ESSAYS IN APPLIED MICROECONOMICS

By

Nikolay Ushakov

A DISSERTATION

Michigan State University

in partial fulfillment of the requirements

Submitted to

for the degree of

Economics – Doctor of Philosophy

2021

ABSTRACT

ESSAYS IN APPLIED MICROECONOMICS

By

Nikolay Ushakov

Chapter 1: Are There Incentives to Improve the Search Engines in the Age of Information
Overload?
Information overload on the Internet creates a natural demand for higher quality search engines.
In this paper, I compare the current advertising (indirect) model of search engines financing with
the hypothetical paid (direct) model. I find that under monopoly in innovation activities indirect
monopolist has much lower incentives to improve the quality than the direct monopolist. Explicit
modeling of entry and quality competition in a static framework leads to the conclusion that under
the indirect model only one firm could profitably enter producing the minimally acceptable by
consumers quality. A dynamic framework predicts more firms entry but only because the firms are
colluding against consumers by saving on quality improvement investments. In contrast, under the
direct model firms’ cooperation leads to higher investment incentives since it permanently raises
industry profit flows. I suggest several alternative policy recommendations to improve incentives
in this market.

Chapter 2: Strategic Control and Exclusivity
This paper extends Hagiu and Lee’s (2011) "Exclusivity and control" article by making control
regime over content in addition to exclusivity as the strategic choice in an industry characterized
by a severe platform competition first for content and then for consumers. Under the assumption
of homogeneous content valuations, the following results are obtained. First, for low and medium
levels of content valuation, there are only affiliation equilibria (both exclusive and multihoming
and the latter maximizes industry profit). For the high level of content valuation, there are one
exclusive outright sale and multiple affiliation multihoming equilibria with the latter maximizing
the industry profits. Finally, there are additional platforms’ pessimistic expectations equilibria

under affiliation regime that give higher payoffs to content providers. Implications for business
strategies are presented.

Chapter 3: Long Term Effects of Minimum Drinking Age Laws on Organ Failure 1
Organ failures are among the leading causes to deaths and the most expensive medical procedures
in the United States. Medical literature has established the association between alcoholism and
chronic dysfunction of organ systems. This paper provides the first causal evidence of the long-
term impacts of increasing the MLDA to 21 in various states in the 1970s-1980s on reducing organ
failures. By delaying exposure to alcoholic beverages, the MLDA 21 likely limits adolescents’
exposure to alcohol and reduce the likelihood of alcoholism in adulthood and thus the risk of
alcohol-related diseases, including organ failures. We find that cohorts exposed to higher MLDA
(=21) had lower probability of having organ failures in later life. The empirical findings show that
limited access to spirits and alcohol before the age of 21 reduced the demand for transplants by
86 and 50 per 100,000 population, respectively, after ten years, given that the average transplants
demanded by the cohort prior to treatment is approximately 155. These findings have important
implications for evaluating the benefits of the MLDA21 legislation. Besides preventing traffic
fatalities, the MLDA21 has significantly reduced organ failures in adulthood, therefore might have
increased productivity and life quality of the generations who were growing up in the presence of
this legislation.

1co-authored with Dr. Minh Nguyen (Department of Economics, Ball State University).

ACKNOWLEDGEMENTS

I would like to thank my supervisor Jay Pil Choi for encouraging me to do original research that ap-
plies to the real world, for demonstrating how to read and solve numerous papers in microeconomics.
I appreciate your continued support and helping me when I needed it.

I would like to thank Andrei Shevchenko for your help in getting to a Ph.D. program in the
US, and for your continued support and help during my studies at Michigan State, for our great
philosophical discussions.

I would like to thank Aleksandr Yankelevich, who served on my committee while he was
affiliated with MSU, for all the time he devoted to reading and making comments for my drafts,
providing great motivating examples, and very personal enthusiastic attitude toward me, helping
me to do original research.

I would like to thank Arijit Mukherjee for teaching me how to write an actual draft of the paper

and teaching me microeconomics, it helped me not only in research but also in teaching.

I would like to thank Thomas Jeitschko for his interest and numerous comments and suggestions
on how to improve and communicate better my ideas, the value of working in teams. I benefited
from being his teaching assistant in microeconomics theory at AEASP summer program helping
students from underrepresented groups to enter Ph.D. programs in economics. His explanations of
solving quality competition games were great and helped in my research.

I would like to especially thank Minh Nguyen with whom we continually worked during my
academic training at Ball State and who is the co-author of my empirical chapter. Thank you for all
your time, and continued belief in our project’s success. Working with you was similar to having a
great internship in empirical methods, thank you for all the resources that you shared and provided
to me. Most importantly, though, I value our great teamwork on the project, many common values,
I think, that helped us to accomplish the project in such a short time. Thank you for being not only
a co-author and committee member but also a friend.

I would like to thank Todd Elder for being a great teacher of empirical labor economics, a

iv

great director of graduate studies who supported me in getting an internship at CSTAT, a great
statistical consulting department at Michigan State, which helped me to improve my empirical
skills significantly, as well as for helping me to find a job at Ball State University to teach business
statistics. Given how busy he is, I really appreciated his and Thomas Jeitschko’s support in helping
to add Minh Nguyen to my committee, being enthusiastic about our research questions, and giving
great comments for potential future research directions.

I would like to especially thank Jeff Biddle, Steve Woodbury for their quick and very informative
response on helping to find historical data on unemployment, alcohol statistics, and other important
variables. Jeff Biddle was so kind to consult me via Zoom on our empirical project and provided
very valuable feedback which was incorporated in the text of Chapter 3. That was great support
and made us much more confident. I want to thank John Goddeeris for introducing me to health
economics and connecting me to his great Facebook group on health economics.

I would like to thank MSU Economics Department office manager Margareth Lynch (who
recently retired) for her kind support during my job market, our former graduate secretary Lori
Jean Nichols and current graduate secretary Jay Feight for their great work in supporting graduate
students.

I want to thank Elaine Nelson, a Ball State University librarian, who helped me to receive
numerous historical documents about the alcohol industry using inter-library loans. Her devotion
to helping me getting great data was amazing and inspired me very much.

I would like to thank Economics Department at Ball State University, especially Philip De-
Cicca and John Horowitz, for their continued support during academic training at Ball State,
encouragement to defend my Ph.D.

I want to thank Stephen Ferris, the Dean of Miller College of Business at Ball State University,
for his personal sympathy to me, interdisciplinary perspective, and encouragement to get Ph.D. and
publishing papers. More importantly, I learned a lot about different countries and the United States
culture by joining his regular lunches during the Covid-19 pandemic.

I want to thank the Higher School of Economics (HSE) and the New Economic School (NES)

v

for giving me the necessary background to enter and successfully receive Ph.D. in Economics. I
am especially feel obliged to Kirill Sosunov (my master thesis advisor at HSE), Lev Lyubimov
(who recently passed away), Dmitry Levando, Sergey Pekarski, and all teachers and students with
whom I interacted at HSE and NES. Thank you Alexei Savvateev for teaching me mathematics like
nobody ever did, for showing the beauty of mathematics.

I want to thank the team at Skolkovo Institute for Emerging Markets Studies, Bill Willson
(who passed away in 2017), Sam Park, Meng Zhao, Nan Zhou, who played an important part in
motivating me to pursue Ph.D. degree.

I would like to thank Søren Johansen, a great statistician of our times and a very nice person,
whose class I had the chance to take during the summer of 2008. His advice and methods expanded
my appreciation of statistics.

I want to thank my Russian and Thai family for your continued support and for believing in
me. I want to thank my Father Volodya, who passed away because of lung cancer in 2015, who
always believed I can succeed in my studies and research, who was very bright in mathematics,
taught me how to drive a car, and devoted many hours to help me during my college studies. I
want to thank my Grandfather Melis, who passed away in 2016 because of dementia, and who was
a person of great humor, responsibility for his family, and energetic person, who worked in the
mining industry and traveled across all Soviet Union and internationally too, was truly social, loved
sports and politics. I want to thank my Mother Olga for her heroic devotion to our family, her love,
and her deep attachment to me. I want to thank my wife Noon for your love, pushing me to achieve
more, for making and sharing a lot of great photos, and traveling together. I want to thank my
Uncle Vanya (a poet Meister Janus) for helping me to make the right decisions in life, helping me
to be a good person, and helping me to become one of the best students in class in high school. I
want to thank Grandmother Luda for her love and for praying for me and all our family all the time.
I want to thank the Mother and Father of my wife, Khon, and Peak, for their love and support. This
dissertation is our mutual achievement!

I would like to thank my classmate Andy Chou, and friend Brian Payne who I met while being

vi

at Michigan State, I was lucky to meet you guys. I would like to thank numerous friends and people
I have met in Russia, Thailand, and United States, and other countries I visited. Thinking of you
gives me hope for the future of humanity.

May The Force Be With Us!

vii

TABLE OF CONTENTS

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

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CHAPTER 1 ARE THERE INCENTIVES TO IMPROVE THE SEARCH ENGINES
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1.5 Benchmark: Monopoly in Quality Investments .
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CHAPTER 2 STRATEGIC CONTROL AND EXCLUSIVITY .
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IN THE AGE OF INFORMATION OVERLOAD? .
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Platforms’ and Content Providers’ Strategic Choice of Control and Exclusivity 55
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CHAPTER 3 LONG TERM EFFECTS OF MINIMUM DRINKING AGE LAWS ON
ORGAN FAILURE (CO-AUTHORED WITH DR. MINH NGUYEN) .
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Introduction . .

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3.2 Background on Organ Transplantation in the US . . . . . . . . . . . . . . . . . . . 91
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3.3 Data .
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3.5 Results . .
3.5.1 Effects of the MLDA21 for Spirits on the Transplant Demand . . . . . . . . 94
3.5.2 Effects of the MLDA21 for Alcohol on the Transplant Demand . . . . . . . 95
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APPENDIX A FIGURES FOR CHAPTER 1 . . . . . . . . . . . . . . . . . . . . . . 98
APPENDIX B FIGURES AND DERIVATIONS FOR CHAPTER 2 . . . . . . . . . . 100
APPENDIX C FIGURES AND TABLES FOR CHAPTER 3 . . . . . . . . . . . . . . 107
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APPENDICES .

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BIBLIOGRAPHY .

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ix

LIST OF TABLES

Table B.1: Second Stage Industry Profit Under Outright Sale (Homogenous Content Valuation)100

Table B.2: Second Stage Industry Profit Under Affiliation (Homogenous Content Valuation) 101

Table C.1: Timing Of Lowering the Minimum Legal Drinking Age Below and Raising to

21 Years for Distilled Spirits During 1970s and 1980s . . . . . . . . . . . . . . . 117

Table C.2: Timing Of Lowering the Minimum Legal Drinking Age Below and Raising to

21 Years for Any Type of Alcohol During 1970s and 1980s . . . . . . . . . . . . 118

Table C.3: Estimated Effects of MLDA 21 for Spirits and Alcohol on Demand for Transplants119

x

LIST OF FIGURES

Figure A.1: Willingness to Pay Of Two Types of Consumers for Different Levels of Search

Engine Quality and Advertising Profits per Consumer

. . . . . . . . . . . . . . 98

Figure A.2: Optimal Choice of Search Engine Quality Under Indirect vs Direct Model of

Search Engine Financing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Figure B.1: Comparison of Equilibria in Basic (Exogenous Control) Versus Extended

Model (Endogenous Control) . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure C.1: Effect of Increasing MLDA for Spirits on Demand for Any Organs

. . . . . .

. 107

Figure C.2: Effect of Increasing MLDA for Any Alcohol on Demand for Any Organs . . . . 108

Figure C.3: Effect of Increasing MLDA for Spirits on Demand for Livers

. . . . . . . . . . 109

Figure C.4: Effect of Increasing MLDA for Spirits on Demand for Kidneys

. . . . . . . .

. 110

Figure C.5: Effect of Increasing MLDA for Spirits on Demand for Lungs

. . . . . . . . . . 111

Figure C.6: Effect of Increasing MLDA for Spirits on Demand for Hearts . . . . . . . . . . 112

Figure C.7: Effect of Increasing MLDA for Any Alcohol on Demand for Livers . . . . . .

. 113

Figure C.8: Effect of Increasing MLDA for Any Alcohol on Demand for Kidneys . . . . . . 114

Figure C.9: Effect of Increasing MLDA for Any Alcohol on Demand for Lungs . . . . . .

. 115

Figure C.10: Effect of Increasing MLDA for Any Alcohol on Demand for Hearts . . . . . .

. 116

xi

CHAPTER 1

ARE THERE INCENTIVES TO IMPROVE THE SEARCH ENGINES IN THE AGE OF

INFORMATION OVERLOAD?

1.1 Introduction

With the introduction of the Internet, the amount of information that consumers observe has
increased significantly and continues to rise every day. According to statistics1 every 60 seconds
571 new websites are created on the Internet, 347 new blog posts are made on WordPress, 72 (400)
hours of video are uploaded on YouTube, 41 thousand of new posts appears on Facebook, 278 (350)
thousand tweets are made on Twitter, 3600 (65000) photos are uploaded on Instagram and 14 new
songs are uploaded on Spotify. In addition in 2017 every 60 seconds 50 new reviews appeared on
Yelp.

In order to process this vast and constantly increasing amounts of information, individuals use
search engines. Internet Live Stats documents that about 2.6 billion searches are made on Google
daily. Since the human ability to process such a vast data is limited, and the data quality varies,
hence, there is a natural demand for the better search engines helping to organize and certify this
data for the consumer. The importance of the search engines is not just confined to the search
engine market itself, search engines potentially affect the efficiency of the whole economy, being
an essential infrastructure for the New or Information-based economy.

In this paper, I study the incentives of search engines to improve the quality of their algorithms
assuming there is a significant demand for quality improvement by some consumers. I focus on
the critical feature of this market that consumers obtain the search engine service for free, but they
generate significant advertising revenues used to finance the creation of the search engine service
for consumers (I call it an indirect business model). I ask is it possible that such an indirect business
model creates an obstacle to the quality improvement incentives? Under what conditions such an
1See Woollaston (2013) and updated versions of statistics for 2017 (see go-globe.com (2017))

is shown in parentheses whenever available.

1

obstacle may happen? How could the market structure affect the outcome? What market structure
is predicted for such an indirect business model? I compare the outcomes of the indirect model
with a hypothetical scenario when the search engine producer could only charge consumers directly
for its service (I call this the direct model).

First, I find (in Proposition 1) that an indirect innovator monopolist chooses the minimally
acceptable quality for consumers (such a quality that makes consumer indifferent between using
the search engine at zero price or to use the outside option) and makes the service free. In contrast,
the direct monopolist creates a higher quality and charges a higher price.

The reason why the indirect monopolist creates lower quality than the direct monopolist is that
it could not be compensated by charging a higher price for higher quality without losing significant
advertising revenues due to reduced participation by the less willing to pay for quality consumers.
Second, I find (in Proposition 2) that the static or one-shot (interpreted as the long-term
competition when firms commit to long-term quality improvement directions) quality competition
between equally able innovator search engines leads to the significant quality improvements but
completely dissipates expected profits. Hence, such competition does not occur in equilibrium
since only one firm enters the market in the indirect model and produces the minimally acceptable
quality for consumers. In contrast, the direct model predicts much higher quality and the number
of entered firms depends on the degree of income/tastes heterogeneity of the more willing to pay
for higher quality consumers.

The intuition why only one firm enters in the indirect model under static quality competition
is the following. Since in the indirect model the service is free for consumers, then the firm that
produces higher quality attracts all consumers, and given that each firm could always increase its
quality a bit higher even if it is costly to do so results in a severe quality competition completely (in
expectations) dissipating all ad revenues. As a result, it is never profitable for both firms to enter
the market since they could not cover the positive entry costs.

Third, I find (in Proposition 3) that the dynamic quality competition generalizes the static quality
competition when the time required to innovate is long enough. Also, the dynamic framework

2

revelas that in cases when the time required to innovate is relatively short, both firms enter, and the
Pareto best (from the firms perspective) equilibrium represents collusion on creating the minimally
acceptable quality. In contrast, under the direct model, firms cooperate on prices and create much
higher than the minimally acceptable quality since such investments raise permanently the industry
profit flows.

The intuition of potential collusion on quality is the following. If the time required to innovate
is not long enough, then firms could use investments in quality improvement as an instrument of
the punishment. Since the time required to innovate is not long enough, then the deviation by
increasing the quality above the collusive level would raise the profits only temporarily till the
moment when the rival will respond with a punishing war on quality. The punishment is a credible
strategy since charging the maximum quality guarantees winning in this market with a zero net
profit.

Fourth, in the discussion section of the paper, I show (in Proposition 4) that taking the search
engine market for consumers in isolation from the rest of the economy results in the following
welfare comparison. The total welfare of the indirect model is always lower than of the direct
model. Consumer welfare comparison depends on the assumptions regarding the outside option
value and the degree of heterogeneity of type 1 consumers. For example, if the outside options are
different and depend on the willingness to pay for the search engines, then the minimally acceptable
quality predicted by the indirect model does not make any consumers better than the outside option,
so the consumer welfare is the same as for the outside option. I also show how the model could be
extended to take into account the externality that the quality of the search engines creates for the
other markets of the economy leading to potentially very significant additional welfare losses from
the indirect model.

Fifth, in the discussion section of the paper I show (in Proposition 5) how to justify the important
assumption that each search engine produces only one service (i.e., could not second degree price
discriminate different types of consumers supplying different quality-price options) by introducing
the quality spillovers (or "search results scraping") to the inferior alternative rival. I find that in the

3

presence of the significant but still partial spillovers it is profitable to enter by an inferior alternative
firm with the hope to attract some loyal consumers through a minor horizontal differentiation
and spillovers absorption. Such an entry significantly reduces the profitability of introducing a
premium paid service in addition to the basic free service since the premium higher quality service
reveals higher quality search results to the rivals who could use it in the main basic market to steal
significant advertising revenues. In contrast, under the direct model, spillovers do not play such
a role since either the inferior alternative firm does not have enough differentiation to enter the
market or since the entering firms could cooperate on prices internalizing spillovers.

In conclusion, I discuss several alternative policies that could cure or relieve the incentive
problems identified above. The best way this market to be organized is to make search engines
using the direct model. It does not mean that the advertising should be banned. It means, though,
that the search engine function and advertising functions should be served by the independent
entities. In this case, the consumer will pay directly to the search engine producer for the service
and may choose whether to participate in the advertising platform by sharing its search history and
providing attention. In case a person agrees to participate, then she receives the price for purchasing
her information and her attention while using the search engine. An alternative scenario would
be replicating the iPhone and Android industry conditions where iPhone does not have access
to significant advertising revenues and have to use direct model creating significant innovation
incentives, while Android having significant indirect revenues makes its product much cheaper or
more accessible.

1.2 Literature Review

The founders of Google, Sergey Brin and Larry Page, in their paper describing the key initial
innovation of Google, Brin and Page (1998), in Appendix A: Advertising and Mixed Motives,
discuss three examples of mixed motives (or biases) that an advertising-based business model
could have. The first example is a search for a cellular phone, where a consumer may want to
see the search results explaining the risk of driving and using the cellular phone at the same time,

4

while the sellers of the cellular phone would be just interested in selling the phone to the consumer.
The second example is related to biasing results to the favorable websites ("friendly" companies)
away from competitors and to the possibility of such behavior due to the difficulty even for the
experts to evaluate search engines. The third example is a situation when some well known (for
example the airline) company has to pay for the advertising on a search engine (and hence incur
an economic loss) since the advertising based search engine would not have an incentive to show
the link to the company’s website in its organic links. Also, they point out that not all ads may
create such adverse mixed motives, for example, advertisers may compete for consumers through
advertising or advertise something that is genuinely new. More generally, they proposed the idea
that the better is the search engine from the consumer point of view, the fewer advertisements
needed to find what they want and hence higher quality search engines eventually would erode the
advertising business model. The authors conclude "But we believe the issue of advertising causes
enough mixed incentives that it is crucial to have a competitive search engine that is transparent
and in the academic realm."

The three examples of mixed motives are very important and the second example is very similar
to the accusation of FTC and European Commission related to Google’s practice of biasing results
in favor of its services. The idea proposed in this paper, although also related to the incentives
misalignment due to the presence of the advertising business model, is different.
In all three
examples above it is assumed that the search engine already knows how the organic and sponsored
links should be ideally (from the social point of view) implemented. Hence, the lack of transparency
(or asymmetric information) is the principal obstacle to discipline (either through reputation costs
or government sanctions) the search engine against biasing under the advertising based model.

In this paper, I study the role of advertising model for the incentives to create better information
about the websites in the first place. I focus attention on the incentive problems that an advertising-
based monopolist (or a colluding group of search engines) might have when the potential and the
need for quality improvement for consumers is almost unlimited in the age of information overload.
A closely related paper is by Spence (1975) who compares, in my terminology, the direct

5

monopolist’s private incentives to create quality with the socially optimal incentives. He finds that
if the monopolist could not price discriminate, then it may either overinvest or under-invest in the
quality improvement depending on the comparison of the willingness to pay for the quality by the
marginal consumer with the average consumer. In particular, if the marginal consumer’s willingness
to pay for higher quality is lower than the average willingness to pay, then the monopolist would
under-invest in quality from the social point of view. In this paper I suggest that the fact that the price
in the search engine market is zero might indicate that the indirect model’s marginal consumer has
much lower willingness to pay that the direct marginal consumer analyzed by Spence. Hence the
quality distortion is more severe under the indirect model than under the direct model. Moreover,
the public good nature of the search engine and resulting externalities from the search engine to
all other sectors of the economy creates additional welfare loss (gain) from lower (higher) quality
search engines.

White (2013) analyses a situation when consumers use a search engine to buy products, and
hence he proposed a model of a monopolist search engine which intermediates between merchants
and consumers. The search engine is assumed to be free for consumers (but they have to pay for
the products bought) and merchants are charged a fee for participation. By changing the fee, the
monopolist may regulate the number of merchants in the market and hence the prices (the more
merchants there are, the lower are the prices) which affects consumer participation decision. It is
assumed that in order to search consumers have to incur a search cost. Moreover, if they search, then
the willingness to pay for the product is not affected by the search engine’s quality. Search engine’s
quality could only reduce the cost of search and hence increase the participation by consumers.
Increased participation by consumers may either reduce or increase the price charged by merchants,
and the corresponding conditions are derived. Hence, higher quality may lead either to an increase
or a reduction of the monopolist’s profits extracted from merchants. In an extension, it is shown that
if the search engine also provides organic results, then the higher quality increases the number of
merchant shown in the organic results, and, then, the increased competition by merchants dissipates
profits to be extracted by the monopolist search engine. Hence, the monopolist does not have an

6

incentive to improve the quality too much.

Taylor (2013) studies a situation of competing in quality search engines and studies the relation
between the search quality and revenue cannibalization. The author explicitly models the choice
between organic search results and sponsored search results. Revenue cannibalization happens
when higher quality organic search results attract more attention of consumers than the sponsored
links. He finds that even if it is costless to produce quality, there is an upper bound on the quality
above which competing search engines will not improve the quality.

Burguet et al. (2015) examines the incentives to provide reliable search results of a monopolist
search engine funded by advertising. The authors provide microfoundation to the substitution
effects between organic and sponsored search results.
It is assumed that consumers search for
content in organic search engine while they search for products at the sponsored search engines.
The key trade-offs are the following. Higher quality for consumers of both organic and sponsored
results attracts consumers to use the search engine. On the other hand, better organic results
quickly divert consumers to publishers websites, and if the organic search is of higher quality,
then publishers could easily target ads, and hence consumers will demand less sponsored search
results. Given the identified trade-offs, the proposed model allows analyzing the welfare effects of
integration between the search engine and a small fraction of content providers.

Etro (2021) compares a device-funded platforms, like Apple’s iPhone, with ad-funded platforms,
like Google’s Android, and finds that incentives of a device-funded platform in setting commissions
on external apps and providing its own apps are largely aligned with those of consumers and much
less aligned for the ad-funded platform. This is similar to what I find in respect of the higher
alignment of incentives of directly funded search engines models as compared to indirectly or
ad-funded model. As I remark in conclusion of my paper, iPhone and Android hybrid, paid and
ad based, model could be considered as potential direction in which search engine market can
converge if higher-quality paid search engines will be introduced at some point in the future.

The papers by White (2013), Taylor (2013), and Burguet et al. (2015) all focus on the bias
that happens within the indirect model assuming that there is competition between organic search

7

results quality and sponsored search revenues. In particular, the cannibalization bias happens if the
advertising revenues depend negatively on the search engine quality2.

In contrast, the indirect monopolist distortion identified in this paper may exist independent of
whether there is cannibalization effect between sponsored links and organic links since in the direct
model all links are organic. Moreover, the quality improvements I am referring in my paper are of
a more medium to long-run nature when a search engine can improve both organic results quality
as well as sponsored results quality which would prevent the cannibalization effect. On the other
hand, advertising revenue in practice consists not only from the search ads, but the ad revenues
that a search engine may create at other platforms owned the dominant search engine (for example,
Google advertises on YouTube, Android Play Store, and any Internet websites participating on
AdSense platform) and which may be to much less extent subject to the cannibalization effect.

1.3 Stylized Facts About the Internet Search Engine Market

The following stylized facts on the internet search engine market are worth noting. First,
according to the Internet Live Stats (2018) in June 2017 there were about 1.8 billion websites on
the Internet with an annual growth of 69% as compared to June 2016. For comparison, there were
about 29 million websites on the Internet in June 2000. Hence, on average the number of websites
on the Internet grew 35% annually over the last two decades.

As another comparison, there was only one website in 1991 and the average annual growth rate

of the number of websites on the Internet was 753% during the period from 1991 till 2000.

Hence, these figures suggest that there may be a significant demand for higher quality search

engines in order to be able to use this vast amounts of information efficiently.

2White (2013) considered the possibility of a positive relationship between the sponsored
revenues and sponsored search engine quality.
In his framework, higher quality may raise the
monopoly power of the advertising firms resulting in more ad revenues extracted by the search
engine. This effect depends on the parameters of the model, and if certain conditions are not
satisfied, then the opposite effect may occur.

The proposed idea is interesting, but it fits better online retailer context like Amazon than the
Internet engine where consumers search for information not necessarily with the intention to buy
something. The value of such information could not be internalized through the advertising revenue.

8

In 2012 Pew Research Center (see Purcell et al. (2012)) published the results of a survey
conducted from January 20-February 19, 2012 among 2,253 adults age 18 and over, including 901
cell phone interviews. They were asked about the different experiences they have had using search
engines. They said that in their use of search engines they had:

• Learned something new or important that really helped them or increased their knowledge

(86% of search users have had this experience)

• Found a really obscure fact or piece of information they thought they would not be able to

find (50%)

• Gotten conflicting information in search results and not been able to figure out what is correct

(41%)

• Gotten so much information in a set of results that you feel overwhelmed (38%)

• Found that critical information is missing from search results (34%)

Also in this survey, the searchers were asked: "How confident do you feel about your own
searching abilities when using a search engine to find information online?". Just over half of search
users (56%) say they are very confident in their search abilities. Another 37% of search users today
describe themselves as somewhat confident, with fewer than one in ten saying they are not too or
not at all confident in their ability to use search engines to find information online.

Hence, this survey indicates that consumers find the current search engines helpful but there is
room for improvement. To summarize, the first stylized fact states that the amount of information
on the Internet has significantly increased and is projected to rise further creating a natural demand
for higher quality search engines. Moreover, consumer surveys indicate that there are important
areas for potential improvement of the current search engines quality.

Second, historically, Internet search engines never charged consumers positive prices and
provided their services for free to consumers. Search engines’ profits resulted from charging
advertisers for showing their ads to consumers of the search engines.

9

Third, according to StatCounter (2018) as of September 2018 worldwide desktop search engine
market share of the top-5 search engines were the following: Google 89.12%, Bing 4.25%, Yahoo!3
3.15%, Yandex 1.4% (including both Yandex Ru and Yandex), Baidu 0.61%. The current market
shares have not changed much for the available data from 2009 till 2018 with the following average
market shares: Google 89.4%, Bing 4.0%, Yahoo! 3.5%, Yandex 0.8% Baidu 0.6%.

The information on the US market is a bit ambiguous. According to ComScore in February
2016 the desktop market shares of search engines were: Google 64%, Bing 21.4%, Yahoo 12.2%.
In contrast, Statcounter gives the following numbers: Google 79%, Bing 11%, Yahoo 8%.

If the languages define the search engine markets, then in most of the countries of the world
Google has a market share of about 90%. The exceptions are China, Czech Republic, Russia and
South Korea in each of which there is a local competitor with a significant average for last 10 years
market shares: Seznam in the Czech Republic (16%), Baidu in China (70%), Yandex in Russia
(45%), Naver in South Korea (32%). It is notable that the above search engines dominating or
dominated at some point their local markets in a similar way now Google dominates in the world.
Despite the last decade’s significant dominance of Google, in the 90s the search engine markets
in the US and other countries of the world were characterized by much less concentration, more
symmetry in the sizes of key players, more often entry/exit as well as much larger number of
independent (i.e. not powered by others) search engines (see Gandal (2001)).

Fourth, there always existed (although much less during the last decade) free lower quality
search engines which have very low market shares. Currently, such search engines attract consumers
through a certain horizontal differentiation feature (privacy concerns, loyal consumers from 90s
when these search engines were among the leaders).

Fifth, there were instances when one search engine scraped the search results from the other
search engine. One instance of such copying was identified both by FTC and European Commis-
sion4 when it was found that Google used without consent the original content from third party
3Currently Yahoo!Search on the desktop computers is powered by Bing, mobile search is

powered by Google, while the local search is powered by Yelp (see Wikipedia (2021)).

4See European Commission (2013) and Rosch (2013)

10

websites (like consumer reviews from Yelp, TripAdvisor, Amazon and news publishers) in its own
specialized web search services.

Another potential5 instance of scraping or copying of search results was revealed by Google
in 2011. Google, in order to check if Bing was using Google’s search results to improve its
results, asked its engineers to show random results on their website for some rare search terms with
intentional misspellings. Google stated that it observed that those results appeared soon on the
Bing.

It should be noted that although I have presented only two instances when scraping was observed
(or claimed to be observed) but it does not preclude that such a copying happens on a regular basis
in a way that is difficult to identity that actual scraping has happened.

1.4 Baseline Description of the Model

Information overload is referred to a situation when the increase in the amount of available
information on the Internet is not accompanied by the adequate increase in the search engines
quality, preventing the efficient use of all existing information in the process of consumption and
production.

Even though the Internet search engines are so crucial for the economy as a whole, the quality
of the search engines is determined primarily in the search engine market itself. Hence, to predict
the quality of search engines it suffices to focus on the partial equilibrium analysis of the search
engine market per se. However, the welfare analysis of the search engine quality could not be made
appropriately without taking into account the positive (negative) externality that the higher (lower)
quality search engines create for other markets and activities in the economy. I will return to the
discussion of welfare at the end of the paper.

In this paper, I propose a model of Internet search engine market that explains the key stylized
fact of this market that the price of search engine service is zero. I find that such a model does
not create enough incentives for Internet search engines to improve the quality contributing to

5First, see CNN Wire (2011). For a second opinion, see Foley (2021)

11

the problem of information overload. In particular, the current Internet search engine market is
characterized by the presence of the significant advertising revenues that consumers bring to the
search engine6. I call such a situation the indirect model. The game under the indirect model is
described as follows.

Players
There are three types of players.
1) Consumers of search engine services
2) Advertisers
3) Producers of search engines
Players objectives (Payoff functions)
1) Consumers maximize the utility from using search engines.
2) Advertisers maximize profits from buying ad space at the search engines.
3) Search engines maximize the sum of payments by consumers and advertisers net of investment

in quality costs.

Players choices/strategies
1) Consumers make consumption decisions in the search engine market.
2) Advertisers make participation decisions in the search engine advertising markets.
3) Search engines are choosing whether to enter the market, which quality to create and which

price to set to consumers and advertisers.

The direct model is a hypothetical situation on the Internet search engine market where search
engine producers could only charge consumers directly and hence the advertising revenues do not
affect the incentives of the search engine producer. Hence, the direct model game will have only two
players: consumers and search engines. The full description of the direct model is the following.
6The current search engine market is usually considered as a special case of a two- or multi-
sided market (See Rochet and Tirole (2003) and Armstrong (2006)), when platforms serve two
or more distinct groups of customers, and each group’s presence affects the other groups. Such
a description is incomplete for the search engines market where the search engine itself creates
a critical complementary value for consumers and the economy by organizing and certifying all
existing information on the Internet.

12

Players
There are two types of players.
1) Consumers of search engine services
2) Producers of search engines
Players objectives (Payoff functions)
1) Consumers maximize the utility from using search engines.
2) Search engines maximize the sum of payments by consumers and advertisers net of investment

in quality costs.

Players choices/strategies
1) Consumers make consumption decisions in the search engine market.
2) Search engines are choosing whether to enter the market, which quality to create and which

price to set to consumers.

Next, I will give a more detailed description of each type of players in the search engine market.
I assume that the amount of information on the Internet is so high that there is a group of type 1
consumers whose marginal willingness to pay for quality, 
1, is high7. But if all consumers had a
high willingness to pay for the quality improvement in this market, it would be difficult to explain
the key stylized fact that the price for consumers was historically zero in this market. Hence, I
assume that there are type 2 consumers whose willingness to pay for better quality, 
2, is very low
(
2 < 
1), however they prefer higher quality too. The total number of consumers in the market is

 consisting of 
 type 1 consumers and 
 − 
 type 2 consumers.

Type 
 = 1, 2 consumers choose whether to use search engine service or not (and if to use, then
which one) by comparing its consumer surplus from different options. In particular, the consumer
surplus is 

(

) = 


 − 
 for 
 = 1, 2.

7Underlying this willingness to pay for the search engines are the following essential needs:
1. The need for help in organizing vast amounts of information due to human cognitive limitations

which results in the reduction of the search costs.

2. The need for information certification.
3. The need for exclusive online information that is not available offline (blogs, reviews, online

news, personal, governments and companies’ websites, etc.).

13

I assume that there is a minimally acceptable level of quality, 

 
 > 0, below which type 
 = 1, 2
consumers will choose the outside option with the value 
 = 
2

 
 (I assume, for simplicity, that
the outside option is the same for both types). The value of the outside option, 
, is interpreted
as the value of information that consumers may obtain from alternative sources such as inferior
alternative search engines available on the Internet as well as traditional sources like TV, radio,
newspapers or communicating with friends, etc. In the discussion section I consider an extension
where the quality of the outside option will be determined by the inferior alternative search engine
and could be higher than the 

 
 since there is a search engine quality spillover from the innovator
producers to the inferior alternative search engines. In the search engine industry’s jargon such a
practice is called the "scraping" or copying of search results.

Finally, I assume that advertisers do not harm or benefit consumers in any way, the externality
of advertisers on consumers is zero. It means that the welfare analysis of my model does not include
any negative or positive externalities that advertisements may exert on consumers. In contrast, the
main focus of the paper is on studying search engines incentives to improve quality in the presence
of the opportunity to earn significant indirect revenues through advertising.

The number of advertisers is normalized to 1. On average each consumer generates a positive
externality on each advertiser of the size 
 > 0. Such an externality represents additional sales
revenues that firms receive by posting their ads through the search engine’s ad platform. For
simplicity, it is assumed that this externality is constant for all consumers and all advertisers.
Advertisers prefer to post ads on all platforms to achieve the maximum possible audience, i.e. they
multi-home.

A search engine producer maximizes its profit by chooses the quality level 
, the price paid
by consumers, 
, and the price paid by advertisers, 
. In order to choose the quality level 
, the
monopolist invests the sum 
 (
) with 
(cid:48) (
) > 0, 
(cid:48)(cid:48) (
) > 0, 
 (0) = 0. For simplicity, I assume
a quadratic investment cost function, 
 (
) = 1
2
 
2, where 
 is the parameter of technological
progress in the search engine industry.

Figure A.1 and A.2 summarize key assumptions of the model and parameters affecting the

14

choice of price and quality by the search engine.

1.5 Benchmark: Monopoly in Quality Investments

Consider a situation when there is a monopoly in quality investments. In other words, there is
only one firm capable to innovate in this market. First, I will describe how the demand is formed
and then I will formulate the monopolist’s problem. Type 1 consumers will use the service of the
quality monopolist firm if


1
 − 
 ≥ 
 and 
 ≥ 

 
,

while type 
2 consumers will use the service of the quality monopolist firm if


2
 − 
 ≥ 
 and 
 ≥ 

 
.

Hence, the demand function faced by the monopolist is




 =







0

if 
2
 − 
 < 
 ≤ 
1
 − 
, 
 ≥ 

 

if 0 ≤ 
 ≤ 
2
 − 
, 
 ≥ 

 

if 0 ≤ 
 < 

 


.

Consider the indirect model first.
The indirect monopolist’s problem is

(cid:26)


 ( 
 + 
) − 1
2



2

(cid:27)

.


 
 = max
,


Notice, that for any 
 : 0 ≤ 
 < 

 
, the maximal profit is zero, 
 
 = 0. Hence, the
monopolist would choose 
 ≥ 

 
 only if it would result in a positive profit. Let me assume this
condition, 
 
 > 0, and later to check if it is true.

The monopolist’s problem is for a given level of quality to choose whether to charge the low
price and to attract both types of consumers or to charge the high price and to attract only type 1
consumers. And then to choose the optimal level of quality investment. This problem could be
reformulated in the following way

15

(cid:20)

(cid:26)

max
,



 
 = max

(cid:21)

(cid:20)

; max
,



 ( 
 + 
) − 1
2



2


 ( 
 + 
) − 1
2



2

(cid:21)(cid:27)

.

Given the demand and quality 
, the optimal price for the first argument of the above expression



 

 = 
1
 − 
,

while the optimal price for the second argument is



 
 
 = 
2
 − 
.

Substituting the optimal prices gives

(cid:26)

(cid:20)


 
 = max

max



 (
1
 − 
 + 
) − 1
2



2

(cid:21)

(cid:20)

; max



 (
2
 − 
 + 
) − 1
2



2

(cid:21)(cid:27)

.

In case when the indirect monopolist decides to charge the high price, the optimal quality choice

In case when the indirect monopolist decides to charge the low price, the optimal quality choice



 

 = 
1

.



 
 
 = 
2

.

is

is

is

Substituting quality choices into the objective function gives

(cid:32)(
2
)2 


2

− 
 


(cid:41)

.

(cid:33)
(cid:18)(
1
)2


+ 



2

1 ≡

(cid:19)

+ 

 and the

− 




 
 = max

− 



+ 

;

(cid:33)

(cid:40)(cid:32)(
1
)2 

(cid:18)(
2
)2


2

2

(cid:19)

− 
 


+ 

.

16

Denote the first argument of the above expression by 

 


2 ≡
second argument by 

 


Hence, the indirect monopolist’s choice of prices and qualities will depend on whether the first

or the second argument is greater. If the first argument is greater, then the optimal choice is



 
 = 
1

 
 − 
 and 

 
 = 
1

,

while if the second argument is greater, then the optimal choice is



 
 = 
2

 
 − 
 and 

 
 = 
2

.

I will make the following assumption implying that it is more profitable for the indirect monop-

olist to charge the low price.

Assumption 1 I assume the following:

(i) 

 

1 < 

 

(ii) (
2
)2


2 , i.e., (
1
)2

− 
 
 + 

 > 0.

2

2

− 

 + 

 < (
2
)2


2

− 
 
 + 

.

The second condition just states that the profit from creating the quality 

 
 = 
2

 is positive.
The first condition of the Assumption 1 is equivalent to the following condition

(cid:32)(
1
)2 


2

(cid:33)

(cid:32)(
2
)2 


2

(cid:33)

− 



−

− 
 


< 
 (
 − 
) .

This condition states that the indirect monopolist would prefer to charge the low price and to
produce the quality 

 
 = 
2

 if charging the high price and producing 

 
 = 
1

 adds less
direct profit than losing indirect revenue. Such a condition is more likely to be satisfied when type
2 consumers bring significant indirect revenues, 
 (
 − 
) and when it is costly to improve the
quality (
 is lower).

Under the Assumption 1 the indirect monopolist sets the following price and quality:



 
 = 
2

 
 − 
 and 

 
 = 
2

 ≥ 

 
.

17

I will make the following assumption which would allow for the model to predict the key stylized
fact in the search engine market that the search engines provide their services for free to consumers.

Assumption 2. 
2

 < 

 
.

Assumption 2 means that type 2 consumers’ willingness to pay for the quality is so low that it
would not be profitable to create the search engine for type 2 consumers in the absence of advertising
revenues that a search engine could earn from attracting type 2 consumers.

Under Assumptions 1 and 2, the indirect monopolist sets the following price and quality:



 
 = 0 and 

 
 = 

 
.

Consider the direct model.
The direct monopolist’s problem is identical to the indirect monopolist’s problem when 
 = 0.
Like in the indirect model, setting the quality level below minimally acceptable level, 0 ≤ 
 < 

 
,
results in a zero profit, 
 = 0,since consumers do not participate in the market.

Hence, again, I will assume that it is profitable to produce 
 ≥ 

 
 and later I will check if it

is true. Then, the direct monopolist’s problem is

(cid:26)

(cid:20)

(cid:21)

(cid:20)

; max
,



 
 − 1
2



2

(cid:21)(cid:27)

.


 = max

max
,




 − 1
2



2

For a given level of quality 
, if the direct monopolist chooses to sell its service only to type 1

consumers, it will set the high price




 = 
1
 − 
.

If the direct monopolist chooses to sell to both types of consumers, it will set the low price



 
 = 
2
 − 
.

Hence, the monopolist’s problem becomes

18

(cid:20)

(cid:26)

max



 = max

(cid:21)

(cid:20)

; max



 (
1
 − 
) − 1
2



2


 (
2
 − 
) − 1
2



2

(cid:21)(cid:27)

.

The optimal qualities for each of the arguments are




 = 
1

 and 

 
 = 
2

.

Substituting optimal qualities gives


 = max

Denote the first argument 


Consider the following assumption.

1 =

2

(cid:41)

.

− 

;

(
2
)2 


2

− 



(cid:40)(
1
)2 


2
(
1
)2


− 

, while the second argument 



2 =

(
2
)2


2

− 

.

Assumption 3 I assume the following:

(i) 


1 > 


(ii) (
1
)2


2

2 , i.e., (
1
)2

− 

 > 0.

2

− 

 > (
2
)2


2

− 
 
.

This assumption states that it is more profitable to charge the high price and produce the high
quality than to charge the low price and produce the low quality in the direct model. The second
part of Assumption 3 states that it is profitable to create the high quality.

When the Assumption 3 is satisfied, the direct monopolist chooses



 = 
1

 − 
 and 

 = 
1

 > 

 
.

The last inequality states that the direct monopolist’s quality is higher than the minimally

acceptable level and this inequality is guaranteed if the Assumption 3 is satisfied.
The analysis of this section could be summarized in the following proposition.

19

Proposition 1. Under Assumptions 1, 2, and 3, the indirectly financed search engine charges lower
price, 

 
 = 0, but produces also lower quality, 

 
 = 

 
, than the direct monopolist which
charges higher price 

 = 
1

 − 
 and produces the higher quality 

 = 
1

 ≥ 

 
.

The main intuition of Proposition 1 is related to the idea of the dilemma which type of
consumers to serve by the monopolist given that the monopolist could create only one service8.
Above proposition is illustrated in Figure A.2.

There are two types of demands for quality improvement: the high demand of type 1 consumers
and the low demand of type 2 consumers. Under Assumption 3, in the direct model the reward for
the monopolist is directly linked to the demand of type 1 consumers and, hence, the monopolist
chooses to supply the quality that would satisfy type 1 consumers’ demand resulting in the highest
profit. Supplying the quality level to satisfy the less willing to pay type 2 consumers reduces the
profit in the direct model.

In contrast, in the indirect model serving the type 2 consumers who have lower demand for
the quality improvement is a better option for the monopolist since such types bring significant
ad revenues and allow the monopolist to reduce the investment on quality improvements to the
minimally acceptable level. Raising the quality above the minimal level and charging higher
price would repel type 2 consumers and would lead to the loss of indirect revenue that could not be
compensated by the higher direct profit coming from type 1 consumers under Assumption 1. Hence,
the presence of significant indirect revenues related to type 2 consumers "breaks the link" between
the search engine producer’s incentives to improve the quality and type 1 consumer willingness to
pay for higher quality. Such a situation is especially harmful in the age of information overload
that naturally raises both the private demand of type 1 consumers for higher quality as well as the
public demand of the whole society for better functioning search engines.

8It is assumed that the monopolist could not second-degree price discriminate by creating two
services of basic and premium quality. In the discussion section of the paper, I consider an extended
model with spillovers. Quality spillovers could reasonably explain why each search engine produces
only one service in this market and captures the stylized fact, presented in the previous section, that
the quality spillovers were observed in this market.

20

1.6 Static Competition for Quality

Proposition 1 has shown that if there is only one firm in the market that is able to invest
in search engine quality improvement, then the indirect business model may represent a serious
obstacle for the quality improvement. In this section, am looking at the natural counter-argument
that competition would allow to overcome or even make the indirect model more attractive than the
direct model in terms of search engine quality improvement. Instead of just assuming the quality
competition in the indirect model or direct model, I would like to study under what conditions
such an intense competition would occur by modeling the entry decision in this market. For that
purpose, I am considering a simplest possible static, deterministic quality competition model where
at the first stage firms simultaneously choose whether to enter the market; at the second stage firms
simultaneously choose the quality of their services; at the third stage firms simultaneously choose
prices.

Consider the indirect model.
Let me solve the model by backward induction. Suppose that both firms have entered at the

first stage and their competition resulted in 
 
 > 

 for 
, 
 ∈ {1, 2} and 
 ࣔ 
.

I will assume that it is always optimal for the firm 
 = 1, 2 with superior quality to set the
low price such that all consumers are attracted to receive all possible advertising revenues in the
market9. The following assumption captures this idea.

Assumption 4. 
1(cid:0)
 
 − 

(cid:1) 
 + 

 < 
2(cid:0)
 
 − 

(cid:1) 
 + 

,

where firm 
 = 1, 2 represents the inferior quality firm and 
 ࣔ 
.
Moreover, to simplify the following analysis of quality competition, I will consider an extreme
assumption that type 2 consumers are not willing to pay for higher quality at all, although they
would choose higher quality search engine if all search engines are free.

9If Assumption 4 is not satisfied, then it would be possible to have an equilibrium of the whole
game under the indirect model where both firms enter with one firm creating a premium paid
service while the other firm creating a free service of minimally acceptable quality. I do not focus
on such an equilibrium since it does not satisfy an important stylized fact for the Internet search
engines market that historically paid Internet search engines never existed.

21

Assumption 5. 
2 = 0.

Assumption 5 simplifies10 considerably the analysis of the quality competition below since
under Assumption 4 and 5 the firm with superior quality sets zero price of its service independently
of its and rival’s qualities levels, 
1 and 
2.

Together, Assumptions 4 and 5 imply the following condition


1(cid:0)
 
 − 

(cid:1) 
 + 

 < 

.

Under Assumption 4 and Assumption 5, one can conclude that firms 1 and 2 set zero prices
and since firm 1 has higher quality, it wins all the indirect revenues while firm 2 gets zero indirect
revenue, i.e.,



 

1 = 

 


2 = 0, 

 


1 = 

, and 

 


2 = 0.

Consider now the second stage simultaneous quality choice. Firms choose quality levels to
maximize their profits. Consider the best response function for the quality choice of firm 
 to the
quality choice by the rival firm 
.




∗

 =



 



 + 

0

(cid:110)
(cid:110)

2
 
2(cid:111)


 > 

 
 : 

 > 1

 : 

 ≤ 1

2
 
2(cid:111)

.

if 

 = 0
if 

 =

if 

 =

The best response functions of quality choices do not intersect. It means that in this game there

are no pure strategy equilibria. The only possible equilibria are in mixed strategies.

Let me construct all mixed strategy equilibria. Suppose that firm 
 = 1, 2 plays a mixed strategy
represented by the cumulative density function 

 (
) defined on the support {0} ∪ [

 
, 
static]
10It should be emphasized that qualitatively the analysis will not change without Assumption 5.
To get the result that I obtain under Assumption 5 below it is sufficient to use just Assumption 3.
Assumption 3 guarantees that the only incentive to improve quality under indirect model is to steal
the advertising revenues of the rival and not to earn direct revenue from consumers.

22

where 
static represents a level of quality in a static model when the cost of quality improvement
completely exhausts all advertising revenue in the market, i.e.,

(cid:26)

(cid:27)


2

.

1
2



static =


 : 

 =

In order for firm 
 = 1, 2 to use a mixed strategy 

 (
) in equilibrium, it should be indifferent
between playing any pure strategy in the support of the mixed strategy 

 (
) when the rival firm
plays 

 (
) . In particular, suppose firm 
 ࣔ 
 plays a pure strategy 
 ∈ {0} ∪ [

 
, 
static], then
its expected profit (gross of sunk entry costs) from playing any quality ∀
 ∈ {0} ∪ [

 
, 
static]
given that the rival firm is playing 

 (
) is

(cid:20)

(cid:21)

(cid:18)

(cid:19)



 − 1
2



2

+ (1 − 

 (
)) ·

− 1
2



2

= 
 
,


 
 
 (
, 

 (
)) = 

 (
)

or



 (
) =

2
 
2


 
 + 1




.

Any cumulative probability distribution function should satisfy the conditions: 

 (0) = 0 and

(cid:16)


static(cid:17)





= 1. The first condition implies


 
 = 0.

(cid:16)


static(cid:17)2

0+ 1
2


Substituting 
 
 = 0 into the second condition gives
= 1 and using the definition
of 
static it is seen that the second condition is satisfied. Hence, a mixed strategy equilibrium was
constructed. Notice, that the obtained function 

 (
) is the only solution and it does not depend
on 
.Therefore, it was shown also that there is a unique Nash equilibrium with both 
 = 1, 2 playing
the following mixed strategy







(cid:16)

1
2
 
2



 
(cid:17)2

1



1
2


1




if 
 ∈(cid:104)



 
, 
static(cid:105)

if 
 = 0

,


 = 1, 2.

From the cumulative density function it is seen that If the cost function is convex, 
(cid:48)(cid:48) (
) > 0,
then the probability density function is always increasing on [

 
, 
static], which means that higher
quality values (closer to 
static) are more likely to be drawn than the lower quality levels.



 (
) = 
 (
) =

23

Based on the above analysis it can be concluded that if both firms enter, then firms will use
mixed strategies in the unique Nash equilibrium found above and will get the expected profit (gross
of entry costs) of zero.

In general, there are three equilibria in the entry stage game (see derivations in the Appendix):

1. A pure strategy equilibrium: firm 1 enters and firm 2 does not enter. Firm 1 produces the

minimal acceptable quality and sets zero price.

2. A pure strategy equilibrium: firm 2 enters and firm 1 does not enter. Firm 2 produces the

minimal acceptable quality and sets zero price.

3. A mixed strategy equilibrium: firm 1 enters with probability 1 − 




 , firm 2 enters with
probability 1 − 



 . If only one firm enters, then it sets the minimal acceptable quality and
zero price. If both firms enter, then the mixed strategy equilibrium in quality studied above
follows and firms set zero prices.

(cid:16)

(cid:17)2

The mixed strategy equilibrium predicts that entry by both firms may take place with probability
. The mixed strategy equilibrium should be considered with suspicion since it would

1 − 

disappear if the entry game is sequential or firms could coordinate their entry decisions.





Consider the direct model.
Suppose that both firms entered at the initial stage. The Assumption 5 and the assumption that
type 1 consumers are completely homogenous results in the winner takes all situation at the second
and third stages, unless the qualities are the same, but in that case static price competition results
in zero profits for the firms. Hence there are three possible equilibria at the second stage:
two
pure strategy equilibria when firm 
 = 1, 2 creates monopoly quality and sets the monopoly price
while firm 
 ࣔ 
 sets its quality at zero; a mixed strategy equilibrium when both firms create
monopoly levels with some probability and create zero quality with some probability. As before
whenever there are mixed and pure strategy equilibria, I select pure strategy equilibria to be the
prediction since mixed strategy equilibria could be ruled out either through sequential moves or
some coordination between the firms. Predicting this outcome, only one firm enters in the pure

24

strategy equilibrium (as in the indirect model, there is a possibility of the mixed strategy equilibrium
at the entry stage when both firms enter which could be, again, ruled out in a sequential entry game
or through the possibility of firm’s coordination). The key feature of the direct model is that despite
the winner takes all situation, the monopolist is direct and has an intrinsic incentive to improve
the quality in order to increase its profit. In particular, the entrant (for example, firm 1) sets the
following price and quality:

The entry is profitable if

1 = 
1

 − 
 and 






1 = 
1

.

(
1
)2 
 − 

 > 
.

Notice that the winner takes all situation in the direct model is the artifact of the homogenous type
1 consumers assumption. In particular, if the vertically differentiated preferences are introduced
within type 1 consumers, like in Shaked and Sutton (1983), then it is easy to get the natural
oligopoly situation or the presence in the market of a line of products with different price quality
ratios satisfying heterogenous preferences/incomes of consumers.

In contrast, the winner takes all situation in the indirect model is preserved when the hetero-
geneity in the type 1 consumers preferences is introduced, so the inability to relax competition
through vertical differentiation is the robust feature of the indirect model. Moreover, in the indi-
rect model the winner is the indirect monopolist suffering from the imperfection identified in the
Proposition 1 of no intrinsic motivation to invest in quality improvements since all consumers are
already captured while the price could not be raised from the zero level without significant losses
in advertising revenues.

Proposition 2. In a simple static quality competition model (simultaneous entry choice, simultane-
ous qualities choice, simultaneous prices choice) under the indirect model, in equilibrium only one
firm enters and produces minimally acceptable quality 

 
. In the hypothetical subgame where

25

both firms enter a significant (expected) quality improvement happens but the expected profits
(gross of entry costs) are zero. In contrast, under the direct model in equilibrium a higher than the
minimally acceptable quality 



1 = 
1

 > 

 
 is created.

The key idea of Proposition 2 is that in a situation when firms are choosing their quality once
(for example when search engines commit to the long-term research programs), the competition
between equally capable of quality improvement rivals could lead to the significant expected
quality investments motivated by the desire to win all ad revenues in the market. Even though
such a competition is ideal for consumers (since they get free and high-quality search engines in
expectation), it is too far from ideal for firms who expect net losses since the firms could not cover
the entry costs and hence firms prefer to avoid such a competition for quality in the first place.

1.7 Dynamic Competition for Quality

In this subsection, I relax the assumption of the static or one-shot quality competition while
preserving the assumption that firms by investing some resources could always improve the quality
of their search engines above the quality of the rival search engine. I ask how the dynamic nature of
interaction could affect the entry in this market and incentives to improve the quality of the search
engines.

As before, I assume that there are two symmetric in terms of innovation capabilities firms
2
 
2 defined on [0,+∞] . All firms are
having the quality improvement cost function 
 (
) = 1
assumed to have a common discount factor 
 ∈ (0, 1) . The game consists of the infinite number of
periods 
 = 1, 2, .. At the initial period, 
 = 1, two potential entrants simultaneously decide whether
to enter by investing 
 > 0, which represents the entry cost. The next each period (
 = 2, 3..)
consists of the following sequence of choices:

1. If only one firm entered at 
 = 1, then it chooses its quality level. If both firms entered at 
 = 1,
then if the period is 
 = 2 , 2 + 
, 2 + 2
, .., then firm 1, without loss of generality, chooses its

26

quality first and firm 2, observing the quality of firm 1, chooses its quality second11, 12. 
 is
the time required to innovate, or the necessary time for the investment in quality to result in
the quality improvement. At any other periods, 
 ࣔ 2 , 2+ 
, 2+ 2
, .., firms do not make any
quality improvement choices.

2. If both firms entered, then observing the qualities, they simultaneously set prices every period


 = 2, 3..

3. Consumers choose which service to buy, and all payoffs are realized for the period 
.

As will be seen shortly, there are two qualitatively different possibilities: either both firms enter,
or only one firm enters. Which situation will occur depends on the per period discount factor 
 and
the time required to innovate 
.
Consider the indirect model.
I maintain the Assumptions 4 and 5 in this section which state that type 2 consumers bring
significant enough ad revenues that the superior quality search engine producer would setting zero
price and attracting both groups of consumers.

Consider two possible types of equilibria depending on the per period discount factor 
 and the

time required to innovate 
.

An indirect model equilibrium when (
) 
 ≥ 1
2 .

Suppose that the firms are using the following strategies:
11In the dynamic model, I use sequential quality choice by firms as opposed to simultaneous
considered in the previous section only to make the model tractable. In the Appendix, I present a
dynamic model where firms make simultaneous quality choices, and I get the qualitatively same
result. The difference is that in that case when firms deviate from the collusive outcome, they
randomize the level of quality improvement investments.

12In this basic version of the dynamic game I assume that there are no any side payments and
in particular licensing is impossible. In the Appendix, I consider an extended version of the game
where firm 1, after investing in quality and before firm 2 has invested in its quality, can make a take
it or leave it offer to transfer the technology at the optimal for firm 1 price.

27

Both firms enter in the initial period 
 = 1. At the second period 
 = 2, both firms create
minimal acceptable quality level, i.e., 
 

=2 = 

 
 to attract all consumers at the zero price for the
service. Then, firm 1, at the further investment periods 
 = 2 + 
, 2 + 2
, .., chooses

if 
2
−
 = 

 


if 
2
−
 ∈(cid:16)



 
, 
dyn(cid:17)

.

if 
2
−
 ≥ 
dyn



 



dyn


1
−



1
 =

where 
dyn, by analogy with the static model, represents the quality level such that the in-
vestments required to produce this quality completely exhaust all the present value of advertising
revenues, i.e.,

(cid:26)

(cid:27)

.
Firm 2, at the investment periods 
 = 2 + 
, 2 + 2
, .., chooses


dyn =


 :




1 − 


− 1
2



2 = 0






2
 =

(cid:26)



 


1
 + 


dyn


2
−


if 
1
 = 

 

if 
1
 ∈ (

 
, 




)
if 
1
 ∈ [




, 
dyn)
if 
1
 ≥ 
dyn

,

where 




 is the quality level for which the 
-period gain of all advertising revenue is completely

exhausted through the investments required to create 




, i.e.,

(cid:16)

1 + 
 + .. + (
) 
−1(cid:17) − 1

(cid:27)


2 = 0

.

2







 =


 : 



At all periods 
 = 2, 3, .. both firms ( 
 = 1, 2) set zero price for consumers


 

 = 0.

The above-specified strategy profile constitutes a subgame perfect Nash equilibrium in which
both firms produce the minimally acceptable quality 

 
 and set zero prices for consumers if the
following conditions hold (see the proof in the Appendix):

28

(cid:16)

1 + 
 + .. (
) 
−1(cid:17) ⇔ (
) 
 ≥ 1

2

.





1−
 ≥ 


1−
 − 
 ≥ 0





 1

2
1
2

The first condition represents a condition under when there is no incentive to deviate from
producing collusive minimally acceptable level of quality, 

 
. The second condition states that it
is profitable to enter the market by both firms.

An indirect model equilibrium when (
) 
 < 1
2 .

In this case, the unique subgame perfect Nash equilibrium is that only one firm (firm 1) enters at
the initial period 
 = 1 and creates the minimally acceptable level of quality 

 
 since it becomes
the indirect monopolist.
In this equilibrium Firm 2 never enters since it fears fully exhaustive
competition for quality resulting in zero profits gross of entry costs and negative profits net of entry
costs.

Notice that the reason why only one firm enters is the same as in the static model: firms predict

too intense quality competition at the second stage when the entry costs could not be covered.

To summarize, the above-specified strategies constitute a subgame perfect Nash equilibrium

(see the proof in the Appendix) if the following conditions hold:

(cid:16)

1 + 
 + .. (
) 
−1(cid:17) ⇔ (
) 
 < 1

2

.

 1

2
1
2





1−
 ≥ 


1−
 − 
 ≥ 0





The first equation states that if both firms enter, then each firm has a temptation to start
competition for quality. The second condition states that if firms could collude by producing the
minimally acceptable quality, then the entry would have been profitable by both firms.

Consider the direct model.

A direct model equilibrium when 
 ≥ 1
2

Suppose that 
 ≥ 1

2 and firms are using the following strategies.

29

At the initial period 
 = 1, both firms enter. At the second period 
 = 2 each firm chooses the

following quality






 

 
 =

1
2


1

,

where 




 

 
 stands for cooperative quality under no licensing possibility.
Then, each firm chooses the following price




=2 = 




 

 
 = 
1




 

 
 − 
 =

(
1)2 

 − 
.

1
2

In later periods 
 = 3, 4.. firms maintain prices at the second-period price level 


=2, and in the
further investment periods, 
 = 2 + 
, 2 + 2
, .., firms maintain their qualities at the second-period
quality level 




 

 
, if no deviation happened in the past. If a deviation has occurred, then
firms play a static Nash equilibrium (given the current quality levels) in this period and in all future
periods, which means that firms set prices equal to marginal costs (zero) and do not invest in quality
improvements anymore.

These strategies constitute a subgame perfect Nash equilibrium of the dynamic game (see the

proof in the Appendix).

To summarize, the conditions under which both firms enter and produce quality 




 

 
, and

set prices to 




 

 
, are


1




 

 
 − 


where: 


 
 = 

2

is the one period profit flow (gross of entry and quality
investment costs). The first condition states that if both firms enter, then it is profitable for both to
cooperate on qualities and prices. The second condition states that expecting cooperation on price
both firms enter find it profitable to enter.

A direct model equilibrium when 
 < 1
2

30

 1

2
1
2

(cid:17)

(cid:16)






 
(cid:17)2 − 
 ≥ 0

1−
 ≥ 


 
 ⇔ 
 ≥ 1



 

2
1−
 − 1



2


(cid:16)

,

Suppose that 
 < 1

2 and firms are using the following strategies. Firm 1 enters at 
 = 1 and

creates at the 
 = 2 the following quality and sets in all periods 
 > 1 the following prices



 = 
1

 and 

 = 
1
 − 
 = (
1)2 

 − 
.

Firm 2 does not enter.

Such a strategy profile is the unique subgame perfect Nash equilibrium13 of the dynamic game
since the entry of both firms leads to the full profit dissipation that does not allow covering the
entry investments.

To summarize, the conditions for only one firm entry in the direct model are:

1−
 < 

 ⇔ 
 < 1



2
2
1−
 − 1



 

2







 

 
(cid:17)2 − 
 ≥ 0

(cid:16)

 1

.

The first condition states if firms enter and invest to create the quality 




 

 
, then each
firm will have an incentive to undercut the price of the rival resulting in the static Nash equilibrium
(given the quality 




 

 
) when both firms set prices equal to the marginal costs (which are
normalized to zero). The second condition states that if firms were able to cooperate on prices and
qualities, then it would have been profitable to enter by both firms.

This section’s main conclusions are summarized in the following proposition.

Proposition 3. In an infinite horizon dynamic quality competition model with indirect financing
where prices are set every period and investments in quality are made every 
 periods if 

 ≥ 1
2, then
there exists a subgame perfect Nash equilibrium where both firms enter and collude on producing
the minimally acceptable level of quality 

 
. Such an equilibrium is Pareto superior from the
13Since I assume that firm 1 has a first-mover advantage at the quality investment stages, then
there is a unique equilibrium of the whole game in this case. If firms moved simultaneously at all
stages, then there would be a standard situation that there are two pure strategy equilibria when
either firm 1 or firm 2 enters and a mixed strategy equilibrium when each firm enters with some
probability. As before, mixed strategy equilibria could be ruled out either through the sequential
entry or through the coordinated entry.

31

If 

 < 1

2, then only one firm enters and creates
firms’ perspective to any other equilibrium.
minimally acceptable quality 

 
. In contrast, in the direct model without licensing, if 
 ≥ 1
2,
both firms enter and each produces the cooperative quality 




 

 
 = 1
2 
1

 > 

 
, while if
there is cost sharing, then firms jointly produce the cooperative quality 




 

 = 
1

 > 

 
.
Such an equilibrium is Pareto superior from the firms perspective to any other equilibrium.
If

 < 1

2, then only one firm enters and produces 

 = 
1

 > 

 
.

The main lesson of Proposition 3 is that the lack of cooperative incentive to improve the
quality identified in Proposition 1 could be realized in practice in a dynamic setting under certain
conditions. Dynamic model allows identifying conditions under which collusion on lower quality
is more probable to occur. Besides per period discount factor, a crucial factor is the time required
to make innovation, that is measured by 
 (Alternatively, 
 could be interpreted as the degree of
commitment to the research plan). If the time required to innovate is quite long, then it is impossible
to sustain collusion on quality, and the dynamic model is equivalent to the static model studied
in the previous section. On the other hand, if the time required to innovate is short, then firms
could easily relax quality competition through collusion on lower quality allowing both firms to
enter. The distinction between these two situations could be important from the policy perspective.
In particular, if the time required to innovate is quite long, then one possible policy could be to
subsidize the entry cost 
 such that both firms entry would result in a significant quality improving
competition. On the other hand, such a policy of subsidizing entry costs may be unproductive when
the time required to innovate is short since additional firms would end up colluding on quality.

Notice that, in contrast to the indirect model, in the direct model cooperation on prices and
qualities does not depend on the time required to innovate and depends only on the degree of
patience per period measured by 
. Hence, the direct model predicts a higher probability of several
firms entry since prices could be adjusted quicker that quality investments. Moreover, cooperation
on prices creates significant incentives to invest in quality improvement since such an improvement
increases permanently the profit flows in the industry. Even if firms are not sufficiently patient to
cooperate on prices and qualities, then only one firm enters the market, and such a firm becomes

32

the direct monopolist producing higher-quality search engines.

1.8 Discussion

1.8.1 Welfare Analysis

Search engine market welfare analysis

In this section, I will revisit the Section 5 analysis of the innovator monopolist search engine in-
centives for quality improvements from the normative perspective. I will derive total and consumer
welfare comparisons between the indirect model and the direct model. Since there is a positive
outside option value of 
 for all consumers, I will calculate the welfare without deducting the value
of the outside option value 
, i.e., I will make welfare calculation gross of outside value 
.

Under Assumption 1 and Assumption 2 the total welfare in the market for the search engine

consumers under the indirect model with a monopolist innovator firm is



 
 




 = 

1

 
 + (
 − 
) 
2

 
 − 1
2


.

(cid:16)



 
(cid:17)2


 
(cid:17)2

.

Since, by assumption, 
2

 
 = 
, I get



 
 




 = 

1

 
 + (
 − 
) 
 − 1
2


(cid:16)

Since the price for consumers in the search engine market is zero under Assumption 2, the

consumer welfare in the market for the search engine for consumers is



 
 




 = 

1

 
 + (
 − 
) 
2

 
.

Since, by assumption, 
2

 
 = 
, then and I get



 
 




 = 

1

 
 + (
 − 
) 
.

Notice that the consumer welfare for type 2 consumers is the same as the outside option value,

, while the consumer welfare for type 1 consumers is 
1

 
 > 
 . The latter improvement for the

33

type 1 consumers is due to the simplifying assumption that 
 is common to both types, 
 = 
2

 

. If the outside option value would be type specific in the following natural way, 

 = 



 
 for

 = 1, 2, then the consumer welfare under the indirect model would be identical to the outside option
value which is anyway available to consumers.

Consider the direct model.
Analogous calculations give the following total welfare for the direct model



 




 = 

1

 + (
 − 
) 
 − 1
2


Substituting 

 = 
1

 results in

(cid:16)



(cid:17)2

.



 




 =

(
1
)2 


2

+ (
 − 
) 
.

Since the price is 

 = 
1

 − 
 = (
1)2 

 − 
, the consumer welfare under the direct model

is



 




 = 

.

Summarizing the above calculations it is seen that the total welfare of the direct model is greater

than the total welfare of the indirect model if

(cid:16)



(cid:17)2

(cid:16)



 
(cid:17)2

> 

1

 
 − 1
2




1

 − 1
2


This condition is always satisfied if 

 ࣔ 

 
 since the left-hand side of the equation is equal
to the direct monopolist’s profit function, and the direct monopolist chooses to create the quality


 since it maximizes its profit and hence the left-hand side of the above inequality. On the other
hand, the consumer welfare is higher in the indirect model due to the simplifying assumption that
the outside option value is common to both types of consumers and equals to 
 = 
2

 
. If the
outside values were naturally defined as 

 = 



 
 for 
 = 1, 2, then the consumer welfare in both
models would have been the same.

34

Also, notice that the fact that consumer welfare equals the outside option value, 

, in the
direct model is the result of the simplifying assumption that type 1 consumers are all the same,
which allows the monopolist to extract all consumer value above the outside option value. The
introduction of the type 1 consumer heterogeneity could make the consumer surplus higher under
the direct model than under the indirect model but it will also introduce some standard deadweight
loss associated with underproduction of the service when the price is above the marginal costs.

Welfare analysis of the whole economy

As I mentioned before search engines play an essential role as the infrastructure of the New or
Information economy affecting both online and offline world. Hence a proper welfare analysis of
the search engines quality should take into account the externalities (either good or bad) on all other
markets and activities which use search engines as the inputs. The simplest possible extension of
the baseline model that could capture such a feedback effect is the following.

Let 
 is composite Hicksian good that represents all markets and activities in the economy
I normalize the price of the composite Hicksian good to 1.
except the search engine market.
Search engine market is represented by the search engine service quantity consumed, 


 , and
each consumer has a unit demand for search engines, i.e. 


 ∈ {0, 1} . Let 

 (
) represents
the income of consumer 
 = 1, 2 generated in other markets than the search engine market per
se. A consumer of type 
 = 1, 2 has quasi-linear preferences and hence maximizes the following
quasi-linear utility function

(cid:110)

(cid:110)

(cid:111) + 



(cid:111)

,

max
∈{0,1},

≥0








subject to the budget constraint

max












, 









 + 

 = 

 {
} ,

where 

 (
) is the type 
 = 1, 2 consumer income and 
 is, as before, the value of the outside
option if consumers decide not to use any search engines and which is common to all consumers
(for simplicity).

35

I assume that the consumer 
 = 1, 2’s income is increasing in the quality of the search engine,


(cid:48)

 {
} > 0.

Substituting the budget constraint into the utility function gives

(cid:110)

(cid:110)

(cid:111) − 






 + 

 {
}(cid:111)

.

max
∈{0,1},

≥0








max












, 


This simple model demonstrates that the quality of the search engine affects consumer utility
not only in the search engine market per se, but also through a positive (or negative) externality
that better (or worse) search engines create for the economy as a whole. The information overload
concept captures both effects of higher quality on the search engine market per se as well the effect
that search engine quality generates for the rest of the economy. Next, I will calculate the total and
consumer welfare of the search engine quality for the whole economy.

Consider the indirect model.
The total welfare for the whole economy under the indirect model of search engines is

(cid:20)

(cid:104)



 
 









 =



1

 
 + (
 − 
) 
 − 1
2




 
 









 =



1

 
 + (
 − 
) 


The consumer welfare for the whole economy under the indirect model of search engines is



 
(cid:111)(cid:105)

.



1



1



 
(cid:111) + (
 − 
) 
2
(cid:110)


 
(cid:111)(cid:105)
(cid:110)

+(cid:104)
(cid:110)


 
(cid:111) + (
 − 
) 
2
(cid:110)



 
(cid:17)2(cid:21)
(cid:16)
(cid:105) +(cid:104)
(cid:35)
(cid:111) + [

1 {
1

} + (
 − 
) 
2 {
1

}] .

.

Consider the direct model.
The total welfare for the whole economy under the direct model of search engines is
+ [

1 {
1

} + (
 − 
) 
2 {
1

}] .

+ (
 − 
) 









 =



 


The consumer welfare for the whole economy under the direct model of search engines is

(cid:34)(
1
)2 

(cid:110)(
1
)2 
 + (
 − 
) 


2



 









 =

Hence, I can calculate the total welfare difference for the indirect model as compared to the

direct model in the following way

36



 
 









 − 

 









 =

(cid:20)(cid:20)
+(cid:104)



1

 
 − 1
2


(cid:8)

 
(cid:9) − 
1 {
1

}(cid:17) + (
 − 
)(cid:16)



1

 − 1
2


−

(cid:16)





1

(cid:16)



 
(cid:17)2(cid:21)

(cid:20)

(cid:16)



(cid:17)2(cid:21)(cid:21)
(cid:8)

 
(cid:9) − 
2 {
1

}(cid:17)(cid:105)

+


2

.

The first term in squared brackets is negative for 

 ࣔ 

 
 (since 

 maximizes the expression
2
 (
)2) and it measures the loss from using the indirect model in the search engine market


1
 − 1
per se. If 

 > 

 
, then the second term is negative and it measures the loss resulting from the
indirect model for the rest of the economy’s markets and activities. Hence there is an additional
total welfare loss for the economy as a whole from using the indirect model.

Hence, the welfare analysis of the indirect versus direct model of the search engine market

could be summarized as follows.

Proposition 4. Under the assumptions of Section 5 (innovator monopolist), the total welfare
under the indirectly financed search engine market considered in isolation from the other markets
is lower than the total welfare under the direct model.
In a model with homogenous type 1
consumers, consumer welfare is higher under the indirect model if the outside option values are
the same and equal to 
1 = 
2 = 
2

 
. If the outside options values are different and equal to

1 = 
1

 
; 
2 = 
2

 
, then the consumer welfare equals to the value of the outside option, 

,
in both direct and indirect models but the total welfare is higher under the direct model. Taking
into account the effect of the search engine quality on other markets and activities results in an
additional welfare loss (both total and consumer) under the indirect model as compared to the
direct model.

1.8.2 Explanation for the One Product Assumption

One crucial possible explanation why the innovator monopolist may decide not to introduce the
paid higher quality version in addition to the basic version (of a minimally acceptable quality) under
the indirect model is that there is an inferior alternative search engine producer in the market which

37

is not able to innovate but can absorb the spillovers from the innovator’s quality. As a result, the
creation by the innovator monopolist of a premium higher quality service would allow the inferior
alternative search engine to improve its quality even higher than the quality of the innovator’s basic
service if the innovator would not adjust the quality of the basic service accordingly. However,
such an adjustment (which will be an increase) in the basic service quality provided for free for
consumers would reduce the profits of the premium quality sector and could make it not profitable
to create such a premium service in the first place.

In contrast, under the direct model, the entry into the inferior alternative sector may not be a
profitable project. The reason is that in the direct model there are no ad revenues and the only
source of income comes from charging consumers directly. However, some consumers, who were
happy to participate in the search engine market when the price of the search engines was zero, may
not participate in the market when the price is positive. As a result, in the direct model the market
size shrinks and in case if firms do not cooperate on prices, then only one firm could profitably
enter. If firms could cooperate on prices, then several firms may enter. However, notice, in both
cases spillovers do not reduce the incentive to improve the quality. In the static model case, only
one firm enters and, hence, there is no inferior alternative that would absorb the spillover. In the
dynamic model, any spillovers are fully internalized though cooperative price setting. Moreover,
if there is vertical differentiation for type 1 consumers, then a natural oligopoly could easily be the
outcome when several firms enter and create a line of search engines with different price-quality
options.

Let me demonstrate this idea for the static model by extending the baseline model a little
bit. Since the inferior alternative firm is not able to create the quality above the level of the
innovator monopolist firm, then the only possibility for the inferior alternative firm to get some
profit is through horizontal differentiation. Hence, I will assume for simplicity14 that some type
2 consumers value an additional feature Ò that is not present in the innovator firm’s service and
which is present in the inferior alternative firm’s service. I will refer to such consumers as type 2
14I assume that all type 1 consumers do not value such an additional feature, which could easily

be relaxed without loss of generality.

38

loyal consumers and there are 
 (
 − 
) of them. The willingness to pay of type 2 loyal consumers
for such an additional feature is 
 ≡ 
2Ò. Other consumers do not value the additional feature Ò
at all. Hence, the consumer surplus of type 2 loyal consumers from using the inferior alternative
alternative search engine with a feature Ò is 

2,
 (
 
) = 
2 (

 
 + Ò) − 

 
, where 

 
, 

 

are the price and quality set by the inferior alternative search engine. Other consumers (type 2
non-loyal consumers and type 1 consumers) have the same consumer surplus as in the baseline
model. I will make the following assumption.

Assumption 6. 


 
 + Ò > 

 


Assumption 6 states that type 2 loyal consumers think that the overall quality is higher than the

minimally acceptable quality created by the innovator monopolist firm.

I will consider an entry game between the innovator monopolist search engine and an inferior
alternative search engine. The entry for the innovator monopolist costs 
, while the entry cost for
the inferior alternative firm is 

 
. The entry choice happens simultaneously. If both firms enter,
then the innovator firm chooses the quality level 
, while the inferior alternative firm automatically
absorbs the spillovers from the innovator firm and creates the quality 

 
 ≡ 

. For simplicity, I
will assume that "absorbing" the spillovers is free for the inferior alternative firm, while creating
the quality by the innovator costs 
 (
) = 1

2
 
2. Finally, at the third stage, firms set the prices.

Consider the indirect model. Under Assumptions 1 (stating that the innovator monopolist would
prefer to set its price and quality such that both types of consumers are attracted) and Assumption
2 (stating that the innovator monopolist creates minimally acceptable quality at the zero price for
consumers) hold and if both firms enter, then at the third stage, the price set by both firms is zero,
and the (vertical) quality is at the minimally acceptable level



 
 = 0, 

 



 
 = 0, 

 
 = 

 
, and 

 



 
 = 


 
,

where 

 
, 

 
 denote the price and quality set by the innovator monopolist, while 

 


 


, 

 


 

are the price and quality set by the inferior alternative firm. Notice, that type 1 and type 2 consumers

39

would never use inferior alternative search engine since in their view its quality is below the outside
option quality of 

 
. In contrast, under Assumption 6, type 2 loyal consumers value the additional
feature Ò enough to prefer the inferior alternative search engine to the innovator monopolist’s search
engine of the minimally acceptable quality 

 
.

Hence, in equilibrium, both firms enter if

 
 
 = 
 (
 + (1 − 
) (
 − 
)) − 
 − 1


 
 = 

 (
 − 
) − 

 
 > 0

 


2


(cid:16)



 
(cid:17)2

> 0

.

Consider now a situation when the monopolist innovator decides to introduce a higher quality
premium search engine with quality 

 and price 
 
, in addition to the basic service with quality

 and price 
. I am assuming that the introduction of the premium service with the higher quality,


 > 
, is profitable for the innovator monopolist, and then I will present the conditions on parameter
values when this assumption is correct and when not.

In order for the innovator monopolist not to lose the basic free service market to the inferior
alternative firm (with the quality 

 
 = 


), the following constraint should be satisfied for the
basic service

The problem of the innovator monopolist is


 ≥ 

 
 = 


 and 
 ≥ 

 
.

(cid:26)



1(cid:0)

 − 
(cid:1) + 
 (
 + (1 − 
) (
 − 
)) − 
 − 1


 


 = max

,


It is seen that the above constraint should hold with an equality (
 = 

 
 = 


) in order to
maximize the profit in the premium sector. Hence, the profit function of the innovator monopolist
could be rewritten as


 = max





1 (1 − 
) 

 + 
 (
 + (1 − 
) (
 − 
)) − 
 − 1
2


The optimal qualities are

(cid:0)

(cid:1)2(cid:27)

.

2


(cid:0)

(cid:1)2(cid:27)

.

(cid:26)
 
1
 (1 − 
) 
, if 
1
 (1 − 
) 
 > 

 




 
, if 
1
 (1 − 
) 
 < 

 


40



 =

and 
 = 

 
 .

Hence, it is seen that the quality of the premium service negatively depends on the degree of
the partial spillover 
. For a relatively high spillover 
 and especially if it is too costly (
 is low)
to create the premium service, it may be optimal not to create the premium service at all and just to
enter with the minimally acceptable quality level 

 
 to attract most of the consumers with a free
basic service.

Assumption 7. 
1
 (1 − 
) 
 < 

 
.

Assumption 6 states that if the degree of spillovers is high enough, then it is not profitable to
create a separate premium paid service, so it is profitable to create just one free service with the
minimally acceptable quality.

Consider the direct model. Under Assumption 5 (stating that type 2 consumers are not willing
to pay for the search engines at all, i.e. 
2 = 0) if both firms enter, then they will charge the
following prices:



 = 
1 (1 − 
) 
, and 




 
 = 0.

As a result, firms get the profits


 = 
1 (1 − 
) 
 − 1
2



2 − 
, and 



 
 = −

 
.

Therefore, it is seen that it is never profitable to enter by the inferior alternative firm in the direct

model market and only the innovator monopolist enters and sets the price and quality

and gets the profit



 = 
1

 and 

 = 
1




 =

(
1
)2 


2

− 
.

This subsection is summarized in the following proposition.

Proposition 5. Under Assumptions 5, 6, and 7 in the indirect model with quality spillovers, both an
innovator monopolist and an inferior alternative firm enter the market; indirect monopolist avoids
creating a premium paid service and provides only a free basic service of the minimally acceptable

41

quality 

 
. In contrast, under the direct model, only the innovator monopolist enters15 and creates
much higher than the minimally acceptable quality, 

 = 
1

 > 

 
.

1.9 Summary and Conclusions

The development of the Internet and other information technologies lead to significant infor-
mation accumulation. That has created a natural demand for higher quality search engines. In this
paper, I suggest the currently ubiquitously used advertising based (or indirect) model to finance
search engines could pose an important obstacle in the search engines incentives to supply the
quality of the search engines fully satisfying the demand by many consumers and society as whole.
To establish this result, I compare indirect with the direct model of search engine financing. I find
that the indirect monopolist has a relatively low incentive to improve the quality. The intuition
is that once all consumers are attracted, further quality improvements could not be monetized.
For example, suppose the indirect monopolist increases the quality above the minimum acceptable
level and decides to charge higher (positive) price to consumers. In this case, a significant part of
consumers whose willingness to pay is low will prefer not to participate in the market by choosing
the outside option (such as using inferior free search engines or traditional sources of information
such as TV, radio etc). Hence, the increase in the direct revenue may not be able to compensate the
decrease in the indirect revenue under realistic parameter values. Hence, it can be concluded that
the indirect model of search engine financing creates an obstacle to quality improvement incentives
if the search engine becomes a monopolist in innovation activities.

After showing that a combination of the monopoly in innovation activities and indirect model
of search engine financing leads to insufficient incentives to improve the search engines quality, I
turn to the question will competition lead to higher quality, and more importantly, will competition
happen in this market in the first place? In order to answer these questions, I considered a three-
15Again, the fact that only one innovator enters is due to the simplification that type 1 consumers
are homogeneous. In practice, due to vertical differentiation of type 1 consumers like in Shaked
and Sutton (1983), several innovator firms may enter providing search engines with different
quality-price characteristics satisfying different groups of type 1 consumers.

42

stage model where at the first stage firms simultaneously choose whether to enter the market, at the
second stage simultaneously choose the level of quality and at the final stage choose prices. I find
that in the indirect model if both firms enter, then a significant quality competition happens. But, in
such a subgame the expected profits are completely dissipated, which means that in a pure strategy
equilibrium only of the firm would enter this market and, hence, the actual quality competition
would never happen in practice.

Despite the interesting insight obtained in the static model, it neglects potentially important
dynamic aspects of quality competition. Moreover, an important measure of competition as the
number of active firms in the market could have a very different interpretation when dynamic
aspects are introduced. In particular the one-shot or static model would characterize well quality
competition where the nature of technology is such that firms need to commit to long-term research
directions when the choice is made once and it affects profitability over relatively long period of
time. Hence, I consider a dynamic competition framework that generalizes the static model for the
case when the time required for innovation is relatively long. In contrast, if the time for innovation is
relatively short, several firms may enter and successfully collude by producing minimally acceptable
quality. The parameter measuring the time required to innovate is an important policy indicator.
If it could be identified that the search engine market is characterized more by long-term quality
competition with a significant time required to innovate, then an important policy tool could be
the subsidization of the entry costs for the innovative rivals. In contrast, such a subsidization may
be useless if the nature of quality competition is dynamic and, hence, allows entering firms to
collude on quality with the incumbent. In contrast, the direct model predicts significant incentive
to improve the quality independent of the time required for innovation and the number of entered
firms since quality improvements permanently increase the industry profit flows.

In the section devoted to welfare analysis I point out that the proper welfare analysis of the
search engine market should not only consider the search engine market per se, but also to take
into account the positive (or negative) externality that a higher (or lower) quality search engines
create for all the markets in the economy. It is this externality underlies the motivational idea of

43

the information overload in this market. I find that the direct model predicts higher total welfare
both for the search engine market per se as well as the economy as a whole. Consumer welfare
comparison of the direct and indirect model depends on the assumptions regarding the value of the
outside option, the degree of consumer heterogeneity as well as the strength of the externality of the
higher quality search engines to other markets. In particular, if the strength of the latter externality
is high enough, then the consumer welfare could be higher under the direct model than under the
indirect model.

Finally, since the key result of the paper depends on the assumption of the one service search
engine I give an explanation for this assumption. Moreover, the proposed explanation is justified by
the anecdotal evidence and stylized facts in this market. In particular, I suggest that the introduction
of the quality spillovers (or "search results scraping") to the inferior alternative rival gives a
compelling explanation for the one product phenomenon. I find that under the indirect model in
the presence of the significant but partial spillovers it is profitable for the inferior alternative firm
to enter with the hope to attract some loyal consumers through a minor horizontal differentiation
and spillovers absorption. Such an entry significantly reduces the profitability of introducing a
premium paid service in addition to the basic free service since the premium higher quality service
reveals higher quality search results to the rivals who could use it in the main basic market to steal
significant advertising revenues. In contrast under the direct model, spillovers do not play such
a role since either the inferior alternative firm does not have enough differentiation to enter the
market profitably or since the entering firms could cooperate on prices internalizing spillovers

In my view, the current search engine market is characterized as either quality innovation
monopoly situation or collusion in quality innovation activities that prevents the quality improve-
ments in the interests of society. Hence, the incentives to create premium paid search engines
should be improved in the interest of society. If the reality is characterized by the monopoly in
innovation activities situation, then in the indirect model a quality spillover from the premium
to the basic segment reduces the incentive for the R&D capable firm to invest in the premium
segment. In this case, under the indirect model improving intellectual property protection which

44

would reduce the quality spillovers (or scraping), would incentivize the creation of the premium
paid services segment. On the other hand, if the reality is characterized by the presence of several
capable to innovate firms (potential or actual) and the reason that they do not invest much in quality
improvement is that either there is a winner takes all situation in a static framework or collusion in
quality in the dynamic framework, then another approach may help. One way to avoid the winner
takes all situation is to introduce the price floor in the premium segment. Such a price floor will
guarantee that the entrant in the premium segment will not have the ability (even though it will have
an incentive) to steal the ad business of the incumbent by lowering the price of its higher quality
service to zero which would induce significant retaliatory quality improvements by the incumbent,
the expectation of which would deter entry. In the cooperation/collusion context, a premium service
price floor would help (especially in the absence of side payments) since the premium segment firm
may have much lower profits (at least initially) due to the significant costs of quality improvement
and hence there are significant incentives to deviate by lowering its price and attracting the basic
segment consumers. Price floor would allow establishing a premium segment where firms may
cooperate on price and investments (including licensing of innovations) to improve the premium
segment quality to the demanded by the society level.

Another possible policy is to consider under the indirect model is subsidization of entry that
would promote the static competition. Since the static competition represents commitments to long-
term research directions, the funding of fundamental research related to search engines algorithms
may induce quality competition in this sector despite its dissipative nature. The main risk to this
policy strategy is related to the dynamic interactions that maybe inherent to the quality improvement
technology in this market and that may induce quality collusion wasting any government subsidies
to promote entry in this market.

In my view, the best way this market to be organized is to make search engines using the
direct model. It does not mean that the advertising should be banned. It means, though, that the
search engine function and advertising functions should be served by the independent entities. In
this case, the consumer will pay directly to the search engine producer for the service and may

45

choose whether to participate in the advertising platform by sharing its search history and providing
attention. In case a person agrees to participate, then she receives the price for purchasing her
information and her attention while using the search engine. An alternative scenario would be
replicating the iPhone and Android industry conditions where the owner of iPhone, Apple, does not
have access to significant advertising revenues as the owner of the Android, Google, and, hence,
Apple has to use the direct model creating significant innovation incentives, while Google, having
access to significant advertising revenues, makes its product much cheaper or more accessible.

46

CHAPTER 2

STRATEGIC CONTROL AND EXCLUSIVITY

2.1 Introduction

What if competing two-sided platforms do not take as given the regime of control over content
pricing (outright sale or affiliation), but strategically choose over content control? What is the
motivation for a strategic choice of the control regime for platforms and content providers? Will
platforms and content providers be able to maximize their joint industry profit under different
conditions? Do equilibria exist in this case, and what kind of equilibria will we observe in the
market? Will we observe exclusive equilibria or not? Will we observe outright sale or affiliation
types of content control? What will determine certain types of equilibria? Who will benefit and
lose from strategic interaction over control? Those are the motivating questions.

The focus of the paper is on software industries such as video games and media broadcasting
which are characterized by severe competition between two-sided platforms. In those industries, an
important weapon in competition is the ability to attract content exclusively as well as, potentially,
to set the regime of control over content. The reason is that one of the main ways to vertically
differentiate for platforms is to have exclusive content. On the other hand, the allocation of control
rights over content between a platform and content providers determines the net consumer surplus
from content that, again, determines the degree of attractiveness of the platform for consumers.

This paper extends Hagiu and Lee (2011) by asking what if the regime of control, outright sale

or affiliation, is strategically chosen as opposed to exogenously given.

As a first pass, the paper considers a model with homogeneous preferences over content which
corresponds to the Example 3 in Hagiu and Lee (2011) as well as several simplifying assumptions
discussed in the section describing the extended model. This simple specification facilitates
extension while at the same time gives the baseline answer to the posed questions. It also could
serve as a benchmark for further generalizations of the framework for arbitrary content preferences.

47

The main results of Hagiu and Lee (2011) are replicated, and it is demonstrated that the industry
profit is higher under affiliation multihoming regime. Then, equilibria of Hagiu and Lee (2011)
are derived in their framework: under outright sale regime there is a unique exclusive equilibrium
for any level of content valuation; under affiliation regime, for any level of content valuation
there are multiple equilibria (unique exclusive and multiple multihoming), and if platforms could
coordinate (selection criterion applies), then all content provider’s profits from content are extracted.
This establishes the conflict of interests concerning control regime between platforms and content
providers which motivates Hagiu and Lee’s (2011) conjecture for the possibility of strategic choice
over control to achieve the maximum industry profit. The goal of this paper is to formalize this
idea and to explore its implications.

The key findings of the paper are the following.
First, for low and medium values of content (that does not induce consumer tipping for exclusive
outright sale) platforms will never choose outright sale regime of control in equilibrium in contrast
to the model with exogenous control regimes1. The explanation is that platforms will always have an
incentive to deviate from the outright sale exclusive option to the affiliation exclusive option since it
allows platforms to soften their competition for content and to transfer less of their surplus to content
providers. Plus, such a deviation creates enough resources to be profitable for both the deviating
platform and content providers. Moreover, in this case, there are multiple affiliation equilibria
(multiple exclusive and multiple multihoming), and multihoming gives higher industry profit than
exclusivity. If platforms could coordinate (selection criterion applies), then affiliation multihoming
equilibrium which maximizes industry profit is the outcome such that platforms extract all content
providers profits.

Second, for the case of high valuation content (that could potentially lead to the consumer tipping
in favor of one of the platforms if signed exclusively with one of the platforms under outright sale
1Notice, Hagiu and Lee (2011) in their Corollary 3 show that (but for the case of strategic
content provider) that second stage profits of both platforms are higher under exclusive affiliation
than in exclusive outright sale which could motivate platforms to avoid vertical integration into
content and spin off content into affiliation regime. In this paper, it is shown that it is actually an
equilibrium outcome.

48

regime) the following results are obtained. There are two types of equilibria: exclusive outright
sale and multihoming affiliation. However, multihoming affiliation creates higher industry profit,
and if platforms could coordinate (again, if the selection criterion applies), then they could always
choose a multihoming content allocation. An interesting implication of endogenous control regime
choice is that now content providers with the high valuation, even in the case when platforms could
coordinate on equilibria that are best for platforms and worst for content providers, get a significant
share of industry profit. Moreover, this share increases as content valuation increases. The main
reason is that if platforms extract too much profit from content providers in multihoming affiliation,
then each platform has an incentive to propose an exclusive outright sale contract that content
providers will accept since content providers have too low profit in multihoming affiliation. This
result is very different as compared to exogenous control regime model where the inability to choose
control regime plays the role of a commitment device allowing platforms (when coordinated) to
extract all content profits independent of how high is the content valuation.

Third, if platforms could not coordinate (and, thus, selection criterion does not apply), then
there are additional (as compared to the basic model with exogenous control regimes) equilibria
due to possible pessimistic expectations of platforms regarding the behavior of content providers.
In particular, any platform would always prefer (whenever it does not participate in the bidding for
content) content provider to switch to exclusive affiliation option from the rival, rather than exclusive
outright sale option. The reason is that outright sale option creates higher vertical differentiation
between the platforms and, thus, makes platform competition for content more severe and results
in higher platforms profits transfer to content providers. Thus, in those pessimistic platforms’
expectations equilibria content providers can extract additional (as compared to the basic model)
profits from platforms. Those additional affiliation equilibria appear for any level of content
valuation and, thus, there are equilibria where content providers extract not only all content profit
but also profits from selling platforms. Nevertheless, ability by platforms to coordinate (selection
criterion applies) allows them to avoid such pessimistic platforms expectations.

These findings are summarized in Figure B.1. It allows a comparison of the basic model of

49

Hagiu and Lee (2011) with exogenous content control sets of equilibria and those of the extended
model with endogenous control over content.

Currently, most literature on two-sided markets is related to the analysis of platform pricing
decisions in order to get all sides on board. The benchmark articles that have formalized two-sided
markets models are Rochet-Tirole (2003, 2006) and Armstrong (2006). The key aspect of two-sided
markets is the presence of indirect network effects between the sides that platforms should take into
account when they choose prices such that to bring all sides on board. On the other hand, those
articles do not consider the possibility of exclusive contracts and, thus, implicitly assume that there
is a commitment by the competing platforms for setting price only non-exclusively.

Choi (2010) considers exclusive content in two-sided markets, but exclusivity is exogenous; it
is exclusive because it is technologically impossible or too costly to encode such content on the
other platform and not because of an exclusive contract. In this case, each platform has exclusive
content that makes natural for some consumers to multihome in order to get access to all exclusive
content.

The role of exclusive contracts in two-sided markets was analyzed (to the author’s knowledge)
in two articles. First, Armstrong and Wright (2007) extend a basic model of Armstrong (2006)
to allow platforms to propose exclusive contracts and finds that such exclusive contracts could
undermine competitive bottleneck equilibria (where sellers multihome and buyers singlehome),
and such exclusivity is beneficial for sellers and adverse for buyers. The second article, Hagiu
and Lee (2011), and which is extended in this paper, entirely focuses on exclusive contracts (and
control) in two-sided markets and addresses the question of how control regime over content (that is
given exogenously) affects exclusivity. Two articles use quite different modeling strategies, where
Armstrong and Wright (2007) considers more general formulation while Hagiu and Lee (2011)
fine-tune the model to reflect software platform industries features. Despite this, a similar result to
Armstrong and Wright (2007) is found in Hagiu and Lee (2011) where multihoming (or competitive
bottleneck) equilibrium is undermined but only for outright sale regime. In contrast, the affiliation
regime is characterized by multiple equilibria (unique exclusive and multiple multihoming) and

50

given platforms could coordinate multihoming regime is always chosen as it brings higher industry
profit.

The research on control regimes of content in multi-sided platforms is emerging. Hagiu (2007)
analyzes the distinction between "merchant" mode (buying from seller and reselling to buyer or
"outright sale regime" in this paper) and "two-sided platform mode" (enabling affiliated sellers to
sell directly to affiliated buyers or "affiliation regime" in this paper) but in a monopoly framework
and takes those regimes as exogenously given to compare advantages and disadvantages of both
regimes under different scenarios (whether chicken-and-egg problem is severe or not, whether
degree of complementarity between seller’s products is high or not, whether there are incentives to
invest in seller’s product quality and whether there is asymmetric information regarding the seller’s
product quality). Hence, while Hagiu (2007) does not deal with platform competition issues, it
gives additional motivations for the role of control regimes and, thus, as Hagiu and Lee (2011) point
out, the focus of there and this paper specifically on the control over content pricing should not be
viewed as the only source of difference in the surplus of consumers under the two regimes. In other
words, their model (as well as this paper) could be in principle extended to account for additional
incentives related to transferring control over content to content providers such as incentives to
invest in content quality, sales efforts, etc. and not only on the control over content pricing.

Other few examples of non-price decisions analysis in two-sided markets include Hagiu and
Wright (2014) who study the choice of intermediation mode (marketplace or reseller) depending
on the trade-offs related to allocation of rights over non-contractible decisions between sellers
and platforms; Hagiu and Jullien (2010) who analyze incentives to divert search by information
intermediaries that enable buyers to search for affiliated sellers.

The main finding of this paper that platforms have an incentive to give control over content
prices to content providers reminds the result of Bonanno and Vickers (1988) showing that vertical
separation between manufacturer and retailer segments may relax price competition, leading to
higher profits that manufacturers could extract from the retailers.

Section 2 describes the game that includes timing, consumer preferences, content providers

51

and selection criterion used. Section 3 replicates the Hagiu and Lee’s (2011) results for the case
of exogenous control regimes in order to motivate incentives to choose control regime. Section
4 introduces the extended model and solves it. Section 5 concludes and discusses some business
strategy implications of the obtained results.

2.2 Model

There are two competing two-sided platforms A and B who interact with consumers and content

providers (denoted by C).

Let us call the model of Hagiu and Lee (2011) as the basic model and the model proposed here

as the extended model.

The timing2 of events is the same for the basic model and the extended model: first platforms
determine conditions of interactions and bid for content, then observing those bids, content providers
decide which platform to join (or join both or none), after that platforms and content providers (if
they have control) set platform and content prices3 and, finally, consumers decide which platform
to participate in observing the prices of platforms, content allocation between the platforms and
prices of content. The main difference between the basic model and extended model lies in what
conditions of interaction with content providers can be chosen by the platforms in the first stage
and what conditions platforms consider as given exogenously. Those differences are determined
below in detail. We proceed by backward induction.

2.2.1 Consumer Participation Decisions

It is assumed that platforms are horizontally differentiated for consumers and not for content
providers.

2The sequential timing of the game reflects a common situation in the software industries where
commitment to deliver content in advance helps to solve chicken and egg problem, see Hagiu
(2006) who focuses on the role of commitment in two-sided markets.

3As a first pass, the focus is on non-strategic content providers who do not internalize their price
decision on the demand for platforms. That assumption could be justified in case of small content
providers.

52

Consumers with a horizontal taste parameter 
 distributed uniformly over [0, 1] with a total
number of consumers equal to one. Consumers experience horizontal differentiation cost of 

 if
they participate in platform A and (1 − 
) 
 if they participate in platform B; platforms A and B are
situated at 0 and 1 points of this interval, respectively. Also, there is a platform stand alone value 

derived by consumers and which is common for all consumers. It is assumed that both platforms,
A and B, have the same stand alone value (platforms are symmetric) and it is high enough such that
the whole market of consumers is covered.

In addition to common stand alone value, consumers derive a common surplus value 
 ( 
) from
the membership of each additional content provider, where 
 is the price of content. There are 

content providers. In order to participate in a platform A, consumers have to pay participation (or
access) price 

 and 

 - for platform B.

Consumers’ utilities from platform A and B are:


 
 = 
 + 


 ( 
 
) − 

 − 





 = 
 + 


 ( 

) − (1 − 
) 
 − 



Thus, each consumer compares utilities from A and B in order to make a participation decision
in A or B4 Then, the demand for platform A and B will be determined by the number of types

below and above the following marginal type (cid:98)
 : 
 
 = 



(cid:98)
 =

+ 


 ( 
 
) − 


 ( 

) − 

 + 



2


1
2

and demands for platform A and B that account for both the case of no tipping and case of a

tipping in favor of one of the platforms are:

4It is assumed that platforms stand alone value perfectly substitute each other. Thus consumers
have only unit demand for standalone value. Horizontal differentiation parameter may capture
some first party content that is valued differently by different consumers.

53



0(cid:98)


1


 
 =

2 + 


( 
 
)−


( 

)−

+


2 + 


( 
 
)−


( 

)−

+



2 + 


( 
 
)−


( 

)−

+



, if 1
,if 0 < 1
, if 1

< 0

> 1

2


2


2


< 1


 
 = 1 − 
 


2.2.2 Platforms’ and Content Providers’ Consumer Pricing Decisions

Given allocation of content between platforms and conditions of that allocation (control over content
pricing and whether content is exclusive or not) platforms and content providers (if they have control
over content prices) maximize their profits subject to the anticipated demand of consumers. Without
loss of generality marginal costs of platforms and content providers are set to zero.

In case when control over content prices belongs to platforms (it is called an outright sale regime

of control), platforms maximize the sum of the profits from platforms and content as follows:


 = 





,
 


{
 
 · (

 + 


 ( 
 
))} 5

where 
 ( 
 
) = 
 

 ( 
 
) is the profit from one piece of content and 
 ( 
 
) is the demand
for content. The same problem is for platform B. It is shown in Lemma 1 in Appendix that it is
optimal in general for platform A (and B) to set content price equal to the marginal cost, i.e. 
 
 = 0
( 

 = 0). The intuition is that it is more profitable to increase the vertical quality of the platform
by providing more surplus from content to consumers and then to extract it through higher platform
access prices.

In case when control over content belongs to content providers (it is called affiliation control

regime), platform A (and B) chooses only the price of access and the platform’s problem is

5Notice, that throughout the paper the consumer demand is assumed to take the same form for
every content and content is independent (no substitutability or complementarity between different
contents), then every content will have the same price and consumers will consume the same amount

 
 (
) 

 ( 
 
 (
)) 

 =

of each content, then profits from content from one consumer areÞ 


Þ 




 

 ( 
 
) 

 = 

 
 

 ( 
 
)

0

0

54

Content provider C’s problem is


 = max




{
 


}

(cid:110)



 ( 

)(cid:111)


 = max



where 
 ( 

) = 
 ( 

) 

 and 
 is the demand by consumers for the platform where C sells
its content. Notice, that the bar (over 
) indicated that C takes platform demand as given, assuming
that C is relatively small6. So 
 could be omitted in the C’s problem in this case.

2.2.3 Platforms’ and Content Providers’ Strategic Choice of Control and Exclusivity

Here the first stage of players interaction is described. The main difference between Hagiu and Lee
(2011) and this paper is emphasized.

2.2.3.1 Basic Model

In the basic model, it is assumed that some conditions of interactions are given exogenous, while
others are determined through a bidding game. The basic model considers the regime of control
over content as given exogenously. That regime of control could take two forms: outright sale or
affiliation. Outright sale control regime means that content provider transfers control rights over
pricing (and cash flows from content) to platforms. Affiliation control regime means that content
providers retain control over content pricing (and corresponding cash flows from content sales).
Thus, in the basic model (where those regimes are not chosen but taken as given) the analysis is
done separately for two regimes of control.

As mentioned above still in the basic model platforms may choose the following conditions of
interaction: whether content provider joins the platform exclusively or multihome by conditioning
6Hagiu and Lee (2011) call this case a non-strategic content provider and relax this assumption by
analyzing the implications of one strategic content provider and show that results could significantly
change in this case. This possibility under considered extension is left for future research.

55

price of access to the platform on exclusivity/multihoming. Therefore, in the basic model platforms
compete (it is called a bidding game) for the content by making simultaneously take-it-or-leave-it
bids for content conditional on whether content joins the platform exclusively or not.

2.2.3.2 Extended model

In this paper, it is considered that platforms could also choose control regime during the bidding
game in addition to exclusivity and, therefore, condition their bids on both dimensions (i.e., strategic
control and exclusivity).

Extension of the model was motivated by the observation of Hagiu and Lee (2011) that there
is a conflict of interests in the basic model, where platforms would prefer affiliation regime, while
content providers would prefer the outright sale. Moreover, most important, that the sum of industry
profits is higher under affiliation regime, Thus, participants could potentially engage in strategic
bidding to choose the regime with the highest industry profit. This conjecture is formally studied
in this paper by extending the first stage bidding game to condition platform bids over content not
only on exclusivity but also on the regime of control.

In order to motivate incentives for the strategic choice of control the outcome of the basic
model game is considered based on the simple example 3 from Hagiu and Lee (2011), and then
equilibrium for the extended model is studied using the same example 3.

2.2.4 Content Providers’ Coordination and Equilibrium Selection Criterion

In order to solve the basic model as in Hagiu and Lee (2011) it is assumed that content providers
could coordinate on most efficient outcome from their joint perspective at the stage of the game
where they make decisions to join the platforms. This is a "strong equilibrium refinement" (Aumann,
1959) and it allows to deal with potential multiplicity of Nash equilibria at the stage of content
providers participation decisions by focusing on equilibria that are coalitionally stable among

56

content providers7.

For the purpose of making a clean comparison this paper follows Hagiu and Lee (2011)
approach to select equilibria when there are multiple equilibria. The approach is the following:
it is assumed that industry participants (platforms and content providers) could always coordinate
on the equilibrium that has maximum industry profit. If there are multiple equilibria that generate
maximum industry profit, then it is assumed that platforms are able to select equilibria that are best
for platforms and worst for content providers.

2.3 Benchmark Results

Consider the simplest possible setting in order to derive basic intuition how the introduction of

the possibility of strategic choice over control will shape the interaction in the market.

Such a simple setting corresponds to Example 3 in Hagiu and Lee (2011), where the valuation
of content by consumers 
 is the same across consumers and consumers want to buy at most one
unit of each content. Therefore, content provider that has control over content pricing is able to
extract all consumer surplus (
 = 0) by setting content price equal to the valuation of content by
consumers (

 = 
). Therefore, under affiliation regime the content market is characterized by



 = 
, 
 = 
, 
 = 0

Under outright sale regime the content market is characterized by



 = 0, 
 = 0, 
 = 


7As noted in Hagiu and Lee (2011), it is not an objective of current framework to build a
general model of multilateral bargaining with externalities that are explored in Segal (1999), Segal
and Whinston (2003), de Fontenay and Gans (2007). Potential inefficiencies generated in stage 1
bargaining game are sensitive to assumptions governing agent beliefs, the transfer space, and the
extensive form of the game; this paper abstracts from such frictions as a first pass. Incorporation
of such frictions could be an interesting as well as challenging direction for future research. Prat
and Rustichini (2003) and Bloch and Jackson (2007) provide conditions under which the industry
efficient outcome will result in different bargaining games.

57

As discussed in previous section in general under outright sale platforms have incentive sell
content for free (or at a marginal cost) and, thus, to attract more consumers and earn profit by
raising platform access prices to consumers8.

Also, for simplicity of calculations and exposition let us consider that the number of content

available is one (
 = 1) and horizontal differentiation parameter is one (
 = 1).

2.3.1 What Are the Incentives to Choose Control?

As defined before, the game consists of two major stages. In the first stage the allocation of content
providers between platforms happens on different possible conditions of interactions related to
control and exclusivity. In the second stage, platforms compete in access prices for consumers and
content prices are set either by platforms or content providers depending on the control regime. Let
us proceed by backward induction.

There are two possible allocations of content in both regimes of content control: all content

multihoming or all content is exclusive with one platform9.

Each control regime is given exogenously and considered separately below.

2.3.1.1 Outright Sale

It is shown in the Appendix that the second stage profits of platforms are10


 (0) =

1
2

8In this particular example, total welfare from content is independent of content price and, thus,
only the sum of content price and platform access price matters (see Lemma 1 and its proof in the
Appendix). Thus, the content price could always be normalized to be equal zero and then to adjust
accordingly platform access price.

9This is proved in Hagiu and Lee (2011) in their Proposition 1 under the assumption of the
bidding game considered here as well as equilibrium refinement used. It means that the allocation of
content that maximizes industry profit (subject to second stage price competition between content
providers and platforms) is always an equilibrium outcome.

10Notice, there are no second stage profits of content providers as they do not have control over

content pricing and cash flows.

58


 (1) = 


(cid:16)

; 
 − 1

(cid:16)

(cid:17)2

1 + 

3
2

 .11
(cid:17)2


 is defined to take the value of first argument if 
 < 3

1 − 

3
2


 (−1) = 
 {
 < 3} ·
(cid:17)2

1+ 

3
2

; 
 − 1

(cid:16)



where 
 (Ɗ
) is the second stage platform profit given that this platform has Ɗ
 more content

than the rival12. Function 

(no consumer tipping) and the second argument otherwise (consumer tipping).Function 
 {
 < 3}
takes the value 1 if 
 < 3 (no consumer tipping)and zero otherwise (consumer tipping).

The following table shows total industry profits for outright sale control regime in case of

multihoming and exclusivity.

As seen from Table 1 industry profit is always higher under exclusivity as compared to mul-
tihoming. The reason is, on the one hand, is that under outright sale exclusivity creates strong
vertical differentiation advantage for platform A as compared to platform B and, thus, platforms
industry itself becomes more profitable. On the other hand, under multihoming platforms that have
control over both content prices and platform access prices are tempted to undercut each other in
both content prices and platform prices resulting to transferring all surplus from new content to
consumers.

Next, given that the outcome of the second stage game is known, the first stage bidding game

over content allocation is analyzed, and the equilibria of the whole game are characterized.

Potentially, there are two types of equilibria in the outright sale regime: exclusivity and

multihoming. The conditions for them to occur are considered below.

11This formulation allows for competitive tipping. By competitive tipping it is meant a situation
where because of quality advantage through exclusivity one platforms attracts all consumers, but
is not able to set monopoly price as there is a competitive pressure from the potential entrant (so
called competitive finge). Analysis of monoply tipping could be an interesting direction for future
research. Demand for platforms can be used to show that there is no tipping for 
 < 3.
12Thus, in this particular example where N=1, Ɗ
 = 0 means multihoming; Ɗ
 = 1 - exclusivity
in favor of the platform (A); Ɗ
 = −1 exclusivity in favor of the rival platform (B).

59

In the following analysis it is assumed a tie breaking rule in favor of the platform A, i.e., when
content provider is indifferent whether to sign the exclusive contract with the platform A or B, the
choice is A.

Exclusive outright sale equilibrium analysis in the basic model
In order for exclusive (with
A against B) equilibrium under outright sale regime to occur in the basic model, no player in the
bidding game should have an incentive to deviate.

Content providers no deviation conditions13:

Participation condition for C


 ≥ 0

 
1

Incentive compatibility conditions for C


 ≥ 
 
1

 
1


 + 
 
1





 ≥ 
 
1

 
1




(2.1)

(2.2)

(2.3)

where 
 
1


 is the bid of the platform A (superscript 
 means exclusivity condition, 
 - multi-
homing, 1 - outright sale, 2 (used later) - affiliation). Condition 2.1 is the participation condition
for C. Condition 2.2 - incentive compatibility condition for C to prefer exclusivity with A than
multihoming with both A and B. Condition 2.3 - incentive compatibility to stay exclusive with A
rather than with B.

Platform A’s no deviation (participation) condition:
13All no deviation conditions are classified into participation conditions and incentive compati-
bility conditions. Participation conditions for platforms reflect whether platform signs any contract
(exclusive or not) and for content providers - whether they participate in the bidding game. Given
a player participates, incentive compatibility conditions determine which control and exclusivity
option are preferred.

60

Platform B’s no deviation ((non-) participation) condition:

; 
 − 1


 ≥ 
 {
 < 3} ·

(cid:17)2

(cid:16)

1 + 

3
2







 {
 < 3} ·

(cid:16)

1 − 

3
2

 − 
 
1
(cid:17)2


≥ 


(cid:16)

(cid:16)

1 − 

3
2

(cid:17)2
 − 
 
1




(cid:17)2

1 + 

3
2

; 
 − 1

(2.4)

(2.5)

(cid:26)2

(cid:27)

Notice, we only need to consider deviations by platforms that induce content providers to switch
to another platform under exclusivity and do not need to consider deviations that induce multihoming
as one platform cannot unilaterally induce multihoming in general (it is always possible to consider

 → −∞ or small enough and it is realized in such
exclusive equilibria under assumption that 
 

an equilibrium).

Conditions 2.3,2.4,2.5 imply:


 
1

 = 
 
1


 = max


; 
 − 1

,

3
which constitute equilibrium bids together with 
 
1



 → −∞).

 

Hence, there is a unique equilibrium allocation of industry profits between platforms and content


 such that 2.2 is satisfied (for example,

, 
 
1

providers under exclusive outright sale regime.

In this case exclusive agreement allows to vertically differentiate one platform and increase
second stage industry profit, but all this additional profit and even more goes to C as a result of
severe competition between platforms to get C exclusively in the first stage.

Multihoming outright sale equilibrium analysis in the basic model Consider no deviation
conditions for content providers:

Participation condition for C

61


 + 
 
1

 
1


 ≥ 0

Incentive compatibility conditions for C


 + 
 
1

 
1


 ≥ 
 
1





 + 
 
1

 
1


 ≥ 
 
1




(2.6)

(2.7)

(2.8)

where 2.6 is a participation condition for C, while 2.7,2.8 state that there is no incentive for C

to deviate to exclusive contracts either with A or with B.

For platform A:

where 2.9 is platform A’s participation condition in bidding for C, while 2.10 states that A has

no incentive to attract C on the exclusive terms.

For platform B the constraints are analogous to A:

(2.9)

(2.10)

(2.11)

Participation condition for A

− 
 
1


 ≥ 
 {
 < 3} ·

1
2

Incentive compatibility condition for A

− 
 
1


 ≥ 


1
2

1 + 

3
2

, 
 − 1

(cid:17)2

(cid:16)



(cid:16)

(cid:16)

(cid:17)2

1 − 

3
2

 − 
 
1




(cid:17)2

1 − 

3
2

Participation condition for B

− 
 
1


 ≥ 
 {
 < 3} ·

1
2

62

Incentive compatibility condition for B

(cid:17)2

1 + 

3
2

, 
 − 1

(cid:17)2

1 + 

3
2

(cid:16)



(cid:17)2

1 + 

3
2

, 
 − 1

(cid:16)



(cid:16)






 − 
 
1
 − 1
 − 1

2

2

+ 
 
1

 ,

(2.12)

(2.13)

− 
 
1


 ≥ 


1
2

Notice, that 2.7 and 2.10 imply:

which holds if and only if


 ≥ max

 
1


 + 
 
1

 
1


 ≥ 
 
1


 ≥ max

, 
 − 1

But 2.11 and 2.13 cannot hold at the same time - a contradiction (We can do similar comparisons
of analogues conditions for C and platform B (2.8 and 2.12) and to achieve a contradiction by
comparing those with 2.9). Thus, there is no outright sale multihoming equilibrium in the basic
model.

Here the situation is similar to the prisoners’ dilemma where platforms are two prisoners: if
they could cooperate and not attract C exclusively, then they could have earned more (each platform
earns 1
2) than if they deviate, which results in outright sale equilibrium described in the previous
section (where each platform earns 
 {
 < 3} ·

(cid:17)2

(cid:16)

2 , ∀
 > 0).
< 1

1− 

3
2

2.3.1.2 Affiliation

As shown in the Appendix under affiliation platforms’ second stage profits are:


 (0) =


 (1) =

1
2

1
2

63

Second stage profits of content providers:


 (−1) =

1
2


 (0) = 
.14


 (1) =

.15



2

where 
 (Ɗ
) is the second stage content provider C’s profit given that this content provider
sells content for the platform that has Ɗ
 more content than the rival platform (Ɗ
 = 0 means
multihoming, Ɗ
 = 1 means exclusivity).

Notice, that the second stage profit of a platform in affiliation regime is 1

2 and does not depend
on whether the content is exclusive or not. This is a result of the combination of homogeneous
content valuation extreme assumption (which means that content providers could extract all surplus
from consumers) as well as C has control over content pricing. This will no longer be true in a
more general setting.

Again, the combination of the assumption of affiliation regime and homogenous content valua-
tion (full extraction of content surplus) leads to a situation where consumers tipping is impossible
under exclusive affiliation.

The following table shows second stage industry profits under affiliation in case of multihoming

and exclusivity.

It is seen from Table 2 that industry profit is always higher under multihoming affiliation as
compared to exclusive affiliation. The reason is that, on the one hand, multihoming allows content to
be sold to all consumers and, on the other hand, despite exclusivity, effectively due to homogenous
14This profit is 
 

 ( 

) + 
 

 ( 

) which for the homogeneous content valuations gives
(
 
 + 
 
) 
 = 

15This profit is 
 

 ( 

) and under the assumption of homogeneous content valuation 
 
 = 1
2
and 
 ( 

) .

64

valuation of content preferences platform A does not gain any vertical differentiation advantage
over platform B and, thus, does not create any additional platforms market profits.

Next, the first stage bidding game is analyzed in the basic model under affiliation. First, the

existence of the exclusive type of equilibrium is checked and, then - multihoming type.

Exclusive affiliation equilibrium analysis in the basic model No player should have an incentive
to deviate.

Content providers:

Participation condition for C


 + 


 
2
2

≥ 0

Incentive compatibility condition for C


 + 


 
2
2

≥ 
 
2


 + 
 
2


 + 


Platform A:

Platform B:


 + 


 
2
2

≥ 
 
2


 + 

2

Participation condition for A

1
2

− 
 
2


 ≥ 1
2

(Non-) Participation condition for B

65

(2.14)

(2.15)

(2.16)

(2.17)

All conditions are analogues to the outright sale case analyzed above, but the profits numbers

1
2

≥ 1
2

− 
 
2




(2.18)

are different due change of control regime to affiliation.

Notice, 2.16,2.17 and 2.18 imply


 = 
 
2

 
2


 = 0

and all conditions are satisfied for small enough 
 


 .
Hence, there is a unique equilibrium allocation of industry profits under the case of exclusivity

for affiliation control regime.

The situation here is different from the outright sale in the following way. Notice, that platforms’
competition become softer when affiliation is allowed, and there is a homogenous valuation of
content (content providers could extract all consumer surplus from content). The latter condition is
important as it leads to no vertical differentiation effect between platforms from exclusivity. This
allows platforms not to pay anything to content providers even though one of the platforms obtains
content exclusively. On the other hand, exclusivity still allows content providers to earn profits only
from selling content to the consumers of the exclusive platform and this profit is not extracted by
the platforms due to competition for exclusivity.

Multihoming affiliation equilibrium analysis in the basic model Again, no player should have
an incentive to deviate:

For content providers:

Participation condition for C


 + 
 
2

 
2


 + 
 ≥ 0

(2.19)

Incentive compatibility condition for C

66


 + 
 
2

 
2


 + 
 ≥ 
 
2


 + 

2


 + 
 
2

 
2


 + 
 ≥ 
 
2


 + 

2

For platform A:

For platform B:

Participation condition for A

1
2

− 
 
2


 ≥ 1
2

Incentive compatibility condition for A

1
2

− 
 
2


 ≥ 1
2

− 
 
2




Participation condition for B

1
2

− 
 
2


 ≥ 1
2

Incentive compatibility condition for B

1
2

− 
 
2


 ≥ 1
2

− 
 
2




(2.20)

(2.21)

(2.22)

(2.23)

(2.24)

(2.25)

Let us focus on symmetric equilibria where both platforms make the same multihoming bids


 = 
 
2

 
2




67

Participation condition for platforms 2.22 and 2.24 determine the upper bound on the multi-

homing bids


 
2

 = 
 
2


 ≤ 0

While participation condition for content providers 2.19 gives a lower bound on multihoming

bids:


 = 
 
2

 
2


 ≥ − 

2

Now let us check whether incentive compatibility conditions for C (2.20 and 2.21) and for

platforms (2.23 and 2.25) are satisfied.

As easily seen from incentive compatibility conditions for platforms (2.23 and 2.25), a deviation
does not change platform second period profits, and, thus, setting deviation bids (for exclusivity)
equal to the equilibrium bids (multihoming)


 
2

 = 
 
2


 = 
 
2


 = 
 
2




will always satisfy those conditions. On the other hand incentive compatibility conditions for
content providers (2.20 and 2.21) are satisfied, which could be shown by substitution of the above
values into those conditions.

Hence, there are multiple multihoming equilibria allocations of industry profit between plat-

forms and content providers with

− 

2

≤ 
 
2


 = 
 
2


 ≤ 0

As discussed in the previous section this paper follows Hagiu and Lee (2011) and uses an
equilibrium selection criterion stating that in case of multihoming platforms could coordinate on
the best for them (and the worst for content providers) equilibrium allocation, i.e.


 
2

 = 
 
2


 = − 

2

Notice, that in this case all profits from content are extracted from C by the platforms.

68

This section analysis is summarized in the following propositions:

(cid:17)2

(cid:16)

1− 

3
2

(Hagiu and Lee (2011)).

(Hagiu and Lee (2011)).

and content providers’ total profit is max(cid:8)2 


Proposition 1.
In the basic model with homogeneous consumer
preferences for content, industry profit is always higher under affiliation than under outright sale
(see Tables B.1 and B.2 ).
Proposition 2.
In the basic model with homogeneous consumer
preferences for content, under outright sale regime there is a unique exclusive equilibrium where
platforms’ total profit is 2· 
 {
 < 3}·
Under the affiliation regime, there are multiple equilibria with highest industry profit coming from
multihoming (see Table B.2). Under the equilibrium selection criterion that first picks the highest
industry profit equilibrium and then chooses the one that is the best for platforms (and worst for
content providers), platforms’ total profit is 1 + 
 while content providers’ total profit is 0.
Proposition 3.
(Hagiu and Lee (2011)). According to Proposition 1 and 2 in the basic model with
homogeneous consumer preferences for content, there is a conflict of interests regarding control
regime between content providers and platforms: platforms would prefer affiliation regime that
gives maximum possible industry profit of 1 + 
, while content providers would prefer the outright
sale regime that generates less industry profit of 


3 , 
 − 1(cid:9).

, 
 − 1

.

(cid:26)

1 +(cid:16) 


3

(cid:17)2

(cid:27)

2.4 Extended Model

As previous section shows that in a simple example with homogenous content preferences there
is a conflict of interests between platforms and content providers regarding the choice of the control
regime and there is a conjecture by Hagiu and Lee (2011) that the regime that maximizes industry
profit will be chosen. This section extends the basic model by introducing strategic choice of
content control where platforms determine both control and exclusivity conditions in the bidding
game16.

16It should be noted that if the parties could jointly sign a multilateral agreement, then it is
pretty evident that maximal industry profit would be realized. However, this section considers a
more realistic setting where there is no such a possibility (for example because of the possibility of
antitrust sanctions or constantly changing economic environment where new content is constantly

69

As the second stage of the game is the same in both basic and extended model, this section
focuses on the extended model first stage bidding game and characterizes equilibria for the whole
game. Like in previous section four possible cases of the conditions of interactions are analyzed
between the platforms and content providers, but now those conditions are entirely determined in
the strategic bidding process.

2.4.1 Simplifying Assumptions

As a first pass let us simplify the extension maximally in order to be able to solve the extended
model but still gain useful insights. First, let us assume that it is impossible for the content provider
to be in outright sale regime with one platform and affiliation regime with another platform. That
case could potentially happen only under multihoming equilibrium as content provider interacts
with both platforms. It is assumed that the choice set of content providers does not have the option
of choosing to multihome with A under outright sale and multihome with B under affiliation (and
vice versa).
It means, that whenever content provider wants to choose multihoming choice, it
should choose either outright sale bids from both platforms or affiliation bids from both platforms.
Second, let us assume that (which is actually proved in the basic model by Hagiu and Lee (2011)
in their Proposition 1) in extended model content providers being homogenous will make the same
(symmetric) decisions in equilibrium (therefore, we rule out any equilibria where the same content
providers could choose different options). It means that, on the one hand, it is assumed that either
all content providers sign an exclusive contract with the same platform or all multihome. On the
other hand, it is assumed that either all content providers choose outright sale regime, or all content
providers choose affiliation regime.

As before all possible cases for control and exclusivity are considered below to check whether

such equilibria exist and are they unique.
changing vertical level of differentiation that makes it very difficult for platforms to collude) and
platforms engage in severe strategic competitive process in determining conditions of interactions.

70

2.4.2 Exclusive Outright Sale Equilibrium Analysis in the Extended Model

No players of the game should have an incentive to deviate:

For content providers. Notice, that new no deviation conditions are added to the system below

which are related to the possibility of deviation to affiliation regime of control for all players.

Participation condition for C


 ≥ 0

 
1

Incentive compatibility conditions for C


 ≥ 
 
1

 
1





 ≥ 
 
2

 
1


 + 

2


 ≥ 
 
2

 
1


 + 

2


 ≥ 
 
1

 
1


 + 
 
1





 ≥ 
 
2

 
1


 + 
 
2


 + 


For platform A:

(cid:16)






1 + 

3
2

(cid:17)2

Participation condition for A

, 
 − 1


 ≥ 
 {
 < 3} ·

(cid:17)2

(cid:16)

1 − 

3
2

 − 
 
1

71

(2.26)

(2.27)

(2.28)

(2.29)

(2.30)

(2.31)

(2.32)

, 
 − 1


 ≥ 1
2

Incentive compatibility condition for A

(cid:17)2

1 + 

3
2

(cid:16)






(cid:17)2

1 + 

3
2

(cid:16)



 − 
 
1
 − 
 
1
(cid:16)

(cid:17)2

1 + 

3
2

(cid:17)2




For platform B:

, 
 − 1


 ≥ 1
2

− 
 
2




(Non-) Participation condition for B

(cid:17)2

(cid:16)

1 − 

3
2


 {
 < 3} ·

≥ 


(cid:16)

1 − 

3
2


 {
 < 3} ·

≥ 1
2

− 
 
2




 − 
 
1




, 
 − 1

(2.33)

(2.34)

(2.35)

(2.36)

There are two participation conditions for platform A stated above (2.32 and 2.33) as when
platform A deviates and chooses not to participate in bidding, C may choose either outright sale
exclusive option from B or affiliation exclusive option from B. The former case corresponds to
the first participation condition 2.32, while the latter - to the second participation condition 2.33.
Notice, that it is not required for both participation conditions to be satisfied as long as C never
chooses option corresponding to the violated participation condition in equilibrium. Thus, we will
have to analyze two cases (and, later, 4 cases for multihoming).

Case 1 (
 
1


 ≥ 
 
2


 + 


2) [If A decides not to participate in bidding, then C will prefer

outright sale exclusive offer from B rather than affiliation exclusive offer from B]

In this case condition 2.33 is redundant in equilibrium as non-participation by A induces C to

choose outright sale and, thus, the only participation condition that A should care about is 2.32.

72

2.35, imply


 
1

 = 
 
1


 = max

(cid:110)

Incentive compatibility condition 2.27 for C and participation conditions for A and B, 2.32 and

(cid:111)

, 
 − 1

2



3

Then, incentive compatibility condition for C 2.29 and (non-) participation condition for B 2.36

imply for 
 
2

 :

(cid:17)2

(cid:16)

1 − 

3
2

(cid:111)

(cid:110) 


6

− 1

,



2

≤ 
 
2


 ≤ max

− 
 {
 < 3} ·

1
2

This condition (as well as the assumption of Case 1) could be satisfied only for the case of
outright sale consumer tipping (
 > 3). The same implication appears for conditions 2.28 and 2.34
for 
 
2

 (these conditions are equivalent to 2.29 and 2.36 as is easily seen after substitution of 
 
1


into 2.34). Conditions 2.30 and 2.31 will always hold if multihoming bids are set sufficiently low.
2) [If A decides not to participate in bidding, then C will prefer

Case 2 (
 
1


 < 
 
2


 + 


affiliation exclusive offer from B rather than outright sale exclusive offer from B]

In this case A’s participation condition 2.32 is redundant, and A’s participation condition 2.33

is relevant.

Notice, that participation conditions for A and B, 2.33 and 2.35, imply for any 
 that


 > 
 
1

 
1

 ,

which contradicts incentive compatibility condition 2.27 for C since content provider would

prefer the offer of B instead of A.

To summarize, in the extended model exclusive outright sale equilibrium exists only for 
 > 3

(corresponds to a outright sale consumer tipping in favor of A).

Notice the difference of extended model as compared to basic model where outright sale
equilibrium exists for any 
. In the extended model additional incentive compatibility constraints
are added related to possibility of deviation to affiliated exclusive contracts. For values of content

 < 3 this creates incentives of platforms to soften bidding for content by inducing content to

73

affiliate. The main reason for softening of the competition for content lies in the fact that under
affiliation content creates less vertical differentiation of exclusive content as transferring control to
monopolist content provider guarantees high content prices. The reason this deviation is impossible
for 
 > 3 is that outright sale allows content providers to extract the whole industry profit and,
thus, no platforms have enough resources to make a deviation to exclusive affiliation attractive for
content providers.

The findings are summarized in the following proposition.

Proposition 4. Under the extended model with the homogeneous content valuation outright sale
(either exclusive or multihoming) could never be an equilibrium for 
 < 3 (no consumer tipping
condition for outright sale regime). For 
 > 3 (outright sale consumer tipping), the outright sale
is an equilibrium.

2.4.3 Multihoming Outright Sale Equilibrium Analysis in the Extended Model

The analysis of multihoming outright sale equilibrium is very similar to the basic model as the
system contains the same conditions as in the basic model plus some additional related to the
ability of platforms to choose regime of control and content providers to have more options to
choose. Thus, the same contradiction as in basic model proves that in the extended model there
is no multihoming outright sale equilibrium. Hence, the proposition. Notice, there is a difference
of interpretation of this deviation under the extended model as compared to the basic model. In
the basic model, this situation was interpreted as the prisoner’s dilemma as deviation resulted in
outright sale exclusive equilibrium that gives platforms less profit than multihoming outright sale
option. Since in the extended model platforms can choose control regime, they may deviate and
find themselves in a potentially better affiliation multihoming equilibrium which is studied next.
Proposition 5. Under extended model with homogeneous content valuation there are no outright
sale multihoming equilibria as in the basic model (and for the same reason since there is always
an incentive for platforms to deviate and attract content exclusively). Under the extended model,
the prisoner’s dilemma interpretation of outright sale multihoming case becomes less relevant

74

since after a deviation platforms may find themselves in an even better situation (like multihoming
affiliation as will be shown later).

2.4.4 Exclusive Affiliation Equilibrium Analysis in the Extended Model

In order for an exclusive affiliation equilibrium to exist, no player should have an incentive to
deviate.

For content providers

Participation condition for C


 + 


 
2
2

≥ 0

Incentive compatibility conditions for C


 + 


 
2
2

≥ 
 
1





 + 


 
2
2

≥ 
 
1





 + 


 
2
2

≥ 
 
2


 + 

2


 + 


 
2
2


 + 


 
2
2

For platform A:

≥ 
 
1


 + 
 
1




≥ 
 
2


 + 
 
2




Participation condition for A

75

(2.37)

(2.38)

(2.39)

(2.40)

(2.41)

(2.42)

(cid:17)2

(cid:16)

1 − 

3
2

− 
 
2


 ≥ 
 {
 < 3} ·

1
2

1
2

− 
 
2


 ≥ 1
2

Incentive compatibility condition for A

(cid:17)2

1 + 

3
2

, 
 − 1

(cid:16)






 − 
 
1
 − 
 
1




− 
 
2


 ≥ 


1
2

For platform B:

(Non-) Participation condition for B

(cid:17)2

(cid:16)



≥ 


1
2

1 + 

3
2

, 
 − 1

1
2

≥ 1
2

− 
 
2




(2.43)

(2.44)

(2.45)

(2.46)

(2.47)


 + 


2 > 
 
1

Case 1 (
 
2


 ) [Optimistic platforms’ expectations17: If A decides not to participate
in bidding, then C will prefer affiliation exclusive offer from B rather than outright sale
exclusive offer from B]

One of platform A’s participation conditions, 2.43, is redundant!
As before, the conditions for equilibrium bids are checked first: participation conditions for

platforms (2.44 and 2.47) and incentive compatibility condition for C, 2.40, imply


 
2

 = 
 
2


 = 0

17As will be shown later such an expectation is always better for platforms and worse for content

providers. Hence the title: optimistic (for) platforms expectations.

76

Then, it is checked whether there is an incentive by all parties to deviate to other options:
incentive compatibility for content providers 2.38, participation condition 2.46 for the platform B
and Case 2 condition imply:

This condition is satisfied only for 
 < 3!
Exactly the same conditions are obtained for incentive compatibility conditions of content

providers and of the platform A (2.39 and 2.45):

(cid:17)2

(cid:17)2

(cid:16)

(cid:16)










2

 − 1
 − 1

2

1 + 

3
2

, 
 − 1

≤ 
 
1


 <



2

1 + 

3
2

, 
 − 1

≤ 
 
1


 ≤ 

2

As easily seen the rest conditions are satisfied if multihoming bids are set to be sufficiently low.
In this case we get an equilibrium like in the basic model, but for basic model this equilibrium
held for any 
. Under extended model for 
 > 3 this equilibrium does not hold anymore as for too
high content valuation there is an incentive to deviate to exclusive outright sale. This deviation
would create consumer tipping in the industry and will allow to extract all industry profit by
deviating parties. Under not too high content valuation, 
 < 3, exclusive outright sale contract
generates not enough profits to make such a deviation profitable.

Notice, there is no other than 
 
2


 = 
 
2


 = 0 equilibrium (only for 
 < 3) allocations under

Case 1.


 + 


2 ≤ 
 
1

Case 2 (
 
2


 ) [Pessimistic platforms’ expectations: if A decides not to participate
in bidding, then C will prefer outright sale exclusive offer from B rather than affiliation
exclusive offer from B]

In this case only A’s participation condition 2.43 is relevant (and 2.44 is redundant).
Notice, that compared to previous case, the only difference in the system of equilibrium con-
ditions is that the right hand side of participation condition of platform A has decreased (compare
2.44 versus 2.43), as platform A expects a more pessimistic outcome from non-participation since

77

C will join B with outright sale exclusive contract and will allow B to more significantly vertically
differentiate itself as compared to A. This means, that A in Case 2 in equilibrium would tolerate
paying higher bid as compared to Case 1 analyzed before. Together, participation conditions for
platforms (2.43 and 2.47) and incentive compatibility condition for content providers 2.40 imply

0 ≤ 
 
2


 ≤ 
 
2


 ≤ 1
2

− 
 {
 < 3} ·

(cid:17)2

(cid:16)

1 − 

3
2

Notice, that all conditions are the same for B as in the previous case and the new participation
condition 2.43 tends to make A even more attractive for C than it was in Case 1. Thus, it is only
required to check whether A and C will not have an incentive to deviate and there is no need to
worry that B will deviate if the bids for B are set exactly the same as they were set for Case 1 above.
Now, in order to A and C not to have incentives to deviate, both incentive compatibility
conditions 2.39 for C and 2.45 for A, stating that both will not prefer outright sale exclusive option,
should hold. Both conditions imply

(cid:17)2

(cid:16)



 − 1

2

1 + 

3
2




, 
 − 1

≤ 
 
1


 − 
 
2


 ≤ 

2

which could hold only for 
 < 3.

Therefore, there are many affiliation exclusive equilibria as shown above with

(cid:17)2

(cid:16)

1 − 

3
2

0 ≤ 
 
2


 ≤ 
 {
 < 3} ·

and B bidding, for example, like in Case 1.
Thus, in addition to unique basic Hagiu and Lee (2011) model equilibrium with 0 = 
 
2


 = 
 
2

 ,
extended model allows exclusive equilibria with positive bids for C for 
 ≤ 3 and there are no
equilibria for 
 > 3.

The intuition for why there are no equilibria for extended model Case 2 for 
 > 3 is the same

as in the Case 1 above.

78

The intuition for why there could be additional equilibria for extended model in Case 2 for

 ≤ 3 is the following. If platform A has a pessimistic expectations (Case 2 - that if it deviates to no
participation, then exclusive outright sale regime with B will occur), then it allows for C to extract
positive bids from A. One can interpret it as pessimistic expectations of A increases bargaining
power of C to extract surplus from A18.

The findings are summarized in the following proposition.

Proposition 6. Under the extended model with homogeneous content valuation, there are multiple
exclusive affiliation equilibria19 that correspond to pessimistic expectations of platform A regarding
actions of C in case of A’s deviation. In pessimistic expectations equilibria, A expects C to choose
outright sale option from B after A’s deviation and, thus, C can get positive bids from A and payoff
of A is less than of B (who do not participate). Nevertheless, assumed selection criterion allows
avoiding those pessimistic expectations equilibria by the platforms.

2.4.5 Multihoming Affiliation Equilibrium Analysis in the Extended Model

No player should have an incentive to deviate.

For content providers:

Participation condition for C


 + 
 
2

 
2


 + 
 ≥ 0

Incentive compatibility conditions for C


 + 
 
2

 
2


 + 
 ≥ 
 
1




(2.48)

(2.49)

18Notice, in this case B, by not signing an exclusive contract with C, earns more than A.
19Notice, in the basic model there is a unique exclusive affiliation type of equilibrium.

79


 + 
 
2

 
2


 + 
 ≥ 
 
1





 + 
 
2

 
2


 + 
 ≥ 
 
2


 + 

2


 + 
 
2

 
2


 + 
 ≥ 
 
2


 + 

2

For platform A:

Participation condition for A

(cid:17)2

(cid:16)

1 − 

3
2

− 
 
2


 ≥ 
 {
 < 3} ·

1
2

1
2

− 
 
2


 ≥ 1
2

Incentive compatibility conditions for A

1
2

− 
 
2


 ≥ 1
2

− 
 
2




(cid:17)2

1 + 

3
2

, 
 − 1

(cid:16)






 − 
 
1
(cid:17)2

(cid:16)

1 − 

3
2

− 
 
2


 ≥ 


1
2

For platform B:

Participation condition for B

− 
 
2


 ≥ 
 {
 < 3} ·

1
2

80

(2.50)

(2.51)

(2.52)

(2.53)

(2.54)

(2.55)

(2.56)

(2.57)

1
2

− 
 
2


 ≥ 1
2

Incentive compatibility conditions for B

(2.58)

(2.59)

(2.60)

1
2

− 
 
2


 ≥ 1
2

− 
 
2




(cid:17)2

− 
 
2


 ≥ 


1
2

1 + 

3
2

, 
 − 1

(cid:16)



 − 
 
1




As for other cases for extended model there are two participation conditions for each platform
depending on platforms expectations of C’s choice after platforms’ deviations. It means, at least
one of conditions 2.53 and 2.54 needs to be satisfied for platform A and expected choice of C
should be realized in equilibrium. The same holds for participation conditions 2.57 and 2.58 for
platform B.

Thus, in general there are 4 possible cases:

(cid:16)
(cid:16)
(cid:16)
(cid:16)

Case 1

Case 2

Case 3

Case 4

(cid:17)
(cid:17)
(cid:17)
(cid:17)


 ≤ 
 
2
; 
 
1


 + 

2


 ≥ 
 
2
; 
 
1


 + 

2


 ≤ 
 
2
; 
 
1


 + 

2


 ≥ 
 
2
; 
 
1


 + 

2


 ≤ 
 
2

 
1


 + 

2


 ≥ 
 
2

 
1


 + 

2


 ≥ 
 
2

 
1


 + 

2


 ≤ 
 
2

 
1


 + 

2

As before, first, the focus is on the simpler Case 1, that is more similar to the basic model.
Then, Case 2 is considered and Case 3 and 4 are omitted as they do not add anything under the
assumption of symmetric multihoming bids (
 
2


 = 
 
2

 ).

81

Case 1(cid:16)


 ≤ 
 
2

 
1


 + 


2; 
 
1


 ≤ 
 
2


 + 

2

(cid:17)[Optimistic platforms’ expectations: if any platform

decides not to participate in bidding, then C will prefer affiliation exclusive offer from the other
(participating) platform rather than outright sale exclusive offer from the other (participating)
platform]

In this case the only relevant participation conditions for A and B are 2.54 and 2.58, respectively,

and 2.53 and 2.57 are redundant.

Like in the basic model, first, it is verified whether no deviation conditions for equilibrium
(multihoming) bids are satisfied. For symmetric multihoming bids, the participation condition for
content providers 2.48 implies:


 
2

 = 
 
2


 ≥ − 

2

On the other hand, participation conditions for platforms A and B, 2.54 and 2.58, respectively,

imply


 
2

 = 
 
2


 ≤ 0

No deviation to exclusive affiliation conditions (incentive compatibility conditions 2.51, 2.52

 are set

for C and 2.55 and 2.59 for A and B, respectively) for all players will be satisfied if 
 
2


as in the basic model.

, 
 
2

Next, notice that there are additional incentive compatibility constraints (2.49, 2.50 for C and
2.56 and 2.60 for A and B, respectively) for all players, related to the possibility of deviation to
exclusive outright sale contract, that should be satisfied. Let us check conditions for A and C
(for B and C they are identical). Incentive compatibility conditions for C and A, 2.50 and 2.56,
respectively, imply

, 
 − 1

≤ 
 
1


 − 
 
2


 ≤ 
 
2


 + 


(cid:17)2

1 + 

3
2

(cid:16)






 − 1

2

82

Satisfaction of this condition will depend on the value of 
 
2

= 0,
corresponding to no extraction of rent from content providers by the two platforms, this condition
will hold for any 
 > 0. Notice that if 
 
2
2 then this condition could not hold for any

 > 0. Also, for 
 > 3 maximum rent extracted by a platform from content providers such that this
condition holds is 
 
2


 . For example, if 
 
2


 < −3

2 . For 
 ≤ 3 setting 
 
2

2 will satisfy this condition.


 = −3


 = − 





Thus, it is found that for low and medium content valuations 
 < 3 (no consumer tipping in
the outright sale regime) platforms could extract all content profits, but for high content valuations

 > 3 (consumer tipping in the outright sale regime) platforms could not extract all profits from
content, maximum each platform could extract is 3
2 , and content providers still get a significant
2 = 
−3. In contrast, in the basic model all equilibria sets were
amount of content profits, i.e. 
−2· 3
independent of the value of content 
, and all profits extraction from C is always an equilibrium.
While in the extended model, such types of equilibria exist only for 
 < 3 and do not exist for 
 ≥ 3.

(cid:17)[Pessimistic platforms’ equilibria: if any platform

Case 2(cid:16)

> 
 
2


 + 


2; 
 
1


 > 
 
2


 + 

2


 
1



decides not to participate in bidding, then C will prefer outright sale exclusive offer from the
other (participating) platform rather than affiliation exclusive offer from the other (partici-
pating) platform]

In this case the only relevant participation conditions for A and B are 2.53 and 2.57, respectively,

while 2.54 and 2.58 are redundant.

Notice, the analysis is very similar to exclusive affiliation equilibrium case. Because, both A
and B may have pessimistic expectations regarding reaction of C to a non-participation of platforms,
there will be equilibria where A and B will make actually positive bids to C, or pay to C! That
could be seen from participation conditions for C and A, 2.48 and 2.53, respectively (similarly for
2.48 and 2.57), that imply

(cid:17)2

(cid:16)

1 − 

3
2

− 

2

≤ 
 
2


 ≤ 1
2
where the right hand side is positive for 
 > 0.
The rest of the analysis of the system proceeds exactly the same as in Case 1.

− 
 {
 < 3} ·


 = 
 
2

,

83

Therefore, additional implication coming from extended model is that there are additional equi-
libria related to pessimistic expectations of platforms which additionally reward content providers.
Notice, though, that under the assumed selection criterion such equilibria are ruled out as it is
assumed that platforms could always coordinate on the best equilibria for them. Nevertheless, if
for some reason they cannot coordinate, additional equilibria with excessive content reward may
be realized even for 
 < 3 and platforms may find themselves in a situation similar to outright sale
equilibrium in the basic model where platforms would prefer that content providers did not exist in
the market since their existence creates destructive competition between the platforms for content.
The findings of this section and the answers to the paper’s main questions of are summarized

below.
Proposition 7.
Under the extended model with homogeneous content valuation, there are
additional equilibria corresponding to pessimistic expectations of platforms that content providers
will choose exclusive outright sale contracts with the rival platform when the platform deviates.
These pessimistic platforms’ expectations allow content providers to extract positive bids from
platforms under multihoming affiliation, a situation that could have never occurred in the basic
model. Nevertheless, equilibrium selection criterion allows platforms to avoid those pessimistic
expectations equilibria.
Proposition 8.
Under extended model (with homogeneous content valuation) for affiliated
multihoming, the maximum share of content profits that platforms could extract depends (weakly
negatively) on 
. For 
 < 3 (no consumer tipping under outright sale), all profits from C could
be extracted, for 
 > 3 (consumers tipping under outright sale) not all profit from C is extracted:
maximum that can be extracted by each platform is 3
2 is guaranteed to be earned
by content providers. This holds even for selection criterion used by Hagiu and Lee (2011) and
is in contrast to the basic model where platforms can extract all profits from content providers for
any 
.
Proposition 9. Under extended model with homogeneous content valuation and with a selection
criterion used by Hagiu and Lee (2011), strategic bidding game over control and exclusivity leads

2 and, thus, 
 − 2· 3

84

to the multihoming affiliation equilibrium that maximizes second stage industry profit. In general
(without applying equilibrium selection) under the extended model with homogeneous content
valuation exclusive affiliation equilibria exist only for 
 < 3, and for 
 ≥ 3 exclusive outright sale
equilibrium exists (and unique for this type) while multihoming equilibria exist for any 
 > 0. For
all values 
 > 0 multihoming equilibria bring higher total industry profits.

2.5 Conclusions

This paper addressed the question of the role of strategic choice of control in addition to
exclusivity for the outcome of two-sided platforms’ competition. A specific but benchmark case
of homogeneous content preferences was considered. As suggested in Hagiu-Lee (2011) it is
demonstrated there is a conflict of interests between content providers and platforms regarding the
regime of control that is given exogenously. Content providers would prefer outright sale regime
and platforms would prefer affiliation regime that maximizes industry profit. An extended model
considered in this paper allows platforms to strategically choose the regime of control in addition
to exclusivity through a bidding game.

The following insights are obtained from the extended model with endogenous control under

the specific case of homogeneous content preferences.

First, in contrast to the basic model with exogenous control of Hagiu and Lee (2011), there are
no outright sale exclusive equilibria for low and medium levels of content valuation (for which there
is no consumer tipping under outright sale) when platforms could condition bids for content on the
regime of control. Deviation by platforms to affiliation works as a commitment to charge higher
prices for content and, thus, to reduce vertical differentiation from exclusive content and, thus, to
soften platforms’ competition for content in the bidding stage. Thus, for low and medium content
valuations there are only affiliation equilibria (multiple exclusive and multiple multihoming), and
multihoming corresponds to the maximum industry profits.

Second, for high content valuation (consumer tipping under outright sale) there is one exclusive
outright sale equilibrium, and multiple multihoming equilibria and the latter correspond to the

85

maximum industry profits. In contrast to the basic model, in the extended model, the minimum
content providers’ payoff is positive and linearly increases with the degree of content valuation.
The reason for the guaranteed reward for high valuation content providers is that if high valuation
content providers are not rewarded enough, any platform has a temptation to propose an exclusive
outright sale option that content provider will accept if not rewarded enough in the first place.
Because such a deviation will create a significant vertical differentiation effect for the platform,
unless platform will not have to pay too much to the content provider to induce such a deviation,
any platform will prefer to deviate. In contrast, in the basic model exogenous affiliation serves as a
commitment for high content prices that results in no vertical differentiation between the platforms
which prevents the temptation by platforms to attract content providers even if it is very cheap to
do that given that in multihoming equilibrium all content profits are extracted.

Third, the extended model is characterized by additional as compared to basic model affilia-
tion equilibria (both exclusive and multihoming) that result from possible platforms’ pessimistic
expectations that content providers will choose exclusive outright sale and not exclusive affiliation
option from the rival when the platform deviates and not participates in the bidding for content. As
emphasized before, exclusive outright sale contract with the rival platform reduces the platform’s
profit much more than affiliation outright sale contract with the rival platform, due to higher vertical
differentiation effect between platforms for exclusive outright sale contract. In such pessimistic ex-
pectations affiliation equilibria, content providers could extract additional profits from platforms as
compared to basic model. Nevertheless, if platforms could coordinate (selection criterion applies),
then such equilibria could be avoided by the platforms.

Therefore, the question of who will win or lose from the introduction of the possibility to choose

the content control regime by the platforms depends on several circumstances.

First, if initially the industry is characterized by exogenous outright sale regime (like possibly
satellite TV or Radio) where exclusive content is the equilibrium outcome, then independent
of content valuation (with or without consumer tipping) platforms could benefit if they could
choose control regime. An essential condition for this is the possibility by platforms to coordinate

86

on equilibria that maximize industry profit and which are best for platforms (selection criterion
applies). Thus, if platforms could successfully coordinate, then the welfare of content providers
will undoubtedly decrease as compared to the initial situation of exogenous outright sale regime,
while the welfare of platforms will increase. On the other hand, if platforms’ ability to coordinate
is limited, and especially if platforms have pessimistic expectations, then there are higher chances
for content providers to improve their situation or at least to have some reward under affiliation
regimes (either exclusive or multihoming) that will be realized in equilibrium.

Second, consider the initial situation of an industry characterized by exogenous affiliation
(which could be possible in the video game industry), and platforms could successfully coordinate
on the multihoming outcome and extract all industry profits. Then for low and medium content
valuation introduction of the possibility to choose control by the platforms will not change the
market outcome. On the other hand, if the exclusive content valuation is very high, the introduction
of endogenous control will significantly redistribute content profits from platforms to content
providers. Thus, such an analysis indicates that for high valuation content industries platforms will
have incentives to maintain affiliation commitment as much as they can (for example by increasing
technological costs of switching to outright sale control regime) in order extract most high valuation
content providers profits. Besides, as before, if platforms could not perfectly coordinate, then the
introduction of endogenous control regime could improve content providers bargaining power due
to pessimistic platforms’ expectations. This should additionally motivate platforms to avoid making
control endogenous.

The next important step is to generalize the extended model to arbitrary preferences over content

and to consider strategic pricing by content providers.

A potentially interesting extension is to incorporate other benefits and costs of the two control
regimes as analyzed in Hagiu (2007) and explore predictions of the model in that case. Such
decisions could be related to advertising expenditures, investments in improving the quality of the
content or distribution channels, etc.

87

CHAPTER 3

LONG TERM EFFECTS OF MINIMUM DRINKING AGE LAWS ON ORGAN FAILURE

(CO-AUTHORED WITH DR. MINH NGUYEN)

3.1 Introduction

Most of the 20th century, after Prohibition was repealed in 1933, in most states, the minimum
legal drinking age (MLDA) in the United States was 21 years. However, the Vietnam War in the
1960s and 1970s, when many 18-year-olds were drafted, and the ongoing increase of the role of
young people in the civil rights movement, social and political change movements of the 1950s and
1960s, increased pressure to give youth more rights which included earlier voting, earlier age of
majority, and earlier drinking age. More than 30 states lowered the drinking age below 21 during the
early 1970s. By the mid-1970s and early 1980s, several influential research publications appeared
such as (Williams et al. (1975), Williams et al. (1983), Cook and Tauchen (1984)) demonstrating
that states that lowered MLDA experienced more youth traffic-related fatalities, while states which
increased MLDA experienced less youth traffic-related fatalities. These research and civil pressures
were an important motivation for Ronald Reagan, although he was initially opposed, to introduce
National Minimum Drinking Age Act in 1984 which required states to set MLDA at 21, otherwise,
they would lose 10% of federal highway funds. That law resulted in all states setting the drinking
age to 21 by 1988.

These events created a great research opportunity and resulted in numerous publications on the
effects of changes in drinking laws on different outcomes of primary interest at that time, which
were related to the immediate effect of MLDA laws on the traffic crashes involving youth and,
related, alcohol consumption by youth summarized in Wagenaar and Toomey (2002). Despite a
consensus1 among most researchers that setting MLDA back to 21 was a most reasonable policy
1Wagenaar and Toomey (2002) identified 241 empirical articles on the topic and concluded that
although about half of research papers found insignificant effects, the other half in 90% of cases
showed that increasing MLDA to 21 had lead to a statistically significant reduction in both alcohol

88

saving significant numbers of lives2, the debate in the public continues and there are opinions that
MLDA should be lowered again3.

In this paper, we are looking at less direct, or immediate, however very potentially important
connection between minimum legal drinking age and demand for organ transplants in the United
States. To our knowledge, it is the first paper that analyzes such an outcome. It is an emerging
area of study. Several recent papers also look at the long-term, less visible, effects of MLDA
laws on such outcomes as alcohol and drug abuse disorders in later life (Norberg et al. (2010)),
on adult (who were adolescents when the MLDA laws changed) alcohol use and driving fatalities
(Kaestner and Yarnoff (2011) ), suicide and homicide deaths among women (Grusza et al. (2012)),
binge drinking later in life (Plunk et al.
(2015)),
alcohol-related chronic disease mortality (Plunk et al. (2016)). This research demonstrates that
MLDA laws should be considered in a much broader context than just immediate effects. Given
that enough time has passed since MLDA changes, we have an opportunity to study such long-term
effects of MLDA to be able to estimate more accurately the benefits and costs of allowing youth to
consumption and traffic fatalities among youth.

(2013)), high school dropouts (Plunk et al.

2However, there is one relatively recent paper by Miron and Tetelbaum (2009) that questions if

the National Minimum Drinking Age Act actually saved lives.

3There were recently many attempts to lower MLDA below 21. In 2008 Missouri, South Dakota,
Vermont and Minnesota considered lowering MLDA below 21 for general population, while Ken-
tucky, Wisconsin and South Carolina have introduced legislation that would lower the drinking
age only for military personnel (see https://abcnews.go.com/US/Politics/story?id=4577105page=1).
Recently, in 2016, New Hampshire, Minnesota and California proposed legislation to lower MLDA
(see https://www.entrepreneur.com/article/269537). All these attempts never were successful at
lowering MLDA for general population, however some proposals to relax legislation for cer-
tain subgroups of population were successful (see https://drinkingage.procon.org/states-that-allow-
underage-under-21-alcohol-consumption/, states where there are exceptions for MLDA21 rule for
religious, medical purposes, or when drinking in the presence of parents among other exceptions).
Another example of a campaign was launched in 2008 in favor of reconsidering MLDA21 is
Amethyst initiative where more than 100 presidents of US colleges suggested reconsidering the
MLDA21 policy, which in practice was perceive by the public as advocating for lowering MLDA
below 21 (see https://fordhamobserver.com/1832/news/amethyst-initiative-questions-21-year-old-
drinking-age/). Their main argument is that MLDA21 policy is less effective, or even counter-
productive on campuses, and promotes more binge drinking than it would have been otherwise.
Their quality of research of specific populations as a college population is poor, preventing any
conclusions based on actual data (see discussion in Wagenaar and Toomey (2002)).

89

drink early.

Conceptually lower MLDA could lead to excessive consumption of alcohol, not just at age of
18-20, but throughout the whole life, which may lead to liver and other organs failure and the need
for organ transplants at some point during their life. There is some preliminary evidence that lower
MLDA results in more binge drinking and less moderate drinking among adults (see Plunk et al.
(2013)). On the other hand, although sometimes ignored in policy debate since relies on using
animal experiments, neurological biology shows (see Chambers et al (2003)) that parts of the brain
responsible for addiction resistance are still forming during ages 18-20 and at the same time at
that age range adolescents prefer to experiment to learn new things (including trying alcohol and
binge drinking), a combination that could lead to alcohol addiction and subsequent need for organ
transplantation.

There are potential empirical challenges in identifying the causal effect of drinking age laws
changes on organ transplantation outcomes. Although MLDA changes are an example of a natural
experiment, to reveal the causal effect, a good empirical strategy must be employed. For example,
MLDA policy in a particular state may be a response to the changing economic, political, and social
factors affecting alcohol consumption behavior which in turn determines future organ demand and
confounding our estimates.

Our method uses variation in the timing of state laws enabling the population of 18-20 youth to
get access to alcohol in some years and prohibiting this age group from getting access to alcohol
in other years. We use fixed state effects to take into account any unobserved factors that could be
different across states (as a taste for alcohol) and stable across different cohorts living in a particular
state. On the other hand, cohort fixed effects take into account any cohort-related trends that are
common across states. We use event study methodology which has the advantage of testing the
existence of pretends and hence giving more credibility in identifying causal effects of the policy.
This is very important given that MLDA changes happened in both economically, politically, and
culturally dynamic times.

90

3.2 Background on Organ Transplantation in the US

According to European Directorate for Quality of Medicine which collects international data
on organ transplantation activity and organ waitlists in 2018, compared to other OECD countries,
the United States is the second country, after Spain, in the number of transplants per million of
population. Not only US is the leader in terms of transplantation activity, it is also second, after
Turkey, in terms of the number of people waiting for an organ per million of population and in
terms of the number of people who die per million of population while being on the waiting list for
an organ.

In 1984, a United Network for Organ Sharing (UNOS) was established to manage Organ
Procurement and Transplantation Network (OPTN) which coordinates organ transportation by
maintaining a database of all transplant candidates and donors for different types of organs.

Although the population of 18-20 years old constitutes a small portion of the overall population,
over time every person who becomes of that age is affected by the law, and in the long term changes
in MLDA laws affect the whole population. Hence any policy evaluation should take into account
the long-run effects of such a policy.

Any behavior leading to the need for organs is potentially very costly for society. For example,
in 2010 the cost of one kidney transplant was about a half-million dollars. Moreover, since there is
a significant deficit of organs, any policy leading to a reduction of people on the waitlist saves lives
since it would increase the number of donated organs per person on the waiting list.

3.3 Data

We use data on cohort state-level incidence of demand for transplants of different organs cal-
culated based on administrative data provided by Organ Procurement and Transplantation Network
(National UNOS STAR file) collected for the period 1990 till mid-20194. OPTN data allows to
analyze the demand for livers, kidneys, pancreas, hearts, lungs, any organs demanded.

4In this version of the working paper we only consider waitlist registration and transplantation

period 2010-mid2019. In later versions we will analyze the 2000s and 1990s.

91

Table C.1 and Table C.2 demonstrate the timing of state laws when the minimum legal drinking
age was lowered to below 21 during the early 1970s and increased back to 21 in the late 1970s and
1980s for distilled spirits (Table C.1) and any type of alcohol (Table C.2). The timing of lowering
and increasing the minimum legal drinking age is from Wagenaar (1981), O’Malley and Wagenaar
(1991), and Britannica ProCon.org.

If we consider minimal legal drinking age for any type of alcohol (see Table A1.1), 5 states had
minimum legal drinking age for distilled spirits below 21 by the beginning of 1970, and 22 states
have lowered the minimum legal drinking age of distilled spirits to below 21 years between 1970
and 1975. Then, these 27 states have raised their minimum legal drinking age for distilled spirits
to 21 years between 1978 and 1988. There were 24 states which did not lower the drinking age for
distilled spirits.

If we consider minimal legal drinking age for any type of alcohol (see Table A1.2), then 17
states had the drinking age below 21 at the beginning of 1970, and 23 states lowered their drinking
age to below 21 during the 1970s. There were only 12 states who did not lower their MLDA for
any type of alcohol.

In exploring the effect of minimum legal drinking age effect on demand for organs, we control
for several characteristics which varied for different birth cohorts within a state. Such characteristics
included per capita income, unemployment, per capita public medical aid, the percentage of adults
who were high school graduates5. We collected that data from different sources. Per capita income
and public medical aid figures are from the United States Bureau of Economic Analysis. Data for
state population is taken from the Census of 2010 and the percentage of high school graduates is
taken from the American Community Survey of 2010. Data on unemployment comes from the
Bureau of Labor Statistics.

5Education variable is omitted from this analysis since we do not have enough observations for
that version of the variable. We are going to include another version of that variable which has
enough observations in next drafts.

92

3.4 Identification Strategy

We are applying event study methodology for the identification of the causal effect of MLDA on
organ transplants. The first approach is a state and cohort fixed effects regression. The following
equation represents this approach:

10



=−5,
ࣔ−1




 = 

 + 

 +



1(
 − 

 = 
)

 + 


 + 


,

(1)

where 


 is the proportion of registered on the transplant waiting list in a specified period in a
state s and belonging to cohort 
 divided by the number of people living in state 
 and belonging
to cohort 
, es is the birth year of the earliest cohort affected by the increase in the MLDA in a
state 
. 1(
 − 

 = 
) are the indicators for leads or lags of cohorts relative to treatment. The
last cohort unaffected by the MLDA increase is omitted and is considered the base cohort. Cohort
and state fixed effects are included in all specifications. 


 is a vector of state time-variant
characteristics. We include in 


 the following control variables:per capita medical funding by
states, unemployment, per capita personal income, the share of high school graduates for population
age 25 and older. We expect to see 
1 < 0, reflecting a negative impact of increasing the minimum
drinking age on the demand for organ transplants.

The key assumption for this approach to be valid is that without the policy change, the demand
for organ transplants of different cohorts in different states should trend similarly. Model described
by equation 1 allows to provide an evidence if that assumption is consistent with the data.

As a preliminary step, we are compiling an individual-level dataset where each row represents
an individual on the waiting list. We consider 2010- mid-2019 as the period of registration. In the
future work we plan to analyze also registration periods of 1990s and 2000s. Then, we aggregate
data to the state-cohort level by calculating the number of people on the waiting list of a certain
year of birth (cohort) and living in a certain state. For each cohort, we created a dummy variable
indicating whether the individuals belonging to that cohort had legal access to alcohol when she/he
was 18-20 years old.

93

Interstate migration is a potential threat to our approach. However, according to

https://www.northamerican.com/infographics/where-they-grew-up, approximately 70-80% of Amer-
icans live in the same state where they were in their adolescence.

3.5 Results

3.5.1 Effects of the MLDA21 for Spirits on the Transplant Demand

States had different timeframes for adopting MLDA21 for different categories of alcoholic bever-
ages: spirits, wine, and beer. In general, state governments were more willing to maintain a low
MLDA for beer, so some states adopted the MLDA21 for spirits and extended that policy to other
beverages. Our hypothesis is that spirits might be most harmful, and exposure to spirits at a young
age more likely causes addiction. Therefore, we will examine the MLDA21 for spirits and for all
alcoholic beverages separately.

We examine the effects of increasing the MLDA to 21 on the demand for transplants by
estimating the equation 1 using the sample of 26 states adopting the MLDA21 between 1978 and
1988. The dependent variable is the number of people demanding for any organ transplants in
the 100,000 population of the state-cohort cells. Limiting the sample to the ever-treated states
identifies the effects of the law using the timing of the law’s passage, and allows us to compare
the outcomes among states that are arguably more similar than the always-treated states. The last
cohort experiencing the non-MLDA21 was omitted in the model.

Estimates are displayed in Table C.3 Columns (1) and (2) and demonstrated in Figure C.1 and
Figure C.2. Prior to the policy change, we find little evidence of differential trends. For k<0, all
treatment coefficients are small in magnitude and never reach statistical significance, even at the
10 percent level. This provides evidence to support our assumption that without the MLDA21
policies, the trends of demand for transplants would have been similar across states.

In contrast, the demand for organ transplants decreases significantly following the MLDA21.
The number of transplants demanded per 100,000 people declines by 86 cases by ten years after
the policy was enacted. To place the treatment estimates in context, the mean demand was 151 per

94

100,000 in the year prior to treatment. The point estimates of the key coefficients are remarkably
similar in magnitude and significance between the specifications with and without covariates. The
effects gradually increase in the magnitude when the cohort is further out from policy enaction.

A number of factors may explain for the pattern of the effects. First, the MLDA21 can decrease
youth’s exposure to spirits directly. When adolescents are not eligible to buy spirits until they reach
the age of 21, the probability of being addicted to alcohol may substantially decrease. Second, the
MLDA21 may also lead to fewer drinking peers and forms the perception that drinking is harmful. It
is also possible that the legislation enforcement was strengthened over the years (Toomey, Rosenfeld,
and Wagenaar 1996).

Figures C.3-C.6 show the results for demand for individual organs:

livers, kidneys, lungs,
and hearts. The patterns are consistent for most organs, except for hearts: the coefficients in the
pre-policy periods are small while the coefficients in the post-policy periods are larger, negative,
and statistically significant.

3.5.2 Effects of the MLDA21 for Alcohol on the Transplant Demand

We run analogous models for the policy that increases the MLDA for any type of alcohol to 21
years old. The estimated effects on the demand for any organs are reported in Table C.1 Columns
(3) and (4) and Figure C.2. Again, the coefficients are small and insignificant in the periods prior
to the policy change, indicating parallel trends in the pre-policy period, supporting our research
design. We can also see that the coefficients are robust to the addition of covariates. The effects of
the MLDA21 for alcohol on demand for individual organs are presented in Figures A5-8.

The pattern observed in Figure C.2, and Figures C.7 - C.10 are similar to the graphs that present
the effects of the MLDA21 for spirit but are less pronounced. This is also consistent with our
expectation since exposure to wine and beer is arguably less harmful and addictive than spirits.

95

3.6 Conclusion

Organ failures are among the leading causes to deaths and the most expensive medical procedures
in the United States. Medical literature has established the association between alcoholism and
chronic dysfunction of organ systems. This paper provides the first causal evidence of the long-
term impacts of increasing the MLDA to 21 in various states in the 1970s-1980s on reducing organ
failures. By delaying exposure to alcoholic beverages, the MLDA 21 likely limits adolescents’
exposure to alcohol and reduce the likelihood of alcoholism in adulthood and thus the risk of
alcohol-related diseases, including organ failures.

We find that cohorts exposed to higher MLDA (21) had lower probability of having organ
failures in later life. The empirical findings show that limited access to spirits and alcohol before
the age of 21 reduced the demand for transplants by 86 and 50 per 100,000 population, respectively,
after ten years, given that the average transplants demanded by the cohort prior to treatment is
approximately 155.

These findings have important implications for evaluating the benefits of the MLDA21 legis-
lation. Besides preventing traffic fatalities, the MLDA21 has significantly reduced organ failures
in adulthood, therefore might have increased productivity and life quality of the generations who
were growing up in the presence of this legislation.

96

APPENDICES

97

APPENDIX A

FIGURES FOR CHAPTER 1

Figure A.1: Willingness to Pay Of Two Types of Consumers for Different Levels of Search Engine
Quality and Advertising Profits per Consumer

Note: This graph represents willingness to pay of type 1 (in green) and type 2 (in brown) consumers for a search
engine of minimally acceptable quality 

 
 vs a higher than minimally acceptable quality 
 > 

 
. Also it shows
advertising profit (in yellow) that each type of consumer brings to the search engine. This graph illustrates that despite
the fact that type 1 consumers are willing to pay for quality improvement, indirectly financed search engine may prefer
not to improve the quality above minimally acceptable by consumers level, 

 
.

98

Figure A.2: Optimal Choice of Search Engine Quality Under Indirect vs Direct Model of Search
Engine Financing

Note: This figure illustrates such parameter values of preferences and technologies when an indirect search engine
will produce just minimally acceptable quality for consumers, 

 
, while direct search engine would produce higher
quality search engine 

 > 

 
 = 

 
.

99

APPENDIX B

FIGURES AND DERIVATIONS FOR CHAPTER 2

Figure B.1: Comparison of Equilibria in Basic (Exogenous Control) Versus Extended Model
(Endogenous Control)

Note: Circles represent multiple equilibria, dots - unique equilibrium. Black color corresponds to basic model, green
color - extended.

Table B.1: Second Stage Industry Profit Under Outright Sale (Homogenous Content Valuation)

Second stage industry profit

(cid:27)

, 
 − 1

(cid:26)

(cid:17)2

1

1 +(cid:16) 


3

multihoming

exclusivity for A against B




100

Table B.2: Second Stage Industry Profit Under Affiliation (Homogenous Content Valuation)

multihoming

exclusivity for A against B

Second stage industry profit

1 + 

1 + 

2

B.1 Derivations

Lemma 1. Under outright sale control regime if total surplus from a piece of content is strictly
decreasing in content price, then it is always optimal for platforms to set content price equal to the
marginal cost (zero). If total surplus from a piece of content is independent of content price, then
each platform cares only about the sum of platform access and content prices and chooses this sum
to maximize its profits.


 = max


,
 


{
 
 · (

 + 


 ( 
 
))}
2 + 


( 
 
)−


( 

)−

+


2 + 


( 
 
)−


( 

)−

+



2 + 


( 
 
)−


( 

)−

+



, if 1
,if 0 < 1
, if 1

2


2


< 0

> 1

< 1

2


 
 = 1 − 
 





 
 =

0(cid:98)


1

(cid:26)(cid:18)1

2

Consider interior solution (no tipping)

+ 


 ( 
 
) − 


 ( 

) − 

 + 



2


(cid:19)

(cid:27)

· (

 + 


 ( 
 
))


 = 





,
 


Denote

Then

(cid:101)

 ≡ 

 + 


 ( 
 
) ;(cid:101)

 ≡ 

 + 


 ( 

)

(B.1)

101

(cid:40)(cid:32)1

2

+ 

 (
 ( 
 
) + 
 ( 
 
)) − 

 (
 ( 

) + 
 ( 

)) −(cid:101)

 +(cid:101)



2


(cid:33)

(cid:41)

·(cid:101)




 = max(cid:101)

,
 


Denote


 ( 
 
) = 
 ( 
 
) + 
 ( 
 
) ; 
 ( 

) = 
 ( 

) + 
 ( 

)

as the total surplus from a piece of content. Then

(cid:17)

(cid:16)(cid:101)



:






or




 ( 
 
) :

(cid:33)

(cid:41)

·(cid:101)



2

(cid:40)(cid:32)1

 = max(cid:101)

,
 

(cid:32)1
(cid:19)
(cid:18)
·(cid:101)

 +
(cid:101)

 =

− 1
2


2

2


+ 


 ( 
 
) − 


 ( 

) −(cid:101)

 +(cid:101)


(cid:33)
+ 


 ( 
 
) − 


 ( 

) −(cid:101)

 +(cid:101)


+ 


 ( 
 
) − 


 ( 

) +(cid:101)


·(cid:101)

 ≤ 0 and = 0 if 
 
 > 0



2

2


2

· 1 = 0,

(B.2)




(cid:48) ( 
 
)

Therefore, if 
(cid:48) ( 
 
) < 0 , then we get a corner solution 
 
 = 0 and(cid:101)

 ≡ 

 according to B.2

and B.1. If 
(cid:48) ( 
 
) = 0, then 
 
 and 

 can take any value such that B.2 and B.1 are satisfied.

(B.3)

2


Derivation of platforms’ second stage profits under outright sale

Outright sale

Case 1 (no consumers tipping in favor of A)
First, let us consider interior solution (
 
 ∈ (0, 1)) or no tipping. As was shown in the Lemma
1 under outright sale in general platforms will choose content prices socially efficiently equal to
marginal costs (zero) and get zero profits from any piece of content (
 (0) = 0). Thus

102


 
 =

1
2

+ 


 (0) − 


 (0) + 

 − 



2



 = max




{


 
}

+ 


 (0) − 


 (0) + 

 − 



2


1
2

+ 



(cid:18)−1

(cid:19)

2


= 0

and




 (

) :

or



 =


 + 


 (0) − 


 (0) + 



2

By analogy, for platform B’s 


(

) :

Solving FOCs gives:



 =


 + 


 (0) − 


 (0) + 



2



 = 
 + 


 (0) − 


 (0)

3



 = 
 + 


 (0) − 


 (0)

3

Substituting into demand gives


 
 =

1
2

+ 


 (0) − 


 (0)

6


Substituting demand and obtained optimal price into expression for profit gives

(cid:18)


 =

1
2


(cid:19)2


 + 


 (0) − 


 (0)

3

103

or

(cid:17)2

(cid:16)


 + Ɗ
 
(0)

3
2



 (Ɗ
) =

Hence, substituting parameter values considered in the text (
 = 1, 
 = 1) and consumer surplus

value for homogenous content preferences 
 (0) = 
 obtain


 (Ɗ
) =

For Ɗ
 = 0 (content multihoming)

1
2
For Ɗ
 = 1 (content exclusivity with the platform)


 (0) =


 (1) =

For Ɗ
 = −1 (content exclusivity with the rival platform)

(cid:17)2

1 + Ɗ


3

2

(cid:16)

(cid:16)

(cid:16)

(cid:17)2

(cid:17)2

1 + 

3
2

1 − 

3
2


 (1) =

And the demand for platform A is


 
 =

1
2

+ Ɗ


6

From this formula it is seen that under multihoming (Ɗ
 = 0) consumer tipping is impossible

Under exclusive outright sale (Ɗ
 = 1)


 
 =

1
2

104


 
 =

1
2

+ 

6

Thus consumer tipping in favor of platform A (
 
 = 1) is only possible under exclusive outright

sale case for


 > 3

Case 2 (exclusive outright sale consumers tipping in favor of A)
In case of consumer tipping to A (
 
 = 1) A’s profit is


 = max {


 
} = max {

 · 1}

Under competitive tipping it should be true that the following incentive compatibility condition

for consumers is always satisfied

or


 
 (
 = 1) ≥ 

 (
 = 1)


 + 
 (0) − 
 − 

 ≥ 
 − 



As platform will make this constraint always binding (otherwise, it could always increase its
price a bit and still attract all consumers and, thus, increase its profits) this condition will hold as
equality and imply



 = 
 (0) − 
 + 



As by assumption there are no marginal costs of producing platforms the only possible equilib-

rium1 (a la Bertrand because of competitive tipping) is

1Suppose not, 

 > 0, then B could always undercut its price and attract all consumers given

that 
 (0) − 
 + 

 = 

 and earn a positive profit.

105



 = 
 (0) − 
, 

 = 0

Substituting obtained price into profit function gives.
For Ɗ
 = 1 (content exclusivity with the platform)


 (1) = 
 (0) − 


For Ɗ
 = −1 (content exclusivity with the rival platform)


 (−1) = 0

Hence, substituting parameter values considered in the text (
 = 1, 
 = 1) and consumer surplus

value for homogenous content preferences 
 (0) = 
 obtain


 (1) = 
 − 1


 (−1) = 0

Combining case 1 and case 2 expressions above for platform profits we obtain expressions for

profits used in the text.

Affiliation

(cid:16)



(cid:17)



(cid:17)
(cid:16)


(cid:17)

(cid:16)

Under affiliation content providers maximize content profits and get 


per piece of content,
per piece of content. All above derived conditions for outright sale are
should be used. Under homogenous
= 0. This gives us expressions for platforms’ profits under affiliation used

and consumers get 

the same for affiliation, but instead of term 
 (0) term 

content valuation 

in the text.

(cid:16)



(cid:17)

106

APPENDIX C

FIGURES AND TABLES FOR CHAPTER 3

Figure C.1: Effect of Increasing MLDA for Spirits on Demand for Any Organs

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for any organs per 100000 population of that cohort. The coefficient in cohort (-1),
the coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

107

Figure C.2: Effect of Increasing MLDA for Any Alcohol on Demand for Any Organs

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for any organs per 100000 population of that cohort. The coefficient in cohort (-1),
the coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

108

Figure C.3: Effect of Increasing MLDA for Spirits on Demand for Livers

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for livers per 100000 population of that cohort. The coefficient in cohort (-1), the
coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

109

Figure C.4: Effect of Increasing MLDA for Spirits on Demand for Kidneys

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for kidneys per 100000 population of that cohort. The coefficient in cohort (-1), the
coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

110

Figure C.5: Effect of Increasing MLDA for Spirits on Demand for Lungs

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for lungs per 100000 population of that cohort. The coefficient in cohort (-1), the
coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

111

Figure C.6: Effect of Increasing MLDA for Spirits on Demand for Hearts

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for hearts per 100000 population of that cohort. The coefficient in cohort (-1), the
coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

112

Figure C.7: Effect of Increasing MLDA for Any Alcohol on Demand for Livers

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for livers per 100000 population of that cohort. The coefficient in cohort (-1), the
coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

113

Figure C.8: Effect of Increasing MLDA for Any Alcohol on Demand for Kidneys

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for kidneys per 100000 population of that cohort. The coefficient in cohort (-1), the
coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

114

Figure C.9: Effect of Increasing MLDA for Any Alcohol on Demand for Lungs

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for lungs per 100000 population of that cohort. The coefficient in cohort (-1), the
coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

115

Figure C.10: Effect of Increasing MLDA for Any Alcohol on Demand for Hearts

Note: this figure plots the balanced event-study estimates of the impacts of the MLDA policy increase. The dependent
variable is the cohort’s demand for hearts per 100000 population of that cohort. The coefficient in cohort (-1), the
coefficient for last cohort not affected by the policy is normalized to zero (and omitted). Control variables include:
per capita income, unemployment rate, share of high school graduates for population of age 25 and older, per capita
medical aid, share of black population. These estimates are taken from a balanced event study sample where we
retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Standard errors are clustered at state
level.

116

Table C.1: Timing Of Lowering the Minimum Legal Drinking Age Below and Raising to 21 Years
for Distilled Spirits During 1970s and 1980s

States raising MLDA
for distilled spirits
to 21 during 1980s

States lowering MLDA
for distilled spirits
below 21 during 1970s
prior to 1970 HI, LA, ME, NE, NY
1970
1971
1972

AK
MT, TN, VT
AZ, CT, DE, GA, IA,
ID, MI, RI, WV, WI
FL, MA, MN, NH,
NJ, TX, WY

Years

1973
1974
1975
1978
1980
1982
1983
1984
1985

1986
1987
1988
1995
States with
MLDA=21
for 1970s
and 1980s

AL

MI

NJ
AK, DE, RI, TN
AL, AZ, CT, FL, MA,
ME, NE, NH, NY
GA, HI, IA, MN,
TX, VT, WI, WV
ID, LA*, MT
WY
LA*

AR, CA, CO, DC, IL, IN, KS, KY, MD, MO, MS, NC, ND,
NM, NV, OH, OK, OR, PA, SC, SD, UT, VA, WA.

Note: the timing of lowering and increasing minimum legal drinking age is from Wagenaar (1981), O’Malley and
Wagenaar (1991), and ProCon.org (2016). * Although de jure Louisiana has increased the minimum legal drinking age
to 21 in 1987, due to a loophole, youth of age below 21 could get access to alcohol, and de facto increase of minimum
legal drinking age happened in 1995, see Bragg (1996). ** Oklahoma (OK) according to DISCUS (1959-1972) all
beverages were 21 except for 3.2 beer -18 for female off-sale, 32 on-sale, Male - 21. In 1976 MLDA because 18 for
both males and females.

117

Table C.2: Timing Of Lowering the Minimum Legal Drinking Age Below and Raising to 21 Years
for Any Type of Alcohol During 1970s and 1980s

States lowering MLDA
for at least some type of
alcohol below 21 during 1970s
CO, DC, HI, ID, KS, LA,
ME, MS, NC, NE, NY, OH,
OK**, SC, SD, WI, WV
AK
MT, TN, VT
AZ, CT, DE, GA, IA, MI, RI
FL, IL, MA, MN, NH, NJ, TX, WY
MD, VA
AL

States raising MLDA
for all types of alcohol
to 21 during 1980s

MI
IL
MD
NJ, OK
AK, DE, RI, TN
AL, AZ, CO, CT, FL, KS,
MA, ME, NE, NH, NY, VA
DC, GA, HI, IA, MN, MS,
NC, SC, TX, VT, WI, WV
ID, LA*, MT, OH
SD, WY
LA*

AR, CA, IN, KY, MO, ND, NM, NV, OR, PA, UT, WA

Years

prior to
1970
1970
1971
1972
1973
1974
1975
1978
1980
1982
1983
1984
1985

1986
1987
1988
1995
States with
MLDA=21
for 1970s
and 1980s

Note: the timing of lowering and increasing minimum legal drinking age is from Wagenaar (1981), O’Malley and
Wagenaar (1991), and ProCon.org (2016). * Although de jure Louisiana has increased the minimum legal drinking age
to 21 in 1987, due to a loophole, youth of age below 21 could get access to alcohol, and de facto increase of minimum
legal drinking age happened in 1995, see Bragg (1996). ** Oklahoma (OK) according to DISCUS (1959-1972) all
beverages were 21 except for 3.2 beer -18 for female off-sale, 32 on-sale, Male - 21. In 1976 MLDA because 18 for
both males and females.

118

Table C.3: Estimated Effects of MLDA 21 for Spirits and Alcohol on Demand for Transplants

VARIABLES
5 years pre-policy

4 years pre-policy

3 years pre-policy

2 years pre-policy

1 year pre-policy

Year the MLDA 21 took effect

1 year post-policy

2 year post-policy

3 year post-policy

4 year post-policy

5 year post-policy

6 year post-policy

7 year post-policy

8 year post-policy

9 year post-policy

10 year post-policy

Observations
R-squared

MLDA21 for Spirits

no controls with controls
7.363
(8.847)
11.730
(9.991)
10.576
(8.106)
7.887
(6.381)

7.892
(13.401)
11.502
(11.802)
9.940
(9.579)
7.163
(7.142)

MLDA21 for Alcohol

no controls with controls
12.430*
(7.028)
10.670
(7.548)
14.657**
(6.530)
7.005
(4.738)

4.089
(9.365)
3.865
(8.061)
10.050
(6.704)
4.492
(4.830)

-3.372
(7.245)
-13.287**
(6.107)
-27.144***
(8.506)
-27.711**
(10.700)
-39.860***
(8.596)
-51.160***
(9.329)
-61.619***
(9.212)
-73.255***
(9.824)
-78.636***
(9.516)
-87.645***
(11.464)
-102.006***
(8.730)
416
0.797

-1.907
(7.656)
-9.777
(7.529)
-22.447**
(10.409)
-22.436*
(11.764)
-33.577**
(14.286)
-43.699***
(15.670)
-53.002***
(18.626)
-63.087***
(21.166)
-67.147**
(25.031)
-74.542**
(30.543)
-86.845***
(31.066)
416
0.802

-1.063
(6.103)
-7.430
(5.677)
-22.527***
(6.957)
-20.739**
(9.085)
-28.107***
(8.792)
-37.510***
(11.040)
-44.025***
(12.577)
-55.401***
(13.552)
-58.989***
(13.176)
-69.134***
(14.259)
-83.885***
(13.251)
592
0.799

2.152
(6.267)
-0.966
(6.958)
-13.288
(8.409)
-8.833
(10.954)
-13.256
(12.083)
-19.498
(14.603)
-23.142
(17.726)
-31.465
(19.395)
-32.210
(20.251)
-38.848
(23.670)
-49.292**
(23.122)
592
0.806

Note: this table shows the impacts of the MLDA policy increase. The dependent variable is the cohort’s demand for
any organs per 100000 population of that cohort. The coefficient in cohort (-1) is the reference cohort and omitted.
Control variables: per capita income, unemployment rate, share of high school graduates for population of age 25 and
older, per capita medical aid, share of black population. These estimates are taken from a balanced event study sample
where we retained only 5 cohorts before first affected cohort by policy and 10 cohorts after. Robust standard errors in
parentheses. *** p<0.01, ** p<0.05, * p<0.1. Standard errors are clustered at state level.

119

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