Coins

centrated market :
ance'
Popular & high competition :
`Laptop'
Less popular & above average
price : `Cable'
Relatively popular & detailed
search : `Cruise'
Low value
`Coins'

variables:

Showing mean value for each category

Table F.11: Robust check: externality co-ecient across categories

Car Ins

Laptop

Cable TV

Coins

Cruise

Externality Index(1)

-.1714833
( .072278 )

-.2950749
(.1050882 )

-.6921709
( .319323 )

-.0419864
(.0399867 )

.0496461

( .0603489)

Externality Index(2)

-.3858009

-.6256772

-1.391457

-1.385585

.1321744

( .1372449 )

( .2365638 )

( .5827886 )

( 1.772531 )

( .0772414 )

No. of adv FE
Sub-category FE
No. of ads FE

X
X
X

X
X
X

X
X
X

X
X
X

X
X
X

The table shows the coecient of the externality index in step 2 of the estimation of 2SLS
regression of log of bid on externality

123

Table F.12: Robust check: dierent externality index denitions

Car Ins

Laptop

Cable TV

Coins

Cruise

top 10%

-.3362724

( .1330385 )

-1.541917
(.6485241 )

-.8776404
(.2510247 )

-.1130883

.1793007

( .0768405 )

( .1057224 )

above your quality

-.5183959
( .579788 )

-.2325425

(0.341)

-.09395

-1.385585

-2.85473

( .3748843 )

( 1.772531 )

(28.34121 )

No. of adv FE
Sub-category FE
No. of ads FE

X
X
X

X
X
X

X
X
X

X
X
X

X
X
X

The table shows the coecient of the externality index in step 2 of the estimation of 2SLS
regression of log of bid on externality

124

APPENDIX G

Proofs for Chapter 3

G.1 Theoretical Proofs

G.1.1 Proof for proposition(3.4.5)

K(cid:88)

k=1

(cid:20)

(cid:125)

(cid:20)

(cid:18)
vj − E

(cid:12)(cid:12)(cid:12)(cid:12)bw

(cid:19)(cid:21)

The prot maximizing objective function for the case of no externality is given as below :

Π(b; vj, sj) = max

b

P rob(bw

j = b[k]) ∗ ck,j

P (k)

j = b[k]

(G.1)

Let b∗ be the equilibrium bid of the no externality case, then I show that b∗(EXTKj

)b1

is the equilibrium bid of externality case. Now in case of externality the ad value is

= vj(EXTKj

Vj,Kj
prot maximizing objective function in the presence of externality.

)b1 instead of vj. Substituting this in the equation above , I get the

(cid:20)

(cid:18)

(cid:19)(cid:21)

Π(b; vj, sj) = max

b

P rob(bw

j = b[k]) ∗ ck,j

vj(EXTKj

)b1 − E

P (k)

j = b[k]

(G.2)

K(cid:88)

k=1

Note that the above transformation does not aect the ranking of the ad values and thus

they also do not impact the ranking of the bid.1. Thus, This can be further solved to:

Π(b; vj, sj) = (EXTKj

)b1

max

b

P rob(bw

j = b[k]) ∗ ck,j

P (k)

j = b[k]

Thus, the solution to the above objective function is b∗∗(EXTKj
bid in the presence of externality. Thus, the externality bid given by b(vj, sj; αK,n, ext) is

)b1, which is the equilibrium

equal to b(vj, sj; n, αK,n)

*(EXTKj

)b1. Taking log this implies the following:

K(cid:88)

k=1

(cid:12)(cid:12)(cid:12)(cid:12)bw
(cid:12)(cid:12)(cid:12)(cid:12)bw

(cid:20)

(cid:18)
vj − E

(cid:19)(cid:21)(cid:21)

(cid:124)

(cid:123)(cid:122)

externality free bid

(cid:125)

(cid:124)

(cid:123)(cid:122)

Log(b(vj, sj; αK,n, ext)

) = Log(b(vj, sj; n, αK,n)

) + b1Log(Extj,Kj

(cid:124)

(cid:123)(cid:122)

(cid:125)

(cid:124)

(cid:123)(cid:122)

)

(cid:125)

observed bid

externality free bid

externality eect on bid

(G.3)

(cid:4)

1assuming monotonic bid

125

G.1.2

lemma(3.4.1) proof:

Recall that in the weighted GSP auction, the advertisers report per click bid. The equilibrium

bid bGSP for advertiser i is given as :

bGSP = Arg max

ˆb

Π(ˆb|vi, si) = max
ˆb

(cid:20)

vi −

γick

K(cid:88)

k=1

E

GSP,[k+1]
w

b

[k]

w = ˆb ∗ si

(cid:12)(cid:12)(cid:12)(cid:12)b

si

(cid:19)

(cid:21)

×P rob(b

GSP,[k+1]
w

≤ ˆb ∗ si ≤ b

GSP,[k+1]
w

)

(G.4)

Consider an alternative auction, which I refer GSP modied (GSPM). In this auction the

advertisers report bid for si number of clicks, where the number of clicks is equivalent to the
advertiser's quality score. The equilibrium bid bGSP M for advertiser i is given as :

(cid:18)

(cid:18)

(cid:12)(cid:12)(cid:12)(cid:12)b

(cid:19)

(cid:21)

E

GSP M,[k+1]
w

b

[k]
w = Ëœbw

bGSP M = Arg max
Ëœbw

Π(bw|vi, si) = max
Ëœbw

vi −

γick

k=1

×P rob(b

GSP,[k+1]
w

si
≤ ˆb ≤ b

GSP,[k−1]
w

)

(G.5)

Ëœb =

ˆbw
si

, then we can rewrite the optimizing problem as

bGSP M = Arg max

Ëœb

Π(bw|vi, si) = max
Ëœb

vi −

γick

(cid:18)

E

b

(cid:19)

[k]
w = Ëœb

(cid:21)

(cid:12)(cid:12)(cid:12)(cid:12)b

GSP M,[k+1]
w

si

×P rob(b

GSP,[k+1]
w

≤ ˆb ≤ b

GSP,[k−1]
w

)

(G.6)

(cid:20)

(cid:20)

K(cid:88)

K(cid:88)

k=1

Now I will use the information that si is know to advertiser i and the auctioneer. Thus, the
above problem can be rewritten to maximize ˇb = ˜b/si so that the optimal bid per click looks

like :

bGSP M = Arg max

ˇb

Π(ˇb|vi, si) = max
Ëœb

(cid:20)
vi −

γick

K(cid:88)

k=1

(cid:18)

E

(cid:12)(cid:12)(cid:12)(cid:12)b

(cid:19)

(cid:21)

[k]

w = ˇb ∗ si

GSP M,[k+1]
w

b

si

≤ ˇb ∗ si ≤ b

GSP M,[k−1]
w

)

(G.7)

×P rob(b

GSP M,[k+1]
w

126

The optimization problem in equation(G.5) and (G.7) are equivalent, Thus, if all other
bcGSP M i

, then advertiser will also have bGSP

advertisers j (cid:54)= i have bGSP

bGSP M
j

=

=

i

.

si

j

sj

This shows that the GSPM equilibrium is one of the equilibrium for GSP, but since GSP
(cid:4)

has unique equilibrium, it implies the two auctions give the same equilibrium bid.

G.1.3 Proof of proposition (3.4.3)

Suppose bidder i bids Ëœb and everyone else is playing according to the equilibrium increasing
bidding strategy b(vj, sj). This equivalently means that bidder i has weighted bid Ëœbw and

everyone else bids the equilibrium weighted bid bw(wj) (refer to lemma(3.4.1) for more

details). Recall that Fw(.) is the distribution of the weighted value ω and Gw(.) is the

distribution of the equilibrium weighted bid bw. To solve for the equilibrium we rst elaborate

on the probability of getting a position. The probability of winning position k can be written

as :

(cid:0)N − 1(cid:1)
(cid:0)K − 1(cid:1)(1 − G(˜bw))k−1(G(˜bw))N−k

K(cid:88)

k=1

zk(Ëœbw) =

(G.8)

as the equilibrium weighted bid is an increasing function of weighted value wj, the above is

equivalent to

zk(b−1

w (Ëœbw)) =

K(cid:88)

k=1

(cid:0)N − 1(cid:1)
(cid:0)K − 1(cid:1)(1 − F (b−1

w (˜bw)))k−1(F (b−1

w (˜bw)))N−k

(G.9)

(G.10)

Consider an ecient equilibrium , then the prot function is given as :

ckzk(b−1

w (Ëœbw))

vj − E

[k]
w = Ëœbw

(cid:19)(cid:21)

K(cid:88)

k=1

(cid:20)

(cid:18) b

(cid:12)(cid:12)(cid:12)(cid:12)b

[k+1]
w
si

Substituting value of zk(b−1

w (Ëœbw)) from equation(G.9) and then dierentiating we get the

above equation we get :

127

)

b

ck

×

[k+1]
w
si

(cid:18)
vj − E(

(cid:19)
(cid:0)N − 1(cid:1)
(cid:0)K − 1(cid:1)(N − k)(1 − F (b−1

(cid:20) K(cid:88)
(cid:0)N − 1(cid:1)
(cid:0)K − 1(cid:1)(k − 1)(1 − F (b−1
(cid:0)N − 1(cid:1)
− K(cid:88)
(cid:0)K − 1(cid:1)(1 − F (b−1

w (Ëœbw)))b

+ ck

k=1

ck

k=1

(G.11)

w (˜bw))k−1)F (b−1

w (˜bw)))k−2F (b−1

w (˜bw))N−kf (b−1

(cid:48)

w (Ëœbw))b

w (˜bw))N−k−1f (b−1
(cid:48)
(b−1
(cid:18)
w (Ëœbw))

w (Ëœbw))b

(b−1
(cid:21)
w (Ëœbw))
(cid:19)

(cid:48)

(b−1
w (˜bw))k−1(F (b−1

w (˜bw)))N−k

d

[k+1]
E( b
w
si
d(b)

)

= 0

I focus on the symmetric equilibrium where bw() = Ëœbw() thus, the above can be rewritten as

(cid:18)
vj − E(

(cid:19)(cid:20) K(cid:88)

(cid:0)N − 1(cid:1)
(cid:0)K − 1(cid:1)(N − k)(1 − F (ωj)k−1)F (ωj)N−k−1 f (ωj)

(cid:48)

b

(ωj)

b

[k+1]
w
si

)

ck

k=1

+ ck

(cid:0)N − 1(cid:1)
(cid:0)K − 1(cid:1)(k − 1)(1 − F (ωj)k−2)N−kf (ωj)b
(cid:0)N − 1(cid:1)
− K(cid:88)
(cid:0)K − 1(cid:1)(1 − F (ωj))b

ck

(ωj)k−1(F (ωj))N−k

(cid:48)

(ωj)

(cid:48)

d

(cid:21)
(cid:18)

k=1

(cid:19)

)

[k+1]
E( b
w
si
d(b)

= 0

(G.13)

(G.12)

128

To further solve the last term lets rst open up the expected price:

(cid:19)

(cid:12)(cid:12)(cid:12)(cid:12)b

(cid:18) b

E

[k+1]
w
si
bk+1:N
= E(
w

si

b1:N−k

w

= E(

(cid:90) Ëœbw

=

0

si
x
sj

(cid:124)

(cid:90) Ëœbw
(cid:18) b

0
[k+1]
w
si

(cid:12)(cid:12)(cid:12)(cid:12)b

=

Ëœbw
sj
⇒ E

F N−k(b−1(x))

(cid:19)

Ëœbw
sj

[k]
w = Ëœbw
|bk+1:N ≤ ˜bw ≤ bk−1:N )
|b1:N−k ≤ ˜bw)
(N − k)F N−k−1(b−1(x))g(b−1(x))

F N−k(b−1(˜bw))

(cid:123)(cid:122)

conditional distribution

(G.14)

dx

(cid:125)

Using integration by parts, we get :

(N − k)F N−k−1(b−1(x))f (b−1(x))

(cid:90) Ëœbw

0

dx −

F N−k(b−1(x))
sjF N−k(b−1(˜bw))

dx

[k]
w = Ëœbw

=

− Γ(˜bw, f (.))

(G.15)

As can be expected the price in generalized second price auction is less than the bid and the

decrease in the bid is dened by Γ(ˆb, sj, g(.)) which is equal to(cid:82) ˆbsj

0

GN−k(x)
sj GN−k(b)

dx.substituting

129

the expected price in equation(G.13) we get:

(cid:18)

(cid:19) f (ωj )

(cid:20) K(cid:88)

(cid:0)N − 1(cid:1)
(cid:0)K − 1(cid:1) (N − k)(1 − F (ωj )k−1)F (ωj )N−k−1

vj − E(

b

[k+1]
w
si

)

+ ck

−

⇒

ck

ck

k=1

(cid:48)

b

k=1

(ωj )

(cid:21)
(cid:18)Ëœbw

(cid:19)
− Γ(˜bw, f (.)))

(cid:0)N − 1(cid:1)
(cid:0)K − 1(cid:1) (k − 1)(1 − F (ωj ))k−2F (ωj )N−k
(cid:0)N − 1(cid:1)
K(cid:88)
(cid:0)K − 1(cid:1) (1 − F (ωj ))k−1(F (ωj ))N−k
(cid:0)N − 1(cid:1)
(cid:18)
(cid:0)K − 1(cid:1) (N − k)(1 − F (ωj )k−1)F (ωj )N−k−1
vj − E(
(cid:0)N − 1(cid:1)
(cid:21)
(cid:0)K − 1(cid:1) (k − 1)(1 − F (ωj )k−2)F (ωj )N−k
(cid:0)N − 1(cid:1)
(cid:18) 1
K(cid:88)
(cid:0)K − 1(cid:1) (1 − F (ωj )k−1(F (ωj ))N−k

(cid:19) f (ωj )

− d(Γ(˜bw, f (.)))

(cid:20) K(cid:88)

[k+1]
b
w
si

(cid:19)

(ωj )

k=1

d(b)

d(b)

d

sj

)

(cid:48)
b

= 0

= 0

ck

sj

+ ck

−

ck

k=1

⇒ vj = E(

b

[k+1]
w
si

K(cid:80)

k=1

ck

sj

f (ωj )
(cid:48)
(ωj )
b

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1) (1 − F (ωj ))k−1(F (ωj ))N−k
ck
(N − k)(1 − F (ωj ))k−1F (ωj )N−k−1 + (k − 1)(1 − F (ωj ))k−2F (ωj )N−k

1 − d(Γ(˜bw,f (.)))

(cid:18)

(cid:19)

d(b)

(cid:21)

)+

K(cid:80)
(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1)(cid:20)

k=1

using 1 − d(Γ(˜bw,f (.)))

d(b)

< 1 I get

≤ E(

b

[k+1]
w
si

)+

K(cid:80)

k=1

ck

sj

f (ωj )
(cid:48)
b
(ωj )

K(cid:80)

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1) (1 − F (ωj ))k−1(F (ωj ))N−k

ck

k=1

(cid:21)
(N − k)(1 − F (ωj )k−1)F (ωj )N−k−1 + (k − 1)(1 − F (ωj )k−2F (ωj )N−k)

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1)(cid:20)

using the auction property that bid is always greater than the price, i.e. E(
⇒ vj ≤ bw
sj

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1) (1 − F (ωj ))k−1(F (ωj ))N−k

K(cid:80)

ck

k=1

+

sj

f (ωj )
(cid:48)
(ωj )
b

K(cid:80)

k=1

ck

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1)(cid:20)

(N − k)(1 − F (ωj )k−1F (ωj )N−k−1 + (k − 1)(1 − F (ωj ))k−2F (ωj )N−k

b

[k+1]
w
si

) < bw

(G.16)

(cid:21)

(G.17)

130

Now to use this inequality in estimation part I will need to substitute the bid distribution

in place of latent distribution using the following equality conditions :

G(bw) = F (ω|N )
f (ω|N )
(ω)
b

g(bw) =

(cid:48)

Thus, equation(G.17) can be written as :

vj ≤ bw
sj

+

K(cid:80)

k=1

ck

sj g(bw)

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1)(cid:20)

(cid:0)N−1(cid:1)
(cid:0)K−1(cid:1) (1 − G(bw))k−1(G(bw))N−k

K(cid:80)

k=1

ck

(N − k)(1 − G(bw))k−1G(bw)N−k−1 + (k − 1)(1 − G(bw))k−2G(bw)N−k

(cid:21)

Next I also show that the upper bound is equal to the equilibrium bid of the analog

generalized rst price auction. The generalized rst price auction (GFP) will have agents

pay their bid for dierent positions, since in this case auctioneer considers a score, the agents

pay their weighted bid. The maximizing prot function would be

bGF P (vj, sj) = Arg max
ˆbsj

ckzk(ˆbsj)

sjvj − bjsj

(cid:20)

(cid:21)

K(cid:88)

k=1

the equilibrium bid will then be :

K(cid:88)

k=1

d(zk(ˆbsj))

d(b)

ck

(cid:20)
sjvj − bjsj

(cid:21)

− K(cid:88)
K(cid:80)
K(cid:80)

k=1

k=1

k=1

ckzk(ˆbsj) = 0

ckzk(ˆbsj)

d(zk(ˆbsj ))

d(b)

ck

→ bGF P = vj −

→ bGF P = vj − G(bw)
∆g(bw)

It can be shown that in case of one position , this equilibrium bid is equal to the equilibrium
(cid:4)

bid of rst price auction.

131

APPENDIX H

Revenue-maximizing number of ads: looking at exible number of ads

The empirical exercise has shown that the advertiser's account for the externality imposed

by other advertisers' presence on the ad space. The bids of the advertiser decrease with an

increase in the number of ads on the page. The natural question then is what is the optimal

number of advertisements on the ad space.

In this section, I propose an addition to the

auction mechanism, that can derive the optimal number of ads on the page. I propose a

new mechanism that adds a pre-auction stage where the optimal number of ads are decided.

following are the steps of involved in the mechanism:

ˆ Bidder:

1. Bidders submit a 2-dimension bid. 1

2. The bid is composed of the bid for an exclusive ad option and a specied per-

centage decrease in the bid for each additional advertisement on the same page.

2

ˆ auction mechanism

1. step 1: Optimal number of ads is decided

2. step 2: GSP auction is held

The proposed auction can derive the optimal number every time an auction is held; in other

words, every time the search is entered in Yahoo!. Using the estimates of the advertisers'

value and externality estimate, we can compare the old and new pricing mechanisms using

simulation. This has been left for future research.

1I am assuming the externality, i.e. the percentage decrease in the bid due to each ad-
ditional bid, is not known to the auctioneer. An alternative specication would be the
advertisers only report the bid, and the auctioneer applies the pre-specied percentage de-
crease.

2the percentage decrease is equal to the externality calculated in the step 1.

132

H.0.1 Simulation details

I now specify the steps involved in the simulation for deciding the revenue-maximizing num-

ber of ads. The steps are repeated for 100 simulation rounds, and the simulation is done

separately for each category.

1. Draw N independent values from the empirical distribution:

vj ∼ ˆHU ( ˆφ)

2. Solve for equilibrium bid using:

Quality ¯s), click rate (ˆck) and externality co-ecient (β1).

3. Pick the revenue-maximizing number of ads:

N∗ = Argmax

N

T R(N )

4. Compare Yahoo!'s revenue in revenue-maximizing N∗ and the average seven ads:

∆(gain) = T R(N∗) − T R(7)

H.0.2 Results

ˆ The revenue-maximizing number of ads: The revenue-maximizing number of ads changes

with each category. The graph(E.25) plots the average number of ads allotted in the

new auction design, along with the condence interval. The product categories cable

TV and laptop are shown to have the highest decrease in the number of ads shown

compared to the current norm of showing an average of 7 ads.

133

ˆ Revenue gain across categories: The new auction design leads to higher revenue for the

search engine. Graph(E.24) plots the average gain in revenue across categories. The

highest gain is observed in the cable TV, followed by the laptop. Notice that although

laptop and car insurance had similar co-ecient for the externality eect, the gains are

dierent. This is because the gain also depends on the quality of the ad. The average

quality is higher for laptop category than car insurance.

134

APPENDIX I

Robustness Check

I.0.1 Robust checks

ˆ Denition of Externality index:

The externality index captures the eect of the quality as well as the number of other

ads on the page. In this paper the relation between the quality and the number of ads

is captured by using a weighted sum of number of ads where the structure is similar

to a euclidean distance. For convenience the index is reproduced below:

(cid:115)(cid:88)

k(cid:54)=K

Extj,m =

ˆs2−j,m

The above denition is used as it captures the dierences over a single ad having high

quality compared to 4-5 ads having lower quality that sum upto the high quality of

single ad. Note that a linear sum over the quality other ads would not have been able

to capture such dierence. The square root is added to normalize the eect of squaring
the average quality (ˆs−j,m). To check the sensitivity of the results to externality

index the step was rerun for alternative denition of the externality index as shown in

Table(F.11). The alternative denitions are as follows:

Externality index(1) = Extj,m = (cid:80)
Externality index(2) = Extj,m = (cid:80)

ˆs2−j,m
ˆs−j,m

k(cid:54)=K
k(cid:54)=K

Overall the table shows that the sign and signicance is not aected by the denition.

ˆ Type of externality:

Another assumption made in the main analysis is that the externality is generated from

the presence of all the other ads. However the externality can be also be generated

from only the high quality ads, or instead only from the ads above you. Table(F.12)

presents results for externality when the eect is only from wither the top ten percent

135

of the ads or from ads with quality above the advertiser's quality. The results show that

externality is still negative and signicant. However, it might be more or less for certain

type of ads depending on the ad category. Another interesting observation is that in

cruise category the advertisers bid is negatively eected if only the ads with quality

above the advertisers ad is considered. This is insightful as for the general externality

that captures the eect of all the ads on the page, showed positive and insignicant

eect. This can be an indication that for cruise the advertisers are specically focusing

only on the competitors that have a higher or similar quality to theirs. Further analysis

on this topic can be done if additional information about the ads is provided such as

the similarity of product sold and price charged for the product. As the advertisers

names are masked such analysis can not be done with the current data

136

APPENDIX J

Data cleaning for Chapter 3

J.0.1 Data cleaning

The data set is provided by Yahoo! as part of the Yahoo! Research Alliance Webscope

program. It gives details about ve dierent categories, namely laptop, cable, coins, cruise,

and car insurance, over 123 days from January 2008 to April 2008. The data has information

about keywords, bid, clicks, ad position, and display frequency. The keywords in the data

set include one of the base category word 'coin,' 'laptop,' 'cable,' and 'car insurance.' Apart

from the base category word, the keywords also include one or more additional words. For

example, 'business laptop' and 'student laptop' are two keywords within the base category

laptop. The additional words provide a more targeted ad. For instance, an ad 'business

laptop' targets consumers that are specically looking for business usage; however, keyword

'laptop' captures a broader search for any laptop need of a consumer. The maximum number

of words in a keyword is 10.

Another key characteristic of this data is the keywords, and the advertiser's id is masked.

This means I can track the same advertiser across ads and time; however, the actual identity

of the advertiser is masked. More details on identifying the base categories are given in

the appendix(J.0.2). To do the analysis, I restrict the dataset to ads on the rst page and

consider only the rst seven ads. The total observations in the raw data set are 207982.

After restricting the data to the rst page, the data has 131524. The restriction to ads on

the rst page is important as the consumers click probability drops drastically as the ads go

beyond the rst page. As seen in g(E) 92% of the clicks are on rst page ads. Additionally,

the data is divided into two parts according to the aggregation needed for consumers or

advertisers analysis. On the consumer's side, the analysis focuses on the click decision on

the consumer. The data provider, Yahoo! Research Lab, aggregated the data for each day-

137

keyword-advertiser-position combination. Let us take an example of observation, for January

1st, 2008, the data reports that the keyword 'business laptop' specied by Walmart that was

displayed in the rst position got 100 displays and ve clicks. For the same keyword and

advertiser, i.e. Walmart ad with keyword 'business laptop,' I will have a dierent observation

for the ad displayed in the second position, which got 50 displays and two clicks. This means

that the data does not aggregate over dierent positions and reports results for each position

and keyword separately. This is an advantage for the consumer side, as the dierent keywords

can help in capturing the dierence in consumer search. Thus, the total observation on the

consumer side analysis is 131524.

On the other hand, for analysis on the advertiser's side, I need information on how the

advertiser maximized prot for each ad. This means here the relevant variation is the bid over

ads and not the keywords. Therefore, on the advertisers side, I aggregate the data on day-

ad-advertiser-position combination.1 This means that when deciding the bid, the advertiser

accommodates the expected clicks and price for each ad across dierent winning positions

over a day. An example of an observation is; on January 1st, 2008, the data reported that

an ad by Walmart was displayed in the rst position, got 200 displays, and ten clicks. The

results of the estimation without the aggregation on the consumer side are similar to the

one without the aggregation. However, as the model assumes that the advertiser maximizes

prot over an ad, the results from aggregation are more aligned with the advertiser's prot-

maximizing strategy. Note that the advertiser can always specify a dierent bid for each

keyword, and in this case, each keyword would be treated as a separate ad in this data set.

So the aggregation is only on the keywords for which the advertiser has specied the same

bid, meaning the bid was maximized over all the keyword that has the same bid per day.

The aggregated data gives 21,599 observations.

The estimation uses subgroups in dierent categories on the basis of similar keywords.

For more detail refer to section(3.6). On the consumer side, the analysis needs an estimation

1Recall the denition of an ad is the set of keywords for which the advertiser has specied

the same bid.

138

of click probability across a position for each market. However, there are some markets

that do not observe any clicks and therefore have to be dropped from the analysis. This

is less than 1% of the data. Apart from this, there are few advertisers that do not get

any click in the data. For these advertisers, I am not able to get the quality score as the

quality score is captured through the advertiser's eect on click probability. Therefore, I

assume the minimum observed quality score in the data as the imputed quality score for

these advertisers. The analysis is robust to assuming less than the minimum quality score,

as well. Note that dropping these observations would have introduced bias in the estimation

as we need to accommodate all the advertisers in the market. Additionally, there was some

market that did not have a consistent observation, meaning they had an observation for

lower ad position but not for higher ad position. These were treated as inconsistent with the

market rules as a lower ad position is only shown when there are ads at higher ad positions.

Therefore these were also dropped from the data.

J.0.2 Within product category variation

Recall that this data has varied product categories, namely `laptop', `cable', `cruise', `coin'

and `car insurance'. Although we know the dierent product categories, the keywords are

declassied and thus the product categories are also declassied.2 To overcome this we ana-

lyze the dierences in the deidentied category and match it to the closest possible category

among [ `laptop', `cable', `cruise', `coin' and `car insurance'] according to the observed fea-

tures. Table(F.10) gives a summary of how variables dier among categories. Additionally

the table(F.10) shows the corresponding mean value for all features for dierent categories.

Let us rst look at features of category 0. This category is characterized by above average

bid and small number of competitors relative to other categories, this is consistent with the

car insurance product category. They are known to be the industry with one of the highest

2the categories are identied through specicity of keyword

139

pay per click.3 This is due to the high prot margins in auto insurance industry(which

is result of it being a highly concentrated market). Other observations about this market

which makes it consistent with the car insurance is that there are no keywords with one

word, again this is consistence with car insurance since you have to at least type two words

`car' + `insurance'.

The next category that stands out is category 2, which is characterized by high number

of competition, high number of ads per search and high number of search queries per day.

Due to its high volume of consumer searches this is likely a consumer good, which makes it

closest to `Laptop' category in the data.4

Apart from this the other category that is easy to identify is category 4. Due to its low

value for search volume , bid and clicks, it is likely to be the less popular category in the data

i.e. `Coins'. Now lets try and identify the last two categories, these ones are very similar and

harder to identify. Thus it is rst important to analyze characteristic of the category left in

the data, which are `Cable' and `Cruise'. `Cruise' is a more popular search category and has

more detailed search that is higher keylength. By analyzing the data it seems category 3 ts

`Cruise' and category 2 ts `Cable'. The table below summarizes the ndings. Note although

these claims are just approximation, we will use them for the rest of the analyzes. Even if

there is some error in identifying the category , we can still use the features of the category

and interpret how and why the results might dier for categories with dierent features.

3refer to these articles for more information :

most-expensive-keywords-in-paid-search-by-cost-per-click-and-ad-spend/
http://www.automotivedigitalmarketing.com/photo/1970539:Photo:28810

- https://www.adgooroo.com/the-
and

4as that is the only consumer good category in the data

140

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