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THREE ESSAYS ON FIRM STRATEGY
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THREE ESSAYS ON FIRM STRATEGY AND PUBLIC POLICY

By

Byung-Cheol Kim

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Economics

2007

ABSTRACT
THREE ESSAYS ON FIRM STRATEGY AND PUBLIC POLICY
By

Byung-Cheol Kim

Firms in oligopoly can take various actions for strategic reasons. Three chapters
in this dissertation respectively address three different topics of consumer information
sharing, preliminary injunction and tying. I am particularly interested in studying
strategic incentives to such firms’ behaviors, market outcome, welfare effect, and
implications on public policies.

In the first chapter, I study oligopolistic firms' incentives to share customer
information about past purchase history in a situation where firms are uncertain about
whether a particular consumer considers the product offerings complements or substitutes.
I show that both the incentives to share customer information and its effects on
consumers depend crucially on the relative magnitudes of the prices that would prevail in
the complementary and substitute markets if consumers were fully segmented according
to their perceptions. This chapter has important implications for merger analysis in which
the primary motive for merger is the acquisition of another firm's customer lists. I also
find that the informational regime firms reside in can have an influence upon the choice
of product differentiation. Additionally, my analysis suggests a new role of middlemen as
information aggregators.

The second chapter in this dissertation offers a model of preliminary injunctions

in the context of antitrust litigations. I study the role of preliminary injunctions as a noisy

information message service in addition to its role of the channel to save a plaintiff‘s
irreparable harms. Interestingly, I find both cases such that either the plaintiff with a high
damage or the one with a low damage moves for preliminary injunctive reliefs as
equilibrium phenomena. 1 not only analyze the decision-makings about the motion for
injunction, optimal settlement offers and litigation/settlement, but also discuss various
issues associated with preliminary injunctions based on my model.

In the third chapter, I study a new rationale for the tying practice between
complementary goods in the presence of switching costs. I find that the monopolist may
strategically commit to tying in order to capture the dymmic rents associated with those
who have relatively high switching costs, especially if the monopolist has an inferior
complementary product to the rival firm’s complementary one. I also show that the
monopolist’s tying may decrease both consumer surplus and social welfare, because

switching costs are endogenously incurred and the consumers end up using an inferior good.

To my wife, Sangeun Lee, and my parents
for their love, patience, prayer and support.

iv

ACKOWLEDGEMENTS

First of all, I would like to thank my advisor, Professor Jay Pil Choi, who has
provided encouragement throughout the entire process and exhibited seemingly endless
patience with his generous time for discussion and detailed comments on all my drafis.
There is no doubt that it would have never been possible to finish this dissertation
without his help. In fact, about four years ago when I had been admitted to several
Economics Ph.D. graduate programs, I had no hesitation in choosing this Michigan State
University over other prestigious programs at least because of his presence in here MSU.
When my colleagues and professors in Seoul National University asked why I had chosen
MSU over other programs — some were arguably high ranked programs and financial
supports were seemingly better, I reminded them of the fact that I would like to study
Industrial Organization under Professor “J ay Pil Choi,” then they understood my decision
without asking further. Now four years later from then, I have no regret for my decision; I
haven’t ever had a reason for such regret. Among lots of significant choices in my life,
my best choice — so, I did a good job as a utility maximizing decision maker — was to
study under his wing.

Of course, I am certain of my indebtedness to other committee members. I would
like to particularly thank Prof. Thomas Jeitschko not only for his generous help for the
second chapter of this dissertation, but also lots of discussion and sharing his superb
intelligence with me for the entire dissertation. It has been a great blessing and honor to
me to have him in my dissertation guidance committee. Professor Carl Davidson has kept
encouraging me to the completion of my dissertation through questions and discussion in

all presentations throughout the academic process. I cannot and won’t forget his

encouragement for my research, which has led me to work hard to finish this dissertation.
Professor Steve Wildman also shared his great insight with me through detailed
comments and questions on every possible opportunity. His comments on the final draft
of this dissertation have improved the quality to a significant extent.

There have been a number of other faculty members who provided invaluable
guidance at various stages of the process. Especially, I would like to thank Prof. Jack
Meyer, Prof. Mike Conlin, and Prof. Susan Zhu who has helped me grow up in
economics through their excellent teaching and sharing their intelligence at any time. I
also express my special thanks to our superb administrative staffs, especially to Margaret
Lynch, Jennifer Carducci, and Stephanie Opatmy-Smith.

In addition, I would like to thank my colleges in our economics department who
has helped me in various ways and discussed the drafts of this dissertation with me,
especially to Brian Mcnamara, Nicholas Sly, Deborah Foster, Nathan Cook, Ilya
Rakhkovskiy, Kwang-myung Hwang, Jongwoo Park and Jaesoo Kim.

Finally, I reserve my very special thanks for my family. My wife, Sangeun Lee,
has helped me in all parts of my life and shared my burdens in everything. Without her
love, patience and support, this dissertation would never have been completed. I also
would like to thank to my son, Hee-Chan, and my daughter, Hee-yeon, for the full of joy
and delight they have brought me. My family is the best gift in this world from my God. I
also express my appreciation to my father, Wuntae Kim, and my mother, Yoonja Lee,
who have prayed to God in every morning with endless love and support. Without their
prayers and support, I could have never done this job. I also thanks to my parents-in-law

who has encouraged and supported me.

vi

TABLE OF CONTENTS

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

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

CHAPTER 1: Customer Information Sharing: Strategic Incentives And New

Implications ................................................................................................................... 1
1. Introduction ..................................................................................................... 1
2. The Model .................................................................................................... 9
3. Sharing ofCustomer Information 13
4. No Sharing of Customer Information ............................................... 20
5. Incentives to Information Sharing and its Effect on Consumers ............... 23
6. Implications of the Model ........................................................... 27
7. Robustness and Extensions ......................................................... 31
8. Concluding Remarks .................................................................. 36
Appendix A 37
Appendix B .............................................................................. 39
References ....................................................................................................... 44

CHAPTER 2: A Model Of Preliminary Injunctions: Is It A Cheap Message

Service? .......................................................................................................................... 47
1. Introduction ..................................................................................................... 47
2. A Simple Model of Preliminary Injunctions .................................................... 52
3. Incentives to file for a Preliminary Injunction ................................................. 57
4. An Extended Model ........................................................................................ 64
5. Discussions for Further Extensions ................................................................. 79
6. Concluding Remarks.............. ..................................................................... 81
References ...................................................................................................... 83

CHAPTER 3: The Strategic Tying With Consumer Switching Costs ............................ 84
1. Introduction ................................................................................................... 84
2. The Model ..................................................................................................... 89
3. The Equilibrium Analysis: with tying and without tying 91
4. The Incentive to Tying and its Effect on the Competitor ....................... 99
5. The Welfare Analysis ................................................................... 105
6. Concluding Remarks ..................................................................................... 107
Appendix ............................................................................................................ 109
References ....................................................................................................... 1 1 1

vii

LIST OF TABLES

CHAPTER 1
l-A-l. Equilibrium outcomes: No information sharing is preferred ............................ 42
1-A-2. Equilibrium outcomes: Information sharing is preferred .................................. 43
CHAPTER 2
2-1. Likelihood matrix for a preliminary injunction ................................................... 56
CHAPTER 3
3-]. Consumer surplus and social welfare with and without tying ................................. 106

viii

LIST OF FIGURES

CHAPTER 1

Figure 1-1. The externality problem in the complementary market ................................ 17
Figure I-A-l. Comparison of equilibrium profits for 0 ~ U[0,1], )7 =0.2 ................ 42
Figure 1-A-2. Comparison of equilibrium profits for 0 ~ U[0,1], )7 =O.5 ................ 43
CHAPTER 2

Figure 2-1. Timing of the game ...................................................................................... 54
Figure 2-2. The plaintiffs with large damages move for injunction ........................ 61
Figure 2-3. The plaintiffs with small damages move for injunction ...................... 63
Figure 2-4. The choices of plaintiffs I ......................................................... 73
Figure 2-5. The choices of plaintiffs II ......................................................... 77
CHAPTER 3

Figure 3-1. The consumer choices in period two ............................................................ 96
Figure 3-A-1. The welfare comparison with and without tying ............................ 110

ix

Chapter 1. Customer Information Sharing:

Strategic Incentives and New Implications

In this paper, we study oligopolistic firms’ incentives to share customer information
about past purchase history in a situation where firms are uncertain about whether a
particular consumer considers the product offerings complements or substitutes. We
show that both the incentives to share customer information and its effects on con-
sumers depend crucially on the relative magnitudes of the prices that would prevail in
the complementary and substitute markets if consumers were fully segmented accord-
ing to their preferences. This paper has an important implication for merger analysis
when the primary motive for merger is the acquisition of another firm’s customer
lists. We also find that the informational regime firms reside in can have an influence
upon the choice of product differentiation. Additionally, our analysis suggests a new

role of middlemen as information aggregators.

1 Introduction

In this paper we study oligopolistic firms’ incentives to share customer information
about past purchase history. More specifically, we consider a situation in which the
relationship (i.e., the degree of substitutability or complementarity) between the prod-
uct offerings by oligopolistic firms is customer-specific, private information unknown
to the firms. Goods are substitutes for some customers and complements for others.
The examples abound. Air travel and rental car service, for instance, can be com-

plements for some travelers who use both modes of transportation in the same trip.

However, they can be substitutes to others, especially for short- to medium—distance
travels.1 Another example is the relationship between printed versions of novels and
motion picture adaptations. For some consumers they can be competing products
whereas for other consumers they can be complements.2

The sharing of customer—specific transaction records allows the firms to update
information about a particular consumer’s preference towards the products. In such a
setup, we analyze the impact of customer information sharing on market competition
and the firms’ incentives to share information. These questions are especially relevant
in electronic commerce where consumers’ records of previous purchases can be easily
traced and stored by electronic "fingerprint."3 Our study also has important impli-
cations for merger analysis in which the primary motive for merger is the acquisition
of another firm’s customer lists.

We consider a simple two-period model to address the issues related to interfirm
information sharing. Each firm collects information about its own sales record. As
a result, at the end of the first period, each firm acquires information concerning
whether or not a particular individual has bought a unit of its own product through

its first-period marketing. In the absence of information sharing, however, each firm

remains uncertain over whether the customer has also bought a unit of the other firm’s

 

1More people rent a car and drive to their destinations as airport security inspections have become
more of a hassle following the 9/11 terrorist attack.

2Motion picture versions were initially thought to be competing against printed versions when
they were first introduced. However, film adaptations and printed novels are widely perceived to be
complements now. See Gentzkow (2007) for more examples.

3E—commerce activities have rapidly grown and play an increasingly important role for the US.
economy. According to the most recent data from the Census Bureau of the Department of Com-
merce, total e—commerce sales for 2006 were estimated at $108.7 billion, accounting for 2.8 percent
of total sales in 2006. The figure for e-commerce sales is an increase of 23.5 percent from 2005. In
contrast, total retail sales in 2006 increased only 5.8 percent from 2005.

2

product. In contrast, with information sharing each firm can learn the complete his-
tory of the past transaction record of a specific consumer. The aggregation of customer
lists allows the firms to infer whether that customer considers the goods substitutes
or complements. We analyze how this customer-specific information concerning the
relationship of the two products can be used as a basis for price discrimination in the
second period.

The analysis of the effects of information sharing on market competition and
each firm’s incentives to share information with other firms is complicated because
the other firms, with whom the customer information might be shared, could be
potential rivals in the substitute market and at the same time partners in the com-
plementary market, depending on consumer types. We Show that the incentives to
share customer information depend crucially on the relative magnitudes of the prices
that would prevail in the complement and substitute markets if consumers were fully
segmented according to their preferences for the two products. The intuition for this
result is as follows. With information sharing, the firms can distinguish consumers
who consider the two products complementary from those who consider them sub-
stitutes. As a result, they charge different prices depending on consumer types. For
consumers who consider the two products complementary, the two firms charge too
much overall with information sharing. This is due to the Cournot effect in the com-
plementary monopoly problem. The two firms could have obtained a higher profit
by cooperatively lowering their individual prices as if they were a merged monopo—
list. This inefficiency in a nonc00perative equilibrium occurs because the two firms
do not internalize the interdependence of their pricing strategies. In contrast, for

3

consumers who consider the two products substitutes, the two firms charge too little
with information sharing from the perspectives of joint profit maximization due to
competition. Without information sharing, each firm who maximizes its expected
profit must post a single price which is an (weighted) average of the prices that would
have prevailed under information sharing. Suppose that the price for consumers who
regard the products as substitutes is lower than that for consumers who consider
them complementary under information sharing. Then, the average price mitigates
the externality problem in the complementary markets. Additionally, the average
pricing relaxes competition in the substitute market enabling them to extract more
rents. On both accounts, the firms are better off without information sharing. Of
course, if we consider the other case where the full information price in the substitute
market is higher than that in the complementary market, information sharing leads
to a higher profit in the opposite manner.

The effect of information sharing on consumers also differs depending on the rela-
tive magnitudes of full information prices in the complementary and substitute mar-
kets and across consumer types. For instance, when the full information price in
the substitute market is higher than that in the complementary market, information
sharing benefits consumers who regard the two products as complements but hurts
those who regard them as substitutes. The impact on consumers is reversed if the full
information price in the substitute market is lower than that in the complementary
market.

The intuition for our main result also provides a new perspective on the deter-
minants of the degree of product differentiation. Firms potentially face a trade-off

4

between a higher profit associated with highly differentiated goods in the substitute
market and the potentially aggravated externality problem in the complementary
market when information sharing is banned and the firms are forced to charge one
price. This implies that the informational regime firms reside in can have an influence
upon the choice of product differentiation.

Our basic model analyzes direct exchange of customer information between the
firms in the market. Our analysis, however, also has implications for other channels of
information aggregation. For instance, our analysis suggests a new role of middlemen
— the intermediaries between the seller of a good and its potential buyers — as infor-
mation aggregators. If the direct exchange of customer information between firms is
banned due to either privacy concerns or antitrust reasons, the presence of middlemen
such as Amazon, eBat , Google check-out can benefit firms and some consumers by
functioning as lawful institutions in the facilitation of information aggregation. To
the best of our knowledge, this role of middlemen has not yet been addressed.4t

In addition, our model provides a new rationale for merger in which the primary
motive for merger is the acquisition of another firm’s customer lists rather than its real
assets.5 Even if a merger does not lead to a higher market-power or cost-synergies by
eliminating some duplications in production or marketing, it still can be a profitable

strategy only due to the value of customer lists held by its merger partner. The recent

 

4See Rubinstein and Wolinsky (1987) and Yavas (1994) for an analysis of middlemen as an
intermediary to reduce transaction costs in bilateral search economies with trade frictions.

5Customer information is one of intangible assets acquired through a merger, according to ’An-
titrust division policy guide to merger remedies (October 2004)’ by US. Department of Justice,
Antitrust division (http://www.usdoj.gov/atr/publiC/guidelines/205108.htm). However, there is
no formal analysis that recognizes customer list as a primary driver of merger.

acquisition of CDNow by Bertelsmann is a case in point. CDNow, a web-based startup
company founded in February 1994, publicly announced that its cash assets were only
sufficient to sustain another six months of operations in March 2000. Its major asset
was its customer list of 3.29 million in June 2000; it did not have substantial physical
assets like other online retailers. In July 2000, however, Bertelsmann acquired CDNow
for $117 million in an all—cash deal appreciating the value of CDNow’s customer base.6
Our study can offer a theoretical foundation for the M&A of a firm whose only asset
is its customer lists in the context of behavior—based price discrimination.7

Our paper is related to two strands of literature: information sharing and behavior-
based price discrimination. There is by now an extensive literature that studies the
issue of information sharing between oligopolistic firms concerning market demand
and production cost. For example, Clarke (1983), Crawford and Sobel (1982), Gal-Or
(1984, 1985), and Novshek and Sonnenschein (1982) address the incentives to share
private information about uncertain market demand that is common to every firm.
Fi'ied (1984), Shapiro (1986) and Armantier and Richard (2003) analyze incentives

to exchange information about private cost that is idiosyncratic to each firm.8 Our

paper, in contrast, considers the sharing of customer-specific transaction records and

 

“See Gupta and Lehmann (2003) for more details about CDNow case and the value of customers.

7See Banal-Estanol (2007) for an analysis of horizontal mergers that explicitly takes into account
sharing of private information of merging parties. However, the nature of private information is
about uncertain demands or costs as in the existing information sharing literature.

3There have also been studies for the incentives to share credit information among financial
intermediaries in the finance literature. Bouekaert and Degryse (2005) and Gehrig and Stenbacka
(2001), for instance, analyze the issue of credit information sharing in the context of entry-deterrence
or as a collusive device.

9

its implications for dynamic price discrimination.

As in our paper, the literature on behavior-based price discrimination considers
how the information gleaned from past sales record can reveal customer-specific pref-
erences which can be used as a basis to practice personalized pricing and its impact
on market outcomes such as consumer- and producer surplus.10 Acquisti and Var-
ian (2005) consider a setting in which rational consumers with constant valuations
for the goods purchase from a monopoly merchant who can commit to a pricing pol-
icy. They show that although it is feasible to price so as to distinguish high-value
and low-value consumers from advances in information technology, the merchant will
never find it optimal to do so, echoing the results from the prior literature on dy-
namic price discrimination.11 They then extend their model to allow the seller to
offer enhanced services to previous customers and find that conditioning prices on
purchase history can be profitable.12 Chen (1997), F‘udenberg and Tirole (2000), and
Taylor (2003), in contrast, consider a duopolistic setting with competition to analyze
the implications of price discrimination based on purchase history. Unlike previous
work on behavior-based price discrimination, our innovation in this paper is to allow
the possibility that product offerings can be either substitutes or complements. The
existing literature typically assumes the relationship between products is one of the

two types and is known to the firms that make strategic choices. One notable excep-

 

( ‘ . . . . . . . .
JSee Lru and Serfes (forthcoming) for several real practices of companies who particrpate in selling
and trading of customer information.

I" For an excellent survey of the literature on behavior-based price discrimination, see Fudenberg
and Villas-Boas (forthcoming).
11This is due to strategic demand reduction by sophisticated consumers. See Stokey (1979).

12For a related issue of consumer privacy, see Taylor (2004) and Calzolari and Pavan (2005).

tion is Gentzkow (2007) who explicitly analyzes the possibility that product offerings
can be either substitutes or complements as in our paper. Even though our paper
and Gentzkow’s share the same basic premise, the focus of his paper is very different
from ours. He is mainly concerned with developing a new econometric technique to
estimate the impact of new goods that accounts for the possibility that the new goods
can be complements to the existing goods.

Liu and Series (forthcoming) is closest to our paper in that it also takes a step
in the direction of examining the firms’ incentives to share their customer-specific
information with other firms. They consider a Hotelling model in which each firm
can collect detailed customer information about their own customers, indexed by a
precise location in the Hotelling model. With information sharing, firms can practice
perfect price discrimination against not only their own previous customers, but also
the consumers who bought from rival firms. However, there is one key difference in
the man qualitative results. In Liu and Serfes, neither firm finds it profitable to
share information when firms have equal customer bases. The incentive to share
information arises only when there is enough asymmetry in their market shares. In
such a case, the sharing of information takes the form of one-way transaction in which
the firm with the smaller customer base sells its information to the firm with the larger
customer base while the "big" firm never has incentives to sell its information to the
smaller rival firm. In our model, however, the information sharing takes place between
symmetrically positioned firms. In addition, the relationship between the two firms
is always competitive and the pooling of information does not reveal any information

about the relationship (complements or substitutes) between the two products, which

8

is a key aspect in our framework. Liu and Serfes and our paper complement each other
in that we explore the incentives to share information in the firms’ quest for qualitative
improvement of information, while they study the same issue from the firms’ strategic
incentives to enlarge the information base.

The remainder of the paper is organized as follows. Section 2 describes the basic
model. In section 3, we derive the market equilibrium in the presence of information
sharing and analyze how the information sharing can be used as a basis for behavior-
based price discrimination. Section 4 analyzes the market equilibrium in the absence
of information sharing. In section 5, we analyze incentives to share information
and the impact of information sharing on consumer welfare. In section 6, we discuss
a couple of interesting implications that can be drawn from our simple framework
such as the role of middlemen and the relationship between information sharing and
product differentiation. In section 7, we explore some possible extensions and check
the robustness of our main results by relaxing some of our initial assumptions. Section
8 concludes. The proofs for propositions are relegated to Appendix A. An explicit

analysis of the example with uniform distribution is contained in Appendix B.

2 The Basic Model

Consider two goods, A and B, respectively produced by firm A and firm B, that
consumers may regard either as complements or as substitutes depending on their
preferences. For simplicity and analytical tractability, we consider only two distinct

groups of consumers: one group of consumers in proportion /\, called group C, regard

the two goods as complements and the other group of consumers in proportion (1— A),
called group S, consider them as substitutes. The proportion A is common knowledge,
where /\ 6 (0,1).

The model is a two—period setting in which each consumer purchases at most one
unit of each good per period. Each firm is able to keep track of individual transaction
records of its customers. In particular, this assumption implies that at the end of the
first period, each firm knows whether or not a particular consumer has bought a unit
of its own good in the first period. This information allows each firm to engage in
behavior-based price discrimination in the second period, that is, charging different
prices to consumers with different purchase histories.

Let us denote a consumer’s purchase decision by (a,b), where a and b respec-
tively refer to decisions concerning products A and B with 1 representing the pur-
chase of the relevant product and 0 representing no purchase. A consumer’s pur-
chase history in the first period then can be described by an element of a set H =
{(0,0), (1,0), (0, 1), (1, 1)}. For instance, a consumer with a purchase history (1,0) is
the one who purchased product A, but not B in the first period.

We consider two potential information regimes. Without any sharing of customer
information at the end of the first period, each firm’s knowledge about each consumer’s
purchase history is limited to its own product. Each consumer’s past purchase his-
tory concerning the other firm’s product is in the dark. With partial knowledge
of customer purchase history, each firm’s information set is coarser than the set of

potential history H. We denote firm A’s information set concerning a particular con-

10

sumer by I~ A = {(0, (b), (1, 96)}, where ([5 stands for non-availability of information.”

Similarly, firm B’s information set can be represented by f B = {(65, 0), ((1'), 1)}. If the
two firms exchange customer lists at the end of the first period, both firms know the
complete history of each consumer’s purchase. In this case, the information set of
both firms concerning each consumer is the same as the set of potential history for
each consumer, that is, [A = 1B = H = {(0,0), (1,0), (0, 1), (1, 1)}.

Within each group of consumers (C or S), we assume heterogeneity of preferences.
More specifically, a consumer of type 6 in group C has the following net surpluses

from each possible choices in each period.

6 — p A — p B both A and B are purchased
“C(PAaPBi 9) = —pz' if only good 2' is purchased (1)
0 neither one is purchased

where pi denotes firm is price for i = A, B and the superscript C indicates that
the consumer belongs to group C. The type parameter 6 represents the consumer’s
reservation value for the pair of products viewed as complementary. We assume that
6 is distributed over an interval [6, 6] with distribution and density functions of F (6)
and f (6), respectively, where with 0 S Q S 6. The consumer in group C does not
derive any benefit from consuming only one good, thus earning the utility of —p,— when
only one good is purchased. The utility from buying neither A nor B is normalized

to zero.

 

l“’Variables associated with the regime of no information sharing are denoted with a tilde.

11

On the other hand, the consumers in group S are heterogeneous with respect to
their relative preferences for B over A. We capture this feature with the parameter
7. More precisely, we assume that consumer type 7’s reservation values for goods A
and B are given by ”A = v —% and ”B = v + :31, respectively. That is, ”B = ’UA +7
for ’7 E [1, 77"] with a positive value of 7 indicating that the consumer prefers good
B to good A.” Let C(7) and 9(7) denote the distribution and the density of 7,

respectively. For simplicity, we also assume that C is symmetric about zero, with

'77 = —1 > 0. A consumer in group S has the surplus of each possible choice as
follows.
max{vA, vB} —- p A — p B both A and B are purchased
S .,,, _. -f ..
u (PAaPBa I) - v,- — p,- 1 only good 2 IS purchased
0 neither A nor B is purchased

(2)
where the superscript S indicates that the consumer belong to group S. The con-
sumer in group S, who regards two goods as substitutes, earns the net surplus of
max{vA, vB} — p A — p B from buying both A and B; the utility of buying only good
i is set to be ’0,- — pi. We assume that v is high enough to ensure that each consumer
in this group buys at least one unit of either A or B .15 The utility from no purchase
is set to zero.

Finally, we assume that a consumer belongs to the same group over the two

 

14The same framework for the horizontal product differentiation is used in Fudenberg and Tirole
(2000).

15This model specification is somewhat restrictive in that we do not allow the consumers in group
S to opt for no purchase. The qualitative results of this paper, however, are robust to the relaxation
of this assumption, which will be discussed in section 7.

12

periods, that is, the group characteristics is a fixed trait. However, we assume that the
parameters 6 and '7' are independently and randomly drawn from their distributions
in each period. This allows us to isolate the strategic incentives to share information
concerning consumers’ preferences towards the products without being concerned with
the issue of customer poaching and/or personalized pricing within the same group,
which has been extensively studied in the literature [see Fudenberg and Tirole (2000),
Taylor (2003, 2004), and Acquisti and Varian (2005)]. Both firms have the same
constant unit-cost of production, d. Finally, F and G satiSfy the monotone hazard
rate (MHR) condition: f (6) / [1 — F (6)] and g(*y)/[1 — C(7)] are strictly increasing in

16

6 and 7, respectively, which ensures the first-order condition for optimization to be

sufficient for the second-order condition.

3 Sharing of Customer Information

If firms exchange their customer lists acquired through the first-period marketing,
they are able to draw inferences about customers’ preferences towards the two prod-
ucts. This implies that they are able to charge different prices depending on whether
consumers consider the two products as substitutes or complements in the second-
period. Consequently, the two groups of consumers are segmented and each firm

plays nonc00perative pricing games in two separate markets.

 

16Roughly speaking, this condition means that the density functions f and g do not grow too
fast, which is satisfied with most of the well—known distribution functions including the uniform,
exponential, and normal distributions.

13

3.1 The market for group C consumers

We first consider the consumers who consider the two goods complementary. It is a
standard result that the two firms acting independently charge too much overall from
the collective viewpoint of the firms. This is due to the externality problem, noted by
Cournot(1838), with two distinct firms acting independently as a monopolist of each
complementary good. The two firms could have obtained a higher profit if they had
cooperatively lowered their individual prices as if they were a merged monopolist.
This inefficiency arises because the independent firms do not internalize the inter-
dependence of their pricing strategies, whereas the merged firm does.17 Consumer
surplus also increases with a merged monopolist due to a lowered total price for the
goods.18

Let us briefly show that this classic result applies to the market for group C

consumers.19 The optimal decision for consumers in group C can be characterized

by a simple cut-off rule:

Buy both A and B 6 Z 6*
if (3)
Buy neither A nor B 6 < 6*
where 6* E pg + pg denotes the threshold consumer who is indifferent between the

 

17This problem occurs as a dual form in the standard Cournot quantity-setting with substitutes,
which Sonnenschein (1968) noted.

18Clearly, this case is still not the first—best outcome: the price with the integrated monopolist is
still above the total marginal cost.

19In a similar vein, an integrated upstream licensor holding patents for several complementary
technologies can charge a cheaper total price compared to the case of separate patent holders for
each innovation. This suggests a welfare-enhancing role for patent pools in case of complementary
technologies. See Lerner and Tirole (2004) for a formal discussion of this issue.

14

two choices. Those with 6 2 6* buy both goods since their willingness to pay for a
pair of complements is greater than or equal to the total price for the two goods, while
those with 6 < 6* buy neither due to a relatively low reservation value for consuming
the two complementary goods. The demand for each good thus is given by 1 — F (6*).

F irm i’s profit maximization problem can be written as

Mgr: n? = (pf? — d) [1— Fa? + 19%)} . (4)
Pi

C

The first-order condition with respect to each firm’s full information price, p 2' , yields

[1- 17(1)? + 195-3)} - (I)? - d)f(p,-C +19?) = 0 (5)

for i = A,B and 2' 75 j. The two first—order conditions implicitly define each firm’s
best-response function of which slope is smaller than negative one. This implies that
two responses meet each other at most once where we find a unique, stable, symmetric

Nash equilibrium that is implicitly defined by

_ C
C d+L_£(_2_P;)_

6
f (2pc) ( )

On the other hand, an integrated monopolist would have solved the following

profit maximization problem

Iggy ,m = (Pm — 2d)i1 - F(Pm)l <7)

15

where Pm denotes the total price for a pair of the two goods under monopoly. The

first-order condition for this problem yields

[1 — F(P”’)i — (Pm — 2d)f(P”’) = 0. <8)

and thus
1 - F (Pm)

Pm = 2d
+ f(Pm)

(9)

By comparing (5) and (8), we find that the left-hand-side of (8) evaluated at the
price of Pm = 2pc becomes negative, which implies that the integrated monopolist
charges less than the sum of prices independent firms would charge in duopoly and
that the profit associated with the monopoly case is larger than the sum of two firms’

C

profits under duopoly.20 Figure 1-1 shows the relationship of p and pm graphically.

 

2”Assuming a uniform distribution of 6 on [0, I] and d = 0, the joint—profit maximizing price for

a pair of complements is equal to :3, and thus one firm is required to charge the price of i and gets

the profit of 1. However, with two firms non-cooperatively competiing, the equilibrium price that
8

each firm charges is % and its profit becomes %.

16

NI

 

...................................................................................
c
.-
o
‘-
-

 

,
0"
a
,c
.
.a
u
a
.0
.
.-
--
n
.
,o
o
.-
l.-
,

 

 

l— F(x)
f(x) .-
1’: :-
..... ' 2
‘--------::. ......... _ 1_F(A.)
' 2f (x)
b
m 2pc A

Figure 1-1. The externality problem in the complementary market

3.2 The market for group S consumers

A consumer who regards the two goods as substitutes buys a unit of either A or

8.21

The consumer will compare the net surplus of each choice and choose the good that

yields a higher surplus. The optimal decision rule is given by

choose A over B

choose B over A

l

 

_f vA—pEZvB—pg (i) 737* (10)
vA—pi<vB—p§ 7>7*

“In the Appendix A. we show this claim rigorously.

17

where 7* E pg — pin Since the demand for firm A is C(7*), the optimization

problem for firm A in the market of substitutes is given by

S S S S

ng NA = (22A - d)G(pB - ml. (11)
PA
The first-order condition for this problem yields
{Mi/879i = WE.» — pi) — (pi — mg — p5) = 0. (12)

An increment in the price of good A leads to an increase in the mark-up for the
inframarginal consumers of good A, which is represented by the first term C(pg --
pi) However, firm A loses some consumers at the margin to firm B because of the
increment in pi, which is captured by the second term, —(p§1 — d)g(pg — pS ). The
best-response of p A to a given p B describes the firm A’s optimal price with this
trade-off considered. In a similar manner, we can derive the best—response function
of firm B.

The equilibrium price is uniquely determined because the best responses have

S S

positive slopes that is less than one. The symmetric equilibrium price of p A = p A =
1,5

is given by

1
pS=d+———. an

The mark-up in the market of substitutes is represented by 1/2g(0). Given the as-

 

22This tie-breaking rule is inconsequential because here we consider a continuum of consumers so
that the point mass of critical consumers is zero.

18

sumption that ”y is distributed symmetrically around zero, a larger value 9(0) indicates
that consumers’ preferences are more concentrated around zero and they have less
diverse preferences for the goods. We thus can interpret the reciprocal of 2g(0) as
the degree of heterogeneity in consumers’ relative preferences towards the two sub-
stitute products, which plays a similar role of the transportation cost (or product
differentiation) parameter in the standard Hotelling model.

The following lemma summarizes and compares the two equilibrium prices for

C S

each group, p and p .

Lemma 1 When each consumer’s group identity ( C or S) is revealed to the two
firms via information sharing, the full information price for consumers in group C is

characterized by p0 = d + [1 — F (2pC)] / f (2pc) and the full information price for

_1__
29(0)'

consumers in group S is given by pS = d + Therefore, the relative magnitudes
of these two prices depend on the distributions F and G. In particular, if the two

goods are perceived to be highly differentiated for group S consumers (i.e., g(0) is low),

S C

p will be higher than p with all other things being equal.

Let 7rC and 71’s denote the equilibrium profits in markets for consumer groups C
and S, respectively. With information sharing, each firm’s second-period total profit

from both markets is given by

n2 = MC + (1 — ms. (14)

19

4 No Sharing of Customer Information

4.1 Bayesian updating about group identity

If firms do not exchange their customer lists, each firm only knows whether a partic-
ular consumer is a newcomer or a returning customer. However, each firm is unaware
of whether a consumer has bought from the other firm or not. When a consumer
is a newcomer, not in its customer list at the beginning of the second-period, the
seller can think of two possibilities: the consumer actually considered the two goods
complementary but did not buy either good because of a relatively low willingness
to pay for a pair of goods, or the consumer regarded the goods as substitutes and
bought a good from the other firm in the previous period. On the other hand, facing
a returning consumer already registered in its present customer list, the seller also
can think of two possibilities: the consumer who considered the goods complements
and bought both goods, or the consumer considering the two goods substitutes chose
its own product over the rival’s.

Each firm will update its prior beliefs about the group identity of a particular
consumer, based on his/her past purchase history. Following a Bayesian updating

process, the posterior beliefs of firm A can be derived as follows.

 

0:, 2 AN)
AA —P [CKO’fbll AF(g’)+(1—A)(1—G(3))
,\(1- F(é))

whaawman= as

 

where A94 and A114 denote firm A’s conditional probability that a newcomer and a

20

returning consumer would consider the two goods complementary, respectively, and
6 and *3" denote the first-period thresholds for critical consumers. Similarly, firm B’s

posteriors are given as

 

 

0 = r .. = AF097)
AB ’ P [CIW’OH AF(6) + (1 — new)
A}; s PriC|(¢,1)i = 3(1— m” (16)

/\(1- F(9)) + (1 - A)(1- 0(3))

where A% and A}; denote firm B’s posteriors that a newcomer and a returning con—
sumer would consider the two goods complementary.

Then, obviously, the posteriors A? and All typically differ from the prior A, unless
/\ is either 1 or 0, for i = A, B. In other words, if there exist consumer heterogeneity
with respect to the relationship to the product offerings, firms (sellers) will have
different posterior beliefs about the group identify of a particular consumer based
on the purchase history. This implies that firms may post different prices to the
consumers depending on whether a particular consumer is a newcomer or a returning
customer, even without customer information sharing. Previous studies found that
the discriminatory pricing can be based on the purchase history in the presence of
consumer heterogeneity with respect to reservation valuations (Taylor, 2004; Acquisti
and Varian, 2005), relative preferences (Fudenberg and Tirole, 2000), or switching
costs (Chen, 1997; Gehrig and Stenbacka, 2004). This paper enriches the literature
of behavior-based price discrimination by introducing another possible basis for the

price discrimination that has yet been addressed, to our best knowledge.

21

4.2 Price competition in the second period

Let us describe the firm’s second-period profit maximization problem without infor—

0

mation sharing. Denote pi and p21 the prices that firm i posts for a newcomer and
for a returning customer, respectively. Firm i expects a newcomer to consider the
two goods complementary with probability A? and thus be also offered the newcomer
price from firm j, for i ;A j. In contrast, firm i expects the newcomer to regard the
goods as substitutes with the remaining probability 1 — A? and thus be offered the

price for a returning consumer from the other firm, p}. As a result, firm A’s profit

maximization problem for a newcomer is given by

rig: «9, = (1)91- d){/\94[1— F ()9?4 +p%)] + (1 — A9,)G (12,13 —p94)}. (17)

Similarly, the optimization problem for a returning consumer reads as

Agata: 7612(1)},1— d) {A114[1 — F (p114 +p%3)] + (l —- A114)C(p%—p114)}. (18)
A

we can easily describe firm B ’s optimization problems as well. With the first-order

conditions from these optimization problems, we can derive the symmetric equilibrium

prices, p94 = 19% = p0 and p114 = pi? = p1, and the associated equilibrium profits

per consumer, no and r1. Each firm’s second-period total profit from two markets

22

without information sharing is given by

A

fit, = We“) + (1 — an — can)” +n<1— F<6>)+<1- A)G(i)lr1

r123 = [AF(9)+(1— ace/>176 +lA(1— Fe» + <1 — A><1—- G<i>>1w1 (19)

where the tilde denotes the case of no information sharing.
Now we are ready to discuss the relationship of the second—period equilibrium
prices with and without information sharing. Intuitively, the prices without infor-

0 and p1, will be located between the full information prices. In

mation sharing, p
the presence of uncertainty about the group identity of a consumer, each firm will
post (weighted) average prices of two full information prices in order to maximize its
expected profits. This is similar to the fact that the firms with incomplete informa-

tion about demands or costs must post a weighted average price to maximize their

expected profit in either Cournot or Bertrand competition.

Lemma 2 The equilibrium prices without information sharing are between the full

information prices, i.e., min{pC, pS} g p0,p1 S max{pC, p5} for any A, 0 _<_ A S 1.

To sum up, if the firms share their customer information, they can charge two

C S

distinct full information prices, p and p , according to the group identity. Without

0 and p1 that are averages of

information sharing, the firms post two different prices p
two full information prices based on consumer past purchase history. Therefore, cus-

tomer information sharing provides a more precise basis for the price discrimination

in the second period.

23

5 Incentives to Share Information and Effects on Consumers

In this section, we analyze the firms’ incentives to share their customer information
with the other firms. One novel feature in our model is that the firms with whom
the customer information might be shared could be potential rivals in the substitutes
market and at the same time partners in the complementary markets, depending on
consumer types. We also study the effect of information sharing on consumers from

an antitrust perspective.

5.1 To share or not

In order to investigate the firms’ incentives to share information, we need to compare
overall profits over the two periods with and without information sharing, not only
because sophisticated consumers may strategically manipulate their demands know-
ing ex post discriminatory pricing, but also because the firms might adopt strategic
pricing in the first period even without information sharing. In this section, let us
first study ex post incentives to share information by comparing the second—period
profits only, and reserve more discussion about strategic considerations for Section 7.

In the second period, we can think of two distinct cases according to the relative

C

magnitudes of full information prices, p and p5.23 Let us first consider the case

in which the full information price in the substitute market is lower than that of

S

complementary goods, i.e., p < p0. Then, no information sharing with the average

 

23If the prices for two groups are identical, i.e., pC = ps, the issue of information sharing is no
longer interesting. Each firm has the same mark-up for both groups. The second-period profits with
and without information sharing become identical.

24

price mitigates the externality problem in the market of complements, as long as
pS is so low that p0 and p0 are far below the joint-profit maximizing price, pm.
Furthermore, average pricing softens competition in the substitute market where each
firm can extract a more rent.24 On both accounts, the firms are better off without
information sharing.

Of course, if we consider the other case where the full information price in the
substitute market is higher than that in the market of complements, information
sharing leads to a higher profit in the exactly opposite manner: with information
sharing, firms can avoid the aggravation of the externality problem in the comple-
mentary market and extract more rents from the consumers who consider the goods

substitutes.

Proposition 1 (Incentives to information sharing) If the full information price in

the substitute market is lower than that of complementary goods, i.e., pS < p0, and

S

p is not so low that p0

and p1 are far below the joint-profit maximizing price, pm,

then firms have no incentives to customer information sharing. For the other case of

C S

p < p , firms can increase their profits with information sharing.
The above proposition tells us that the incentives to share customer information
depend crucially on the relative magnitudes of the prices that would prevail in the

complementary and substitute markets if consumers were fully segmented according

to their preferences towards the product offerings. If the products are not perceived as

 

2" For this argument, we need to assume that those who consider the two goods as substitutes
have a sufficiently high level of the intrinsic valuation of consumption, v. If not, the average prices,
p0 and p1, that are higher than pS may reduce the demand in the market of substitutes to such an
extent that each firm earns a less profit, relative to the full information case.

25

S C

highly differentiated substitutes to the extent of p < p , it is indeed the uncertainty
about consumers’ preferences that makes the firms better off. As far as a policy
implication is concerned, our analysis shows that oligopolistic firms’ commitment
to no customer information sharing — possibly emphasizing privacy concerns — can
arise for a strategic reason. To put it differently, we may view the commitment to
no information sharing as a possible device for tacit collusion. Another interesting
implication for the policy-makers is that firms may not always get worse off even if

S C

information sharing is banned, because for the case of p < p the firms endogenously
will reside in the regime of no information sharing so that the regulation is not binding.
Of course, in the other case of pS < pc, the prohibition of customer information

sharing will decrease the firms’ profits.

5.2 The effects of information sharing on consumer surplus

We find that the effects of customer information sharing on consumer surplus also
depend crucially on the relative magnitudes of the full information prices. If the

full information price in the substitute market is lower than that of complementary

S C

goods, i.e., p < p , the consumers who consider the two goods complementary
become beneficiaries of no sharing of customer information. This is because they
pay less for a pair of both goods, relative to the full information case. In contrast,

no information sharing hurts those who regard the goods as substitutes because the

0

average prices, p and p1, are higher than the full information price, p5. For the

other case of p0 < p5, those in group C prefer information sharing while those in

26

group S do not.

Proposition 2 { Consumer surplus) If the full information price in the substitute

S C

market is lower than that of complementary goods, i.e., (p < p , customer infor-
mation sharing increases the surplus of those who regard the goods as substitutes. In
contrast, the consumers who regard the goods as complements prefer no sharing of

S

their past transactions data. For the other case of p0 < p , those in group C prefer

information sharing while those in group S get better off under no sharing regime.

Our analysis shows that there exist conflicts of interests between different groups
of consumers. Some consumers resist customer information sharing due to its role
in price discrimination, aside from privacy concerns, while others want their pur-
chase history to be shared between the firms to get a better deal. Therefore, we
cannot say that information sharing always makes all consumers worse off or better
off in the presence of uncertainty about consumers’ preferences. Therefore, a ban on

information sharing due to antitrust concerns can be counterproductive.

6 Implications of the Model

Our innovation in this paper is to allow the possibility that product offerings can
be either substitutes or complements across consumers. Fortunately, this novelty
also provides interesting implications beyond the issues directly related to customer-
specific information exchange. The new insights suggested in this section are to wait

for further research; here we briefly provide the intuitive explanations.

27

6.1 Product differentiation and informational regime

The intuition for our main result provides a new perspective on the determinants of
the degree of product differentiation. The standard result in the literature is that
firms typically realize higher profits from more differentiated products when they
compete with substitutes, because firms can mitigate competition by differentiating
their product from those of their rivals.25 When products are complementary for
some consumers, however, there exists an opposing force that potentially reduces
the incentives for higher product differentiation. If the full information price in the
substitute market is higher than that of the complementary market and information
sharing is prohibited, then greater product differentiation aggravate the externality
problem in the complementary market because it causes the prices without infor-
mation sharing to deviate further away from the optimum. As a result, firms face
a trade-off between higher profits associated with highly differentiated goods in the
substitute market and the loss of profits in the complementary market from the ag-
gravated externality problem. This implies that the informational regime firms reside

in can influence their choice of product differentiation.26

 

25d’Aspremont, Gabszewicz, and Thisse (1979) show this result in the Hotelling model where firms
choose their locations at two ends of market segment, which characterizes the well-known "maximum
differentiation" principle.

26Bester (1998) shows that consurners’ imperfect information about the quality of goods may
reduce the firms’ incentives for product differentiation. Interestingly, our model find the source of
less differentiation in the firms’ uncertainty about consumer complementarity.

28

6.2 Middlemen as information aggregators

The model in this paper analyzes direct exchange of customer information between
firms in the market. Our analysis, however, also has interesting implications for other
channels of information aggregation. For example, this paper suggests a new role for
middlemen27 — the intermediaries between the seller of a good and its potential buyers
— as information aggregators. If the direct exchange of customer information between
firms is prohibited due to privacy concerns or antitrust regulation, the presence of
middlemen such as internet retailers Amazon, eBay, Google check-out can benefit
firms and consumers by functioning as lawful institutions that facilitate information
aggregation. This role of middlemen, to our best knowledge, has not been addressed
yet.

Middlemen are expected to play various roles in the markets with trade frictions
and/ or imperfect information. They can lower transaction costs or serve as experts
in certifying the quality characteristics of goods.28 In addition to these traditional
roles, middlemen —— especially information technology (IT)—focused, or internet-based
- may well be information aggregators who are very efficient in collecting, storing,

and managing customer information.

 

”See Shevchenko (2004) for a brief literature review of recent studies on middlemen.

28See Biglaiser(1993), Biglaiser and Friedman( 1994), and Li (1998) for the role of middlemen as
expert traders.

29

6.3 Database co-ops and the M&A for customer information

This paper considers the situation in which consumers are heterogeneous with respect
to their relationship to product offerings, and the relationship — the degree of com—
plementarity — is consumer-specific, private information unknown to firms. In such
circumstance, we have shown that each firm’s customer list can become more valuable
to each firm when integrated with those of other firms. In other word, the informa-
tion pooling generates informational economies of scale. This helps us to understand
how customer information can be valuable as a tradeable asset. In this aspect, our
analysis provides legitimacy for a new business practice such as database co—ops. In
one example, a prospective member firm is required to contribute at least 5000 names
in order to join the Abacus 2B2 alliance.29 This paper provides an explanation for
how and when the benefits from such customer information exchange can arise.

In a similar vein, our study has important implications for the merger analysis
in which the primary motive for merger is the acquisition of another firm’s customer
lists.30 Even if a merger does not lead to higher market-power or cost-synergies
by eliminating some duplications in production or marketing, it can be a profitable
strategy because of the value of customer lists. In reality, we can often observe M&As

arising from such a motive. The CDNow case briefly described in the Introduction

 

29See the details "Who’s is Who among the B-to—B Co—op Databases," Catalog Age, May
1, 2004. We noticed this real world example from Liu and Serfers. As other articles about
the exchange of databases, see the followings: "List 85 Data Strategies: Co—ops kick it up a
notch," Aug 1, 2005 and "List and data strategies: Co—ops get down to business," Sep 1, 2005
( http: //multichannelmerchant .com).

30 Customer information is one of intangible assets acquired through a merger, according to ’An-
titrust division policy guide to merger remedies (October 2004)’ by US. Department. of Justice,
Antitrust division. (http: / / www.11sdo j.gov/ atr/ public/ guidelines/ 205108.htm)

30

is a case in point. Our study provides a theoretical foundation for the M&A of a
firm whose only asset is its customer lists in the context of behavior-based price

discrimination.31

7 Robustness and Extensions

As previously mentioned, sophisticated consumers who expect ex post price discrim-
ination may strategically misrepresent their preferences in order to increase their
overall surplus, which leads us to check the conditions under which our main results
are robust with such considerations. In this section, we also discuss the assumption
that the substitute market is fully-covered to check the robustness of our main re-
sults. Potential extensions include an alternative way to model our key intuition with

a downward sloping demand and a continuous parameter for complementarity.

7.1 Potential strategic misrepresentation of preferences
7.1.1 Under information sharing regime

As previously shown, if the full information price in the substitute market is higher

than that in the complementary market, i.e., p0 < p5, then each firm has ex post
incentive to share its customer past history with the other firms. Then, the so-

phisticated consumers who consider the two goods substitutes may strategically buy

 

31Tadelis (1999) develops a model in which the only asset a firm has is its name. He shows that
there generates an active market for names if buyers cannot observe ownership shifts between sellers.
His model and ours have something in common in that both find the value of intangible assets and
explain their trade between sellers.

31

both goods or neither, instead of buying only one good, in order to avoid the ex-
pected higher second-period price pS. Needless to say, the decision for this strategic
demand manipulation hinges upon the benefit-cost analysis associated with such pos-
sible mimicries. The benefit of pretending to consider the goods complementary is a
lower second-period price than the price without such a disguise, while its cost is a
potential loss of utility in the first period.

More specifically, the consumer in group S can have additional benefit of (5(pS —
pC) by strategically purchasing either both goods or neither good instead of buying
only one good. By doing so, however, this consumer may enjoy less surplus in the
first period because she now buys an additional good without further utility earned32
or loses the first-period utility, max{v A? v B} — qi, that could have been earned if the
consumer had not strategically chosen no purchase. As a result, the consumer will
not misrepresent her preference by buying both goods if the first-period price for a

unit of good is sufficiently high due to either a sufficiently large marginal cost, d, or

reservation value v is sufliciently high.

7.1.2 Under no sharing regime

If the full information price in the substitute market is lower than that in the comple-

S

mentary market, i.e., p < pC, the sophisticated consumers expect no information
sharing in the second period. So, they know that the second period prices will be

based only on whether they are newcomers or returning customers. In such a case, a

consumer’s consumption decision in group C will be based not only on the first period

 

32 We assume away the possibility of resale.

32

surplus but also on its feedback eflect on the second period price. The detailed analy-
sis for this dynamics becomes complex because the marginal type of consumer will
be determined by the first period prices and the expected second period prices which
in turn affects on the first period pricing. We believe, however, that our qualitative
results would not be changed: there would be some restriction on parameters.

On the other hand, a consumer who consider the two goods substitutes expects
that she faces the price for a returning customer if she buys a good from the same
firm, but the price for a newcomer if she switch to the other firm in the second
period. Since she is not informed of her second-period preference, indexed by ’7, at
the beginning of period one, there is no dynamic effect of the ex post discriminatory
prices on the first-period choice. This is similar to the case of the changing preference

in the two-period poaching model of Fudenberg and Tirole (2000).

7.2 Not fully-covered substitute market

In our basic model, every consumer who regards the two goods as substitutes buys
at least a unit of either A or B with the assumption that the common reservation
price v is high enough to ensure that the substitute market is fully covered. Clearly,
this assumption simplifies the analysis to a significant extent because the sharing of
information allows firms to identify consumer preferences for the entire consumers.
Apparently, this assumption may sound somewhat restrictive, but our qualitative
result turns out to be robust to relaxing this assumption.

To see this point, suppose that consumers are heterogeneous in the vertical di-

33

mension — with respect to their reservation price v,- — as well so that the possibility
of no purchase is open to those who have relatively low reservation values for both
goods. Then, even if the firms share their customer information collected through
the initial marketing period, there will be residual uncertainty about consumer pref-
erences. Meeting a consumer who bought neither product, firms cannot tell if the
consumer has considered the goods complementary but did not buy either good due
to a relatively low 6 or if the consumer has regarded the goods as substitutes but
chose not to purchase either product due to a relatively low valuation for both goods.
As a result, the firms must post a weighted average price for unidentified consumers
even after information sharing. As far as identified consumers are concerned, how-
ever, the incentives to share customer information work in the same manner as the
case of perfect identification.

In fact, it must be more realistic to consider this possibility of no purchase; it only
comes at the expense of substantial complication. If our simplifying assumption is
relaxed, the demand for those who regard the goods as substitutes depends not only
on horizontal but also vertical dimensions. So, unfortunately, the model suffers from
technical complexity; little additional insight is gained. The benefits associated with

our simple basic model outweigh its costs.

34

7.3 Complementarity as a continuous variable and downward
sloping demands

In our basic model, consumers are categorized into only two distinct groups and they
have a unit demand per period. This simplification allows us to deliver our main
intuition in a simple and tractable manner; it would be interesting to consider a
downward sloping demand with the complementarity (or substitutability) embodied
as a continuous variable.

In this spirit, let us suppose an individual consumer has a downward-sloping de-
mand for good i , for instance, which is given as Di(pZ-, pj; a) = a — p,- + opj, where
the coefficient 0 measures her complementarity or substitutability: a > 0 is for sub-
stitutes, a < 0 is for complements, and a = 0 is for independent goods. If consumers
are heterogeneous with respect to their complementarities that are correlated over
time, then the exchange of past purchase histories may provide the firms with a bet-
ter estimate for the value of the parameter a, relative to the case where firms do not
share their customer information. For example, given the demand specifications we
have, information about a can be inferred more efficiently with sharing of information
between the two firms if consumers are heterogenous with respect to both a and a.
We believe that our main intuition of this paper can work through this alternative

framework. The full analysis in this direction, however, is beyond of the scope of this

paper.

35

8 Concluding Remarks

We live in a world where electronic commerce through the Internet prevails more
than ever before, numerous innovations in information-technology take place rapidly,
consumers’ records of previous purchases can be easily traced and stored by electronic
"fingerprints," and the issues related to privacy concerns are heard and discussed
daily. Our analysis for customer information sharing is especially relevant in such a
modern business environment. In this paper, we have investigated oligopolistic firms’
incentives to share customer information about past purchase history and the effects
of information sharing on consumer surplus in a situation where firms are uncertain
about whether a particular consumer regards the product offerings as complements
or substitutes.

The key intuition of this paper has several important implications not only for
the issues directly related to customer information sharing, but also for other signif-
icant subjects such as the determinants of product differentiation and the roles of
middlemen. Additionally, this paper sheds a new light on merger analysis in which
the primary motive for merger is the acquisition of another firm’s customer lists. Our

research is an early step which we hope to encourage more research in this direction.

36

Appendix A

Proof of the claim: A consumer in group S (weakly) prefer buying only one
product to buying both, that is, max{vA "FA, vB —pB} 2 max{vA, vB} —pA —pB.

There are four possibilities depending on the relative magnitude of terms in the
maximands. If ”A 2 vB and ”A — pA 2 vB — pB, then max{vA,vB} = ”A and
max{vA — pA, vB - p3} = “A — pA so that the given statement is shown to be true

as follows.

maX{v,4 - 17,4,"03 - p3} - (max{vAavB} - PA '— PB)

=(UA—pA)_(vA—PA—PB)=PB20

If ”A Z vB and ”A —pA < vB —pB,then max{vA,vB} = ”A and max{vA -

PA’UB —PB} = vB -PB-

maX{vA —PAa”B -PB} — (maXI’UAa’UBl —PA _ pB)

=vB-PB-(vA-pA-PB)=vB-(vA-PA) 2 (vB-PBl—(vA-PA) >0

vaA<vB andvA—pA ZvB-pB,thenmax{vA—pA,vB—pB}=vA—pA and

max{vA,vB} — pA — p3 = vB — pA -— pB. In a similar manner, we can show that

maX{vA -PA,UB — PB} - (maXI’UAVUBl “PA ‘ PB)
= (12A —pA) - ('03 -;DA -PB)

=vA—(vB—pB)20

37

As the last case, if ”A < vB and ”A —pA < vB —pB, then we know that max{vA —

pA,vB—pB} =vB-pB and max{vA,vB}—pA—pB =vB—pA—pB.

maX{vA - PAH/‘3 -PB} ‘ (maxii’AivBl — PA " 19B)

=vB—PB—(UB—PA-PB)=PAZO

Q. 13.1).

Proof of Proposition 1

C

Consider the case of pS 3 pi S p , then profits with and without customer
information sharing are arranged such that 7rf 2 r0 and 7rf 2 rs, as long as pi is
not extremely low, i = 0, 1. With the symmetry of distribution G, each firm has the
half of the market of substitutes, i.e., 0(a) = 1 / 2. The second-period profit with no

information sharing is decomposed into

1—A1 l—AO

 

 

 

 

fig —_- A[1— F(6)]7r1+ ”(6M0 + 2 r + 2 7r
which satisfies the following inequality
2 A[1— F(§))«C + ”(6)747 +1;’\7r3 +1355 = H2

Therefore, the profit without information sharing is at least as higher as the profit

with information sharing.

S

For the other case of p0 3 pi S p , then the relative magnitudes of prices are

38

such that rri 3 ac and 7ri 3 rs. In a similar manner, the second-period profit with
no information sharing is shown to be less than or equal to that with information

sharing as follows.

 

 

~ A A l—A 1—A
H2=Afl—FMH1+AFWMQ+—?fld+ 2 E)
S A[1— F(6)]rrC + AF(6)7TC + %WS + 1.2—)‘71'3 = H2

Q.E.D.

Appendix B. Example with uniform distributions
For explicit solutions, let us consider the case in which both 6 and ’7 follow uniform
distributions: 6 6 [0,1] and 'y 6 [—"7,7]. A uniform distribution satisfies the MHR
condition, so the first-order condition is sufficient for the optimization. For simplicity,
let us set the production cost to zero, i.e., d = 0. With information sharing, the full

information prices for each group in the second period are given by
1 _
p :- 3- p 2 All’ (ex-3)

by

441—93. @wfi

Without information sharing, the firms revise their beliefs on the proportions of

the consumers in each group in the process of Bayesian update. Using the first-period

39

equilibrium price q, the posterior probabilities are given by

 

 

— 2
,\0 = “\(2‘1) . A1 2 AU (1)

A(2q)+(1—A)/2’ A(1—2q)+(1—A)/2 (ex-5)

and recall that A0 and A1 are the probabilities that a newcomer and a returner would
belong to group C, respectively. As explained in Section 4, the profit-maximization

problem of firm i for a newcomer is given by

gig; 7r? 2 (p? — d){A0[1— F (p? +P?)l + (1 — ”50(1); ‘ 69)}
i

and for a returning consumer firm i solves the following problem

My; «,1 = (12,1 — d){A1[1— F (pl +1991 + (1 * Alla (P? ‘16)}
pi

where i 75 j. With some algebra, we can derive the symmetric equilibrium prices

without information sharing as

0 _ 373(1— A0)(1— A1) + 672(1— AO)A1+ 7(4A0 + 2A1— 6A0A1)+12A0A1
p 372(1 —— A0)(1— A1)+127(AO + A1 — 2A0A1) + 36A0A1

 

 

1 _ 373(1— AO)(1— A1) + 672(1— A1)A0 + 7(4A1+ 2A0 — 6A0A1)+12A0A1
p 372(1— A0)(1— A1)+127(A0 + A1 — 2A0A1) + 36A0A1

(ex-6)
For these prices, we can readily check p0 = p1 = p0 = :1; if every consumer considers
the goods as complements, i.e., A0 = A1 = 1 and p0 = p1 = pS = 7 if every consumer
regards the goods as substitutes, i.e., A0 = A1 = 0. By substituting p0 and p1 into

40

0

the profit expression, we can also derive the associated equilibrium profits 7T and 7r1

as

«0 p0 {10(1 — 2p0)+<1— 10) (p1 —p0)} (ex-7)

Z

79-1 p1{/\1(1- 2101) + (1 - A1) (I90 ~p1)}

Therefore, without information sharing, each firm earns the total second—period profit

of

 

fi2 = (A(2q) + (Lg—Al) «0 + (A(1— 2g) + (1 g A’) rrl (ex-8)

where the tilde denotes the case of no information sharing.

Table 1—A-1 shows the equilibrium outcomes for 6 ~ U [0, 1] and 7 = 0.2 (p0 =
1/3 > 1/5 = p3) where no sharing regime is preferred. Fig. A-1 graphically shows
this result. Similarly, we summarize the equilibrium outcomes for 6 ~ U [0, 1] and
’7' = 0.5 (p0 = 1/3 < 1/2 2 ps) in Table 1—A-2. Now that the full information price

in the substitute market is higher that for the complementary market, information

sharing will be preferred. Fig. A-2 shows this result.

41

Table l-A- 1. Equilibrium outcomes: No information sharing is preferred.

 

0~U[0, 1], ;=0.2: pC=1/3 > pS=0.2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 

A, q K0 Al p0 pl n H
0.0 0.200 0.000 0.000 0.200 0.200 0.100 0.100
0.1 0.233 0.094 0.254 0.305 0.320 0.101 0.150
0.2 0.257 0.205 0.426 0.319 0.327 0.102 0.147
0.3 0.275 0.320 0.554 0.325 0.330 0.103 0.142
0.4 0.289 0.435 0.655 0.328 0.331 0.104 0.137
0.5 0.300 0.545 0.737 0.330 0.332 0.106 0.132
0.6 0.309 0.650 0.806 0.331 0.332 0.107 0.127
0.7 0.317 0.747 0.864 0.332 0.333 0.108 0.123
0.8 0.323 0.838 0.915 0.332 0.333 0.109 0.119
0.9 0.329 0.922 0.960 0.333 0.333 0.110 0.115
1.0 0.333 1.000 1.000 0.333 0.333 0.111 0.111
profits f
II : no sharing
1/9 .......................................................................................................................... '
“10 II : sharing
0 1 A

Figure l-A-l. Comparison of equilibrium profits for 0 ~ UN, 1], f=0.2

42

 

Table 1-A—2. Equilibrium outcomes: Information sharing is preferred.

 

0 ~ U[0, 1], ;=0.5: pC=1/3 < pS =0.5

 

0

l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
   

 

   

 

A q A0 A1 p p II II
0.0 0.500 0.000 0.000 0.500 0.500 0.250 0.250
0.1 0.458 0.169 0.194 0.381 0.377 0.236 0.172
0.2 0.429 0.300 0.364 0.360 0.355 0.222 0.153
0.3 0.406 0.41 1 0.504 0.351 0.346 0.208 0.143
0.4 0.389 0.509 0.620 0.345 0.342 0.194 0.136
0.5 0.375 0.600 0.714 0.342 0.339 0.181 0.131
0.6 0.364 0.686 0.792 0.339 0.337 0.167 0.126
0.7 0.354 0.768 0.858 0.337 0.336 0.153 0.122
0.8 0.346 0.847 0.913 0.336 0.335 0.139 0.118
0.9 0.339 0.924 0.960 0.334 0.334 0.125 0.114
1.0 0.333 1.000 1.000 0.333 0.333 0.111 0.111
profits

0.25

II : sharing
H : no sharing
01 .......... . .................................................. ............................................... .
0 A

Figure 1-A-2. Comparison of equilibrium profits for 0 ~ U[0, 1], f=0.5

43

 

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46

Chapter 2. A Theory of Preliminary Injunctions:

Is it a cheap message service?

In this paper a model of preliminary injunctions is presented in the context of
antitrust litigations. Following a suggestion of Lanjouw and Lerner (2001), we study
the role of preliminary injunctions as a noisy information message service in addition
to its role as a means to prevent irreparable harm to the plaintiff. Interestingly,
we find both cases in which the plaintiff with a high damage or the one with a
low damage moves for preliminary injunctive relief as equilibrium phenomena. We
not only analyze the decision-making about the motion for an injunction, optimal
settlement offers and litigation/settlment, but also discuss various issues associated

with preliminary injunctions based on our model.

1 Introduction

A preliminary injunction is a court order prior to a final decision on a legal case
based on its a priori assessed merits, in order to restrain a party from a certain
activity during a period until the case will have been decided. Not surprisingly, it
has substantial impact on the decisions of litigants and the outcomes of disputes.1 In
addition, we can frequently see many firms request preliminary injunctions especially
in patent litigations and antitrust cases.

On Oct. 7, 1997 Sun Microsystems Inc. filed a suit against Microsoft in US. Dis-

trict Court for copyright infringement, alleging that Microsoft improperly modified

 

1Lanjouw and Lerner (2001) provides an excellent overview of preliminary injunctions.

47

the Java technology incorporated in Internet Explorer 4.0 and infringed Sun’s trade-
mark by distributing IE 4.0 and related products using the Java Compatible Logo,
even though Microsoft’s Java products failed its compatibility tests and thus violated
their 1996 licensing agreement. On March 24, 1998, US. District Court Judge Ronald
M. Whyte issued the preliminary injunction ordering Microsoft to modify all its soft-
ware products that ship with Java technologies to pass Sun’s Java compatibility test
suite within 90 days.2

In a more recent case, in August 8, 2006 Sanofi-Aventis, the pharmaceutical com-
pany and the holder of a patent on the blood-thinning drug Plavix, and Bristol-Myers
Squibb Co., its US. partner, requested a preliminary injunction against Canadian
drug maker Apotex Inc. to stop its sales of a generic version of Plavix. 011 September
1, 2006 US. District Judge Sidney H. Stein granted the injunction, concluding that
Sanofi-Aventis would suffer irreparable harm if Apotex were permitted to continue dis-
tributing its generic product. Bristol-Myers shares and US. shares of Sanofi-Aventis
rose 8 percent and 3.4 percent on the NYSE, respectively, after the ruling was issued.3

However, despite the economic and legal significance of preliminary injunctions,
there are, unfortunately, very few papers addressing this issue in a form of an economic

analysis. Our analysis has been motivated in large part by two strands of early

 

QSee, Summary of Sun Microsystems v. Microsoft, US. District Court, Northern District of Cali-
fornia, San Jose, Case Number 97—CV-20884. For press accounts for another preliminary injunction
granted in this case on November 17, 1998, see The Wall Street Journal (Eastern edition) Nov 18,
1998, pg. 1., “Microsoft Loses Java Decision In US. Court” and Tech Law Journal Nov 18, 1998
“Judge Whyte Issues Preliminary Injunction in Sun v. Microsoft.”

3Refer the case number [**2] 05-CV—3965 in Southern District of New York for Apotex Inc.
v. Sanofi-Aynthelabo (also known as Sanofi—Aventis). For press documents, see a report in Town-
hall.com, “Judge Halts Sales of Generic Plavix” and Wall Street Journal (Eastern edition) New
York, N.Y.: Dec 29, 2006, “Sanofi-Aventis SA: Court Prevents Canada’s Apotex From Launching
Generic Plavix.”

48

research related to this issue. Firstly, Lanjouw and Lerner (2001) suggest that

in a world with uncertainty about case quality, a preliminary injunction
hearing may be a relatively cheap way to obtain information about how

a court would rule in an eventual trial. (p. 586)

As they mention, one of the reasons that lead the plaintiffs to move for a prelimi-
nary injunction could be found in the plaintiff’s quest for information in the presence
of uncertainty about case quality, which has not been studied yet. In our model,
we incorporate this aspect of preliminary injunctions by offering a model of prelimi-
nary injunctions in which the players can revise their expected winning probability at
trial through Bayesian updating once they observe the court’s decision on the prelimi-
nary injunction. Also, we characterize the injunction rule as an imprecise information
transmission channel, so that the cost of acquiring noisy information can be compared
to its benefit.

The second motivation for our study is found in Bizjak and Coles (1995) who
examine the effects of private antitrust litigation on the stock-market valuation of
the firms. One conspicuous finding in their empirical study is that the request for
inj unctive relief is associated with a reduction in a defendant’s wealth upon filing. This
implies that the participants in stock markets may regard the motion for preliminary
injunctive relief as a reliable signal that may impose behavioral restrictions on the
defendant. In this paper we explore the plaintiff’s incentives to make a motion for
a preliminary injunction and attempt to identify the conditions under which the

defendant’s payoff is negatively related to the plaintiff’s decision to ask for injunctive

49

relief.

In general, one main reason for the plaintiff’s injunction request is to avoid so-
called irreparable harm. In fact, irreparable harm is also one crucial factor considered
when the court rules on the injunction. For this reason the plaintiff with a higher
damage is typically expected to have a stronger incentive to file the motion for pre—
liminary injunctive relief, all other things being equal. Once we view the preliminary
injunction as a noisy information transmission mechanism, however, the above logic
is no longer so straightforward. This is because if the court rejects injunctive re-
lief, then the plaintiff’s expectation for the case quality can be adjusted toward an
unfavorable direction so that his threat of litigation may lose its credibility or the
settlement amount offered by the defendant is diminished. Thus, the incentive to ask
for preliminary injunctive relief becomes more intriguing compared to the obvious
trade-off between the possible avoidance of irreparable harm and the legal cost for
requesting the injunction.

The literature directly concerning preliminary injunctions is quite scant, but there
is by now an extensive literature on (pretrial) settlement and litigation. Bebchuk
(1984) provides a model of litigation and settlement decisions under imperfect infor-
mation. He studies a variety of factors that can affect the likelihood of settlement
and the settlement amount such as litigation costs, the amount at stake, and legal
rules.4 Nalebuff (1987) addresses the issue of credibility in the plaintiff’s threat to

litigate in a framework similar to Bebchuk’s. In his revised model, the settlement

 

"P’ng (1983) offers a model of settlement decisions in the presence of asymmetric information, but
the settlement amount is not endogenously determined, which is endogenized in Bebchuk’s model.

50

demand has a pronounced effect on the equilibrium outcome, as a result, the plaintiff
may increase her settlement demand in order to limit the negative effect of having her
offer rejected.5 Our paper shares a similar feature with Nalebuff’s in the sense that
the plaintiff is concerned about an exposure to the risk that is given by the request
for injunctive relief being rejected. As a paper addressing the antitrust litigation
more directly, we are aware of Briggs, Huryn, and McBride (1996). They study the
effects of private suits on government suits and vice versa. They show that private
plaintiffs are more likely to settle following a government suit than otherwise, which
is supported by data on private suits. Instead, we are particularly interested in the
effect of preliminary injunction rulings on the subsequent final judgment.

On the other hand, Choi (1998) explores the implications of the information re-
vealed in patent litigation for entry dynamics in the presence of multiple potential
entrants. In his model, a patentee can be exposed to the threat of entry if he loses
in the patent litigation initially launched by himself. The fear of losing in patent
litigation in his model can be analogous to the plaintiff’s fear of the disapproval of
preliminary injunction relief.

As previously mentioned, Lanjouw and Lerner (2001) is the closest to our paper
in that it also takes a step in the direction of examining the preliminary injunction.
Our analysis, however, differs from theirs in the mechanism through which the in—
junction works. In their model, firms may request preliminary injunctions in order to

impose financial stress on their rivals as well as to save irreparable harm, whereas the

 

5For the settlement of patent litigation, Meurer (1989) develops a model that analyzes the effect
of the probability of patent invalidity, antitrust policy, and the rules of litigation-cost allocation on
the likelihood of settlement and litigation.

51

ruling on preliminary injunction in ours is also an informational transmission mech-
anism. Recently, Boyce and Hollis (2007) study a patentee’s incentive to move for
a preliminary injunction and show that it may be sought in patent cases to obtain
market power during the period of the injunction. Interestingly, they find that both
the patentee and the alleged infringer benefit from a preliminary injunction because
it may play the role of a court—ordered collusive scheme to charge monopoly prices
and share profits.

The remainder of this article is organized as follows. Section 2 outlines a simple
model of preliminary injunctions in which the plaintiff’s incentive to file the motion
for an injunction is of particular interest. Section 3 gives intuitive explanations for the
analysis of our simple model. In conjunction, a few numerical examples are presented.
In Section 4, we extend our basic model to include the defendant’s settlement stage.
Section 5 contains a variety of possible extensions and their implications. Finally, we

close this paper with brief concluding remarks.

2 A Simple Model of Preliminary Injunctions

For expositional ease, we begin with a simple model which abstracts away from various
aspects of preliminary injunctions. Our strategy is to study this simple version of the

model, and then bring it closer to reality with additional features later.

52

2.1 Players and timing of the game

Consider a legal conflict that involves two risk-neutral players, a plaintiff firm and
a defendant firm, in an infinite time horizon. The game begins at t = 0 when the
plaintiff faces allegedly unlawful actions by the defendant. Before the plaintiff’s filing
of a suit, both parties’ payoffs per period are normalized to zero. At t = 1, the
plaintiff suffers (per period) damages of w due to an action of the defendant. The
extend of the damages are private information to the plaintiff; the defendant knows
only the distribution of possible damages F (w) on m, E] with w < 117.

Upon filing a suit against the defendant, the plaintiff decides whether or not to
move for a preliminary injunction against the defendant’s offending behaviors. Should
the plaintiff file a request for an injunction, the court immediately holds hearings on
the suit and announces its judgment. That is, injunctive relief is either granted or
denied instantaneously. If the injunction is granted, the plaintiff goes to trial in an
attempt to make the ruling permanent; if injunctive relief is denied, we assume that
the plaintiff drops the suit because he expects a negative (net) payoff from going to
trial.

Of course, one may consider the case where the plaintiff proceeds through to trial
even after his request for a preliminary injunction is rejected. Then, however, the
value of the preliminary injunction as an information service becomes zero because
the purchaser of the message service, the plaintiff, does not change his action in light
of what kinds of message he receives. As a result, the only reason for the motion of a

preliminary injunction is restricted to prevent irreparable harm. Since the purpose of

53

our paper is to consider the preliminary ruling as a message service the value of which
is not zero, we adopt such assumption concerning the plaintiff’s actions in response
to the court’s ruling on the request.

Finally it is worth noting that we assume that the court’s ruling on the preliminary
injunction is immediate, whereas it takes one time period for the court to give its final
judgment in litigation, should the plaintiff proceed to trial. This reflects the fact that
litigation is a more time consuming process relative to the preliminary injunction.

Figure 2-1 summarizes the timing of the game that we consider.6

 

 

_ _7

[:0 f‘ 1 F-

I l l g
A plaintiff faces allegedly Realizing his damage w, the If both parties proceed to
unlawful actions by the plaintiff files a suit with or litigation. the court gives its
defendant. without the motion for final judgment on the case.

preliminary injunction.

 

 

 

 

If injunctive reliefs are Each party pays its own
requested. the court litigation cost and follows the
innnediately rules on the judgment without further
injunctive reliefs. actions.

 

 

 

 

Observing the court’s
ruling. the plaintiff decides
to go to trial or drop the
suit.

 

 

 

Figure 2-1. Timing of the Game

 

"The assumption that each party pays its litigation cost at the time when the court announces
its judgment does not make any qualitative difference from the assumption that it occurs at t = 1.

2.2 Assumptions on prior beliefs

Let us assume that there are two possible underlying states concerning the case in
question. In the “valid” state, the plaintiff wins the case at trial, should it come to
a final ruling; whereas in the “invalid” state the court finds in favor of the defendant
at trial, in the event that litigation goes through.7 Let 7r denote the prior probability
that the case would prove to be valid at trial, that both parties commonly hold.8 In
other words, the plaintiff’s and the defendant’s expected winning probabilities are 7T
and 1 — 7r, respectively. We assume that 7r is independent of the plaintiff’s damage
level w.9 This set up reflects the fact that the primary goal of antitrust laws is not to
protect competitors but to support market competition, so that the court’s discretion
need not depend on how much a defendant has been damaged. The court applies the
same discretion for the preliminary injunction and the eventual trial, so that ex ante

each party expects that the injunction will be approved with probability v.10

2.3 The injunction ruling as a noisy message service

The ruling on the preliminary injunction, however, may have two types of errors.
Injunctive relief can be denied with probability a (2 0), even if the true state is
valid. To put it differently, the court mistakenly can deny the requested injunction

even though the court would rule in favor for the defendant at trial. Another type

 

7Here, the terms of “valid” and “invalid” are used in the sense that if the plaintiff’s request for
preliminary injunctive relief is valid, then the court will be in favor of the plaintiff in ruling on
preliminary injunction, barring errors, and in the final judgment in litigation.

8Alternatively speaking, 7r represents the ea: ante mean of a distribution that the variable 7r has.
9We discuss the case where this assumption is relaxed later.

1" One interesting relaxation of this assumption is to consider a more conservative ruling in pre—
liminary injunctions than the judgment in litigation. We discuss this later in Section 5.

55

of error is that the injunction can be granted with probability B (Z 0), even if the
true state is invalid so that the court should have denied it.11 In summary, Table 2-1
shows the likelihood matrix for the ruling on preliminary injunctions, given the true

state of the world.

Ruling
Grant Deny

Valid 1 — (r (l
Invalid :3 l — 5’

 

 

Request for Inj unctive Relief

 

 

 

 

Table 2-1. Likelihood matrix for rulings on the preliminary injunction

Once injunctive relief is requested, each party revises its prior belief 7r into pos-
teriors rrR, with R E {C, D}, depending on the court’s ruling, where C and D are
mnemonics for the court’s decision to grant (C) or deny (D) the request, respectively.
The approval of an injunction occurs either when the court correctly finds a valid
case or when the court mistakenly judges an invalid case to be a valid one. By Bayes’
rule, the conditional winning probability at trial (for the plaintiff) given the message

C is calculated as

C_ (1—a)7r
7r —(1—a)7r+i3(1——rr)' (1)

 

In contrast, the court will not grant the injunction whenever it correctly finds an
invalid case or when it makes the error of judging a valid case as an invalid one. Thus,

the posterior belief that the case will prove to be valid, provided that the message D

 

11The first type or error is referred to as type-I error, false positive or a error, while the second
one is called as type—II error, false negative, or 6 error. Our notations reflect the last alternative, 0:
error and ,6 error.

56

is received, is given by

D_ 071'
_arr+(1—B)(1—7r). (2)

 

Before moving to an analysis, a bit more notation is needed. Letting p and d be
mnemonics for the plaintiff and defendant, respectively, let I,- denote the cost for legal
proceedings associated with an injunction, for i = p, (1. Let cp and ed be litigation
costs associated with the actual trial for the plaintiff and the defendant, respectively.
Each party bears its own costs regardless of the outcome in trial, that is, the American
fee rule is adopted. Both parties discount their payoffs with the same discount factor,
6 6 (0,1).

The assumption that, regardless of the damages caused, a plaintiff will drop a case
in light of an unfavorable ruling on the request for injunctive relief is then given by

the condition that

b
S!

 

(3)

Cp>7I

3 Incentives to file for a Preliminary Injunction

One crucial question that naturally arises when we discuss the preliminary injunction
is what motivates a plaintiff to move for a preliminary injunction. That is, who asks
for injunctive relief and who doesn’t? Without doubt, one classic answer is that the

plaintiff wants to avoid irreparable harm occurring during litigation.l2 This implies

 

12For instance, in the suit regarding Plavix it was reported that Apotex’s generic drug quickly
gained market share after its launch. According to Verispan LLC who collects prescription data, the
generic brand captured 60.2 percent of the total prescriptions written for the week ended Aug. 19,
2006. Such changes in the market share must be a significant damage to the plaintiff, Sanofi-Aventis
and Bristol-Myers.

57

that a plaintiff whose damage is relatively large would have a stronger incentive to
move for a preliminary injunction in order to prevent irreparable losses, other things
being equal. This answer, however, must potentially be adjusted to account for our
second thought if we view the preliminary injunction as an information transmission
mechanism, which should be another important motive for a plaintiff’s choice of
preliminary injunction as Lanjouw and Lerner (2001) suggest.

The plaintiff may attempt to obtain the court’s ruling on an injunction as a
hint for the final judgment at a relatively small expense. Remarkably, the rule on
the preliminary injunction is at best a noisy informative message service due to its
accelerated process: The court can commit the mistake of not granting the injunction
even in the valid state. With such informational effects taken into consideration, the
incentives to file a motion for a preliminary injunction can be more intriguing rather
than an obvious trade-off between the legal costs lp and the potential aversion of

irreparable harm.

3. 1 Plaintiff’s payoffs

Note that in our simple set-up we treat the defendant as a passive player who does
not take any strategic actions. In the next section, the defendant comes on the scene
as a strategic player who must decide on settlement offers.

If the plaintiff of type w does not take any action, he gets damages of w in every
subsequent period. The plaintiff’s payoff without a suit is thus given by —1%5, the

discounted present value of damages through infinite horizon. If the plaintiff with w

58

goes to trial without the motion for injunction, he earns the expected payoff of

(in)

1_5- (4)

 

—w—(lop—(1—rr)

He suffers damages for one period until the trial’s outcome comes. At the expense
of litigation cost op, he can avert this damage permanently if the court finds in favor
of him — which occurs with probability 7r. From the other option —— moving for a

preliminary injunction —— the plaintiff’s expected payoff is given by

—z,, + Pr(C) (a, — (1 — «G)%) + Pr(D) ("i—75') ; (5)

where Pr(C) = (1 — 0) r + ,6(1 — 7r) gives the probability of injunctive relief being
granted and Pr(D) = 1 — Pr(C). The plaintiff must pay the legal cost lp to move
for an injunction, regardless of the court’s decision. With probability Pr(C), the
injunction is granted, then the plaintiff is free from the damages of w for that period.

G and expects to win at trial with

He updates his winning probability at trial to 7r
probability rrG. If injunctive relief is not granted, the plaintifi drops the suit, by our

previous assumption13 so that he ends up with the payoff of no suit at the cost of lp.

 

13The plaintifi drops the suit if the litigation cost is too high or the posterior winning probability

7rD is too low relative to the potential saving of damages.

59

 

3.2 When is the motion for an injunction filed?
By comparing (4) to (5), the plaintiff with damages w prefers moving for a preliminary

injunction to going directly to trial without it, if and only if

6w
1—6'

 

Pr(C)w + (1 — Pr(C)) (Sep 2 1p + or (6)

The left-hand-side of (6) is the plaintiff’s expected benefits from the choice of filing for
preliminary injunctive relief. With probability Pr(C) the injunction will be granted.
Then the plaintiff can avoid his damage w temporarily. Otherwise, he drops the suit
to save the litigation cost. The right—hand-side captures the costs associated with the
motion for injunction. The preliminary injunction costs the plaintiff the legal cost
lp. In addition, if the court mistakenly decides not to grant the injunctive relief even
in the valid state, the plaintiff will suffer the damages that could have been avoided
under an error-free ruling on the preliminary injunction.

From this benefit-cost analysis, we find that there could be two distinct cases de-
pending on the parameters. The first possibility is that the plaintiff whose damage
is relatively high chooses to move for a preliminary injunction, while the one with
a smaller damage opts for going to trial without the motion for injunction. This
case is not surprising, since the marginal saving from preventing irreparable damages
can exceed the potential marginal cost from the court’s erroneous ruling on the pre-
liminary injunction. As illustrated in Figure 2-2, for a sufficiently low a such that
arr—1g; < Pr(C) and for large enough 1,, such that lp > (Sep (1 — Pr(C)), the plaintiff

with w 2 w" chooses to file for a preliminary injunction.

60

Cost of Injunction

  

Benefit of Injunction

0‘6“,“ —P1‘(G))

 

 

 

 

* II
II’ , , 1 ‘ , . .
L‘ Injunction ’ lNo Injunction
‘ 44 D
Figure 2-2. The Plaintiffs with Large Damages Move for Injunction

The numerical example below that satisfies all the assumptions and conditions

listed falls into this first category of equilibrium.

Example 1 Suppose that the parameters have the values such that 7r 2 1 / 2, lp = 5,
cp 2 ed 2 10, (5 = 0.75, a = 0.2 and ,8 = 0.1. Then, according to Bayesian updating
process, the posteriors are derived as rrG = 8/ 9 and er = 2/11. That is, if the court
grants the injunction, the plaintifir ’3 expected winning probability increases to 8/ 9 from
1/2; if the court denies the injunction, it falls to 2/11 from 1/2. With simple algebra,
we can verify that (lep(1—Pr(C)) = 33/8 < lp = 5 and (rrr1% = 130 < Pr(C) = 2% and
w* = 36f z 5.83. The plaintifls with 13.75 > w 2 5.83 request the preliminary

injunction, while those with 5.83 > w 2 5 will go directly to trial without moving for

61

injunctive reliefs. The upper- and low-bound of the damage w can take are determined

by the assumptions under which the plaintifi ’s behavior is rationalized.

The second possibility is that the plaintiff whose damage level is relatively low
prefers asking for a preliminary injunction. This case seems to be counter-intuitive
because the plaintiff with small damages should have a weaker incentive to request
a preliminary injunction. The intuition for this interesting outcome is as follows.
As a plaintiff’s damage increases, his incentive for filing for a preliminary injunction
to prevent irreparable damages gets strong. Nevertheless, given the condition that
curl—i5 > Pr(C), the plaintiff’s disincentive to request a preliminary injunction in-
creases even at a faster rate because of the rate of the unfavorable error toward the
plaintiff in the preliminary ruling. Graphically, we can illustrate this case as in Fig-
ure 2—3: This case happens when marginal cost of the injunction is greater than its
marginal benefit, i.e., (Mfg? > Pr(C), and the legal cost of the injunction is small
enough so that lp < 6cp(1 — Pr(C)).14 As a result, the plaintiff with w < w" ends up
preferring moving for a preliminary injunction to not doing so, where w" is defined

as
* 6cp(1— Pr(C)) — lp
Nam — Pr(C)

 

(7)

 

1"The typical single crossing property holds here.

62

A Benefit

Cost

(ICPU — P1‘(G))

 

 

 

 

 

;, 5

LT 11' W
No Injunction Injunction

>4 . >

Figure 2-3. The Plaintiffs with Small Damages Move for Injunction

Finally, it is worth finding the conditions under which a plaintiff initially files a
suit. In order to make the game start, one of the following two conditions must be
satisfied: either a plaintiff has a higher expected payoff when he goes to trial without
the motion for injunction or when he files for an injunction than when he opts for no

suit. With some algebra, these two conditions simplify to

WI % 6 2 cp or Pr(C) (—6cp + n016%6 + w) 21,, (8)

 

 

We summarize the analysis so far in the following proposition. It is quite interesting
to find that in equilibrium even the plaintiff whose damage is relatively large may

choose not to move for preliminary injunction due to the risk of the noisiness in the

63

judgment on the injunction.

Proposition 1 Given the Assumptions in Equations 3 and 8, the plaintifl with w <
w" moves for preliminary injunction if and only if orrfi > Pr(G) and lp < 6cp(1 —

Pr(C)), where w* is defined as in Equation ’7.
The following numerical example shows this second possiblity of equilibrium.

Example 2 Now consider a different parameter constellation where 7r = 1 / 2, lp = 6,
cp 2 ed = 20, d = 0.9, a 2 0.2 and )3 = 0.1. Since the prior belief and the errors are
the same as in Example 1, the updated posteriors are not changed. However, now we
have such relationships that 6cp(1 — Pr(G’)) z 9.9 > IP = 6, (MT—:53 = 1% > Pr(C) =
2% and w* z 8.67, under which the plaintiffs with 11 > w" 2 8.67 will not move for
the preliminary injunction, while those with 8.67 > w 2 6 will go to trial without the

request for injunctive reliefs.

4 An Extended Model

So far our simple model of preliminary injunctions has ignored the role of the defen-
dant. A more complete model, however, must incorporate a defendant who can also
take strategic actions. Thus, we extend the previous set-up to a more generalized
one in which the defendant can make a take—it-or-leave—it offer for an out-of-court

settlement after observing the court’s ruling on the preliminary injunction.

64

4.1 The strategic defendant

The defendant can make a take-it-or—leave—it offer once the suit is filed against him.
With the plaintiff’s motion for a preliminary injunction filed and then receiving a
particular message, either C or D, the defendant will offer a optimal settlement
amount to maximize his own payoff. Given the defendant’s settlement offer, the
plaintiff decides whether to accept it or not. If the plaintiff accepts the offer, the two
parties settle; if the plaintiff rejects the offer, the parties go on to trial. If the plaintiff
drOps the suit, then the game is over with payoffs remaining as in the status-quo.
On the other hand, without the plaintiff’s motion for an injunction, the defendant
will also make a take-it-or-leave-it settlement offer, based on the rational expectation
about which type of plaintiffs do and do not file for a preliminary injunction. When
both parties go to trial, each party’s payoff follows the court’s final judgment.

There are three possible situations in which the defendant may consider a settle-
ment offer. First, if the plaintiff does not seek a preliminary injunction the defendant
makes a settlement offer of S N15 Second, should the court grant the motion sub—
sequent to the filing of an injunction, the defendant offers SC to settle the case and
avoid further litigation. Lastly, one may consider that case that a filing for injunctive
relief has been denied by the court. In this final case, to maintain consistency with
the base model, we assume that the plaintiff drops the case so that, consequently,
sD=a

In order to study the defendant’s optimal decision concerning a settlement offer,

 

15The superscript N represents the case of no motion for injunctive reliefs. It should be noted
that the offer of S N is made after a plaintiff has decided whether or not to file for a preliminary
injunction.

65

we need to specify the defendant’s payoffs in the various situations that he could
be confronted with. Suppose that the defendant’s per period payoff gain from the
disputed action is given by 9. And note that the defendant’s gain g is not neces-
sarily equal to the plaintiff’s damage w. Hence, the game being played between the
defendant and the plaintiff concerning the action in questions is not a zero—sum game.

Our analysis proceeds backward from the plaintiff’s decision concerning the accep—
tance/ rejection of the defendant’s settlement offer, to the defendant’s decision of an
optimal settlement amount, and, then, the plaintiff’s decision to ask for the injunctive
relief as a function of his per period damages w and expectations concerning possible

forthcoming settlement offers.

4.2 Plaintiff’s decision Whether to settle or not

Let us first consider the case in which a plaintiff of type w moved for an injunction
which the court subsequently granted. Note that at this stage the legal cost for
injunction hearings lp is a sunk cost, independent of the decision concerning settlement
or trial. If the plaintiff accepts the settlement offer SG, the case is resolved and the
state in which the defendant gains the right to the present behaviors in dispute. Thus,
the plaintifi’s discounted present payoff at t = 1, net of lp, from accepting the offer
SC is given by

SC — —. (9)

If the plaintiff rejects the offer, both parties proceed to trial. Then, the plaintiff

pays the litigation cost cp, regardless of the final outcome at trial, but the plaintiff

66

expects with probability 7TG to win at trial and thus make the preliminary injunction
permanent. As a result, the plaintiff’s expected payoff from rejecting the offer S G is
G) (5w

—. (10)

_5._1_
T ( W 1—6

Comparing (9) with (10), we find that the plaintiff of type w accepts the offer if and

only if the offer amount is equal to or higher than 56; where S G is defined by

G 6w
1—6'

 

(11)

We can intuitively interpret the above equality condition. The plaintiff’s total
cost of turning down the settlement offer 50 is the sum of the foregone settlement
offer (50) and his legal costs (dep), which are captured by the left-hand-side of (11).
By contrast, the plaintiff’s benefit from this choice is the permanent avoidance of
his per-period damage w by winning at trial with probability rrG. If the settlement
amount is sufficiently large, the plaintiff will prefer accepting the settlement offer to
turning it down. In this sense, we can see S G as the minimum amount needed to make

0 is defined as the marginal

the type-wG plaintiff agree to the settlement, where w
defendant who is indifferent between agreeing to the settlement at S0 and not, which
is expressed as a function of SG:

0 (1 — 5)(sG + 6gp)

6W0 . (12)

 

11}

Note that the marginal plaintiff 1110 is uniquely —— one-to—one mapping from 2120

67

G

to SC — determined by the settlement amount, which allows us to treat w as the

defendant’s choice variable for the sake of convenience. In other words, the optimal
choice of S G is a dual problem of the optimal choice of wG. The plaintiffs with w 2 wG
will prefer rejecting the offer S6 then going to trial, while those with w < wG will
accept the offer S G.

If the plaintiff makes no motion for injunction, there is no Bayesian updating
process: each party does not change its expected winning probability at trial. In
a similar manner, by comparing payoffs associated with two possible choices, the
marginal plaintiff of type wN is derived as

N (1 - 6)(SN + (Sep)

671' . (13)

 

”(U

The plaintiff with w 2 wN will prefer rejecting the offer SN and then go to trial,

N

while the one with w < w will accept the offer.

4.3 The defendant’s optimal settlement offer

In this subsection, we study the defendant’s optimal settlement offers. Needless to
say, the defendant will choose the settlement amount that yields him the maximum
net surplus. In order to calculate his expected payoff, the defendant first must have a
belief about which types of plaintiffs filed for an injunction in the first place and which
did not. As we explored in the simple model, one needs to consider two possibilities:
the plaintiff with a small damage moves for preliminary injunction or the one with a

high damage opts for it.

68

Let us first consider the case in which the defendant believes that a plaintiff with
w < w requests preliminary injunctive relief while those with w 2 117 do not, assuming
an interior critical type 1D, i.e., w E (w, 717). Then, given a granting of the injunctive
relief, the optimization problem that the defendant faces is to minimize his expected

loss by choosing 50,16 which is given by

 

r§g1E(L) = P(SG)SG + (1— P(SG)) (6cd + «01636); (14)

where P(SG) = F (wG) / F (117) denotes the conditional probability that the plaintiff
will accept the offer 50 given that the requested injunction was granted. Once the
offer is accepted, the defendant pays the settlement amount 80, so the expected
settlement payment is equal to P(SG)SG. If the settlement offer is rejected, the
defendant must pay the litigation cost Cd regardless of the trial’s outcome and may
additionally lose 9 each period from t = 2 on, if he loses at trial. The second term in
(14) represents this expected payment through litigation. As previously pointed out,

the above problem is a dual one with the choice variable of wG as follows:

 

 

 

, _ F(wG) G (5106 F(wG) G (59
r3g1E(L)——F—(fzf—))——(—6cp+7r 1_6)+(1— 1“—’(”L’0)>(66d+7r ) (15)

The first-order condition with respect to wG yields the following optimality con-

 

1"The problem of maximizing net surplus is the same problem as the one of minimizing the
expected loss.

69

dition:

#06
1—6

 

 

 

F(wG)

5 ,G (5
+f(wG) (—5op+«01’:6) — f(wG) (66d+7r01_96) = o, (16)

which shows the trade-off that the defendant faces by adjusting his settlement offer.
A marginal increment in the settlement offer (equivalently, a marginal decrease in
wc) results in not only a higher payment to the plaintiff who would accept the
settlement offer without such an increase, but also to added settlement expenditures
of -6op + #0533}? with the marginal probability of f (wG). The first two terms in
(16) capture these two effects of the marginal increase in the settlement offer. On
the other hand, such adjustment saves the defendant the cost of going to trial with

marginal probability of f (wG), which is the last term in (16). Rearranging ( 16), we

 

derive the optimality condition for wG as
FUUG) G I
+ w = + —— 1 - 6 c + c . 17
f(wG) 9 W0( )( P d) ( )

Adopting the standard assumption that the distribution F satisfies the monotone
hazard rate (MHR) condition, F / f is strictly increasing,17 the solution for wG is

uniquely determined by (17).18 For the closed form solution, if we consider a uniform

 

17Roughly speaking, this condition means that the density functions f do not grow too fast, which
is satisfied with most of the well—known distribution functions including the uniform, exponential,

and normal distributions.

18The uniqueness is evidently proved as we notice that the left-hand side of (16) increases in wG

while the right-hand side is a constant.

70

G

distribution of w on (w, a], then w is given by a function of all other parameters as:

NIH

(_IQ+g+-7-r%(cd+cp)(l—6)). (18)

From either the general expression of (17) or the above closed form solution with
a uniform distribution, we can easily ascertain the following intuitive comparative

statics.

Proposition 2 The plaintiff is more likely to settle as litigation costs get large, the

defendant’s gain from the activities in dispute increases, and the future payofls are
. . . ,G ,G ,G ,0

less valued, all other things being equal (i.e., Q32? > O, Qé’C—‘d— > 0 ; {93%— > 0; 1:53— < 0,

respectively)

Firstly, it is obvious that a plaintiff has a stronger incentive to settle as his litiga-
tion cost (cp) increases, because the option of going to trial gets costly. Secondly, it
is interesting that the plaintiff is more likely to agree upon a given settlement offer as
either the defendant’s payoff gain (9) or the defendant’s litigation cost (ed) increases.
The reason is very simple. As the defendant obtains a higher payoff gain from the
activities in dispute, the defendant will make a larger settlement offer in order to
preserve his gain. Consequently, the likelihood of settlement increases, other things
being equal. This logic applies to the litigation cost in the same manner: if the defen-
dant faces a higher litigation cost, he will offer a larger settlement amount because the
trial becomes less attractive. Thirdly, if future payoffs are valued more highly (i.e.,

as 6 increases), the plaintiff is more likely to proceed to trial because it becomes more

71

important to win in court and thus prevent his per-period loss from being permanent.
In fact, as 6 increases, the defendant’s settlement offer will increase. However, this
channel of such impact passes through the second degree, while for the plaintiff the
impact occurs as the first degree.

On the other hand, it is very interesting to study the comparative statics for the

errors in the preliminary rulings.

Proposition 3 The plaintifl is more likely to settle as the preliminary ruling is more
,0 .

likely to commit a error and less likely to commit [3’ error (i.e.,?“v < 0, that is,
71'

61110 31.10
’33-)00’nd—53—(0).

If the preliminary ruling is more vulnerable to an a error that is unfavorable to the
plaintiff, the plaintiff is more likely to accept the settlement offer (equivalently, less
likely to go to trial). The intuition is as follows. As a error increases, the significance
of the message of G as good news becomes large. Thus, the defendant’s settlement
offer will increase, which results in a larger settlement. In contrast, if the court is
more likely to commit a 13 error, the message of G might have been the result of the
court’s mistake with a higher likelihood. Therefore, the defendant’s settlement offer,
other things being equal, is relatively small so that both parties are more likely to
go to trial. In this aspect, one remarkable implication of our model for preliminary
injunctions is that the nature of court’s preliminary ruling and litigants’ views on
preliminary rulings are important factors that affect the likelihood of settlement and
settlement amount, which has not been addressed yet to our understanding.

When we consider the case in which the defendant faces a plaintiff who does not

72

move for injunctive relief, the defendant’s optimization is given by

 

minE(L) = P(SN)SN + (1— P(SN)) (60d + ”16515); (19)

F(IUN)—F(1Z’)

where P(SN) = 1—F(u‘1)

denotes the conditional probability that the plaintiff

 

accepts the offer SN, conditioned on the fact that the plaintiff did not move for

N

injunction at t = 1. From the first—order condition for w , we obtain the optimality

condition for wN :

F JN —F“~i
01> u>+w129+

 

1
-,;<1- 61(cp + ed); (20)
where a plaintiff with w > w 2 wN goes to trial, and otherwise accepts the settlement

offer S N . For a uniform distribution of w on (w, a], wN is characterized by

MN:

(a+g+%(cd+cp)(1—6)). (21)

[\DIH

4.4 Plaintiff’s decision to seek injunctive relief

By definition, the cutoff type plaintiff, 12'), must be characterized by the equality of the
expected payoffs with and without the motion for a preliminary injunction. Figure 2-4
shows the plaintiff’s initial choice concerning the motion for a preliminary injunction

and the subsequent decision whether or not to accept the settlement offer.

73

Preliminaiy No Injunction
Injunction

6 ~. N ——
11‘ H' M 11' 11‘

 

Settle at $6 Go to trial Settle at SfI Go to trial

A ‘A A

 

V

7‘

 

 

 

 

 

Figure 2—4. The Choices of Plaintiffs I

The choice of making the motion for injunction costs the plaintiff 1,, in legal
expenses, regardless of the court’s eventual preliminary ruling. The injunction is
granted with probability Pr(G), then the plaintiff decides to proceed through litiga-
tion to make the preliminary injunction permanent. If the court does not grant the
injunction, the plaintiff drops the suit to save the litigation cost. Thus, the plaintiff

of type w obtains an expected payoff of

6d!

 

 

——lp + Pr(G) (—6cp — (1— WC)

from moving for a preliminary injunction. If the plaintiff of type 121 goes directly to
trial without requesting a preliminary injunction, he suffers at least the one period
damage of a, but ends up accepting SN with w < wN . For this choice, his expected
payoff is

—u”; + SN — (23)

1 — 6 '
From the equality of (21) and (22), once again we can think of the trade-offs

that the plaintiff faces in terms of the benefit and the cost of moving for preliminary

74

injunctive relief.

(5. ~,

1_6=n+sN on

Pr(G')(w — (Sep) + (1 — a)7r

 

The borderline—type plaintiff prevents his irreparable damage from occurring with
probability Pr(G) when he also pays the litigation cost, because he ends up going to
trial in which he can prevent his damage permanently from t = 2 onwards with the
ex ante probability of (1 — a)7r. These benefits from the motion for an injunction are
captured by the left-hand-side of (24). In contrast, when he moves for a preliminary
injunction, his cost is the sum of the legal cost lp and the foregone settlement amount

S N.19 With some algebra, we derive the critical plaintiff type to be

U—PNGMMpr—fl%%(g+%®d+%M1—®)

(17:66) (a - é) — Pr(G) (25)

 

u}:

 

Comparing the cutoff type of plaintiff in this extended model, a, with that in
the simple model, w*, it is easily noticeable that even after we add the stage of the
defendant’s settlement offer, the intuition that drives the plaintiff to take the move
for the injunction works in a similar manner for both cases.

One remarkable difference is, however, that the w*—type plaintiff — when we do
not consider the defendant’s settlement offer — goes to trial without the motion for

a preliminary injunction, while the w-type plaintiff accepts the settlement offer S N

 

19If we relax the assumption that the plaintiff drops the suit given the message of D, so that we
allow him to go to trial, we can calculate the settlement offer S D from the defendant. In this case,
the cost of the motion for injunction is reduced to 1,, + (SN — SD). Since this possibility does not
change the qualitative results of this article, we keep our present assumption.

75

at the stage of the defendant’s settlement offer. Moreover, in the extended model, we
obviously have more factors as the determinants of the critical type of plaintiff. Now
the defendant’s gain from the allegedly unlawful behavior, indexed by the parameter
9, and the defendant’s litigation cost, denoted by ed, come into play — something

that could be ignored in the simple set-up.

Proposition 4 A plaintifir is less likely to file for the preliminary injunction as either
the defendant’s gain from the behaviors in dispute (9) or the defendant’s litigation cost

increases (i.e., %% < 0 and 32—; < 0).

The comparative statics regarding the parameters of g and cd can also be explained
intuitively. As the defendant stands to gain more from the actions in dispute, he is
willing to make a higher settlement offer. Knowing this, the plaintiff’s incentive to
file the motion for a preliminary injunction gets weakened because the settlement
SN becomes more attractive, other things being equal. In a similar spirit, as the
defendant’s litigation cost increases, the defendant who wants to avoid the expensive
litigation process will offer a larger settlement amount. As a result, the defendant at
the margin will be more inclined to choose not to move for a preliminary injunction.

One benefit from our two-step analysis from the simple version of model to a more
generalized model with the strategic defendant is that it shows how the defendant’s
uncertainty about the plaintiff’s damage level and his interests associated with the
litigation are reflected on the settlement offer; and how this, in turn, affects the

likelihood that a preliminary injunction is sought.

76

4.5 The case of high-damage plaintiffs request injunction

In Subsections 4.3 and 4.4, we analyzed the case in which a plaintiff with small
damages motions for a preliminary injunction. In this Subsection, we study the other
possible equilibrium in which the defendant believes that plaintiffs with w 2 112 request
a preliminary injunction while those with w < 1?) do not.

4—— No Injunction —hj¢— Injunction —>

A

N G
w w W w u

 

Settle at SN Go to trial Settle at SG Go to trial

A L
‘ '

 

 

A ‘
‘ r

V

 

 

 

 

Figure 2—5. The Choices of Plaintiffs II

All the steps in the analysis are made in the exactly same manner as for the
previous case. Therefore, we do not repeat all the details here. The defendant’s

optimization problem when the court grants the injunction is given by

 

Iggl E(L) = P(SG)SG + (1 — P(SG)) (tied + ”016—95) ; (26)

where one should note that P(SG) = (F(wG) -— F(w))/(1 —— F(w)). The first-order

G

 

condition that must be satisfied at w is given by
F(wG) — F(w) 1
+ w = + — 1 — (5 + c ; 27

77

and for the uniform distribution of w on (w, 117], we have the solution for wG as

LOG :

tol—

(w+g+;rlG-(cd+cp)(1—6)). (28)

When the defendant faces a plaintiff who did not move for injunctive relief, he

minimizes the expected loss by choosing wN:

 

minE(L) = P(SN)SN + (1— P(SN)) (6cd + 7r 69 ); (29)
wN 1— d

F(wN)

where P(SN) = Ffli’) .

 

The Optimal wN satisfies the following condition

wN
f(le +wN =g+%(1—6)(op+cd). (30)

 

For the uniform distribution of w on [w, a], we have

wN=

(w+g+%(cd+cp)(1—6)). (31)

ml—

Based on this decision-rule concerning Optimal settlement offers, we once again can
characterize the cutoff plaintiff of type if) as

621)

Pr(G)(SG + 120+ (Sep :1, + 7r1_ 5'

 

(32)

78

 

The borderline-type plaintiff, w, prevents his per period damage if) and is offered
30 when the injunction is granted. In addition, he also saves the litigation cost
because he will not proceed to trial, regardless of the court’s decision on the injunc-
tion.20 These benefits from the choice of moving for an injunction are captured by the
left-hand-side of (32). Clearly, the costs associated with the motion for an injunction
consist of the legal cost, lp, and the foregone potential prevention of the damages by
winning at trial with probability of it, which are represented by the right-hand-side of
(32). Needless to say, the plaintiff will move for the injunction if the benefit of filing
for an injunction exceed the cost. The critical type if) for the uniform distribution is

derived as

 

 

 

where only a plaintiff with w 2 w moves for a preliminary injunction.

5 Discussion of Further Extensions

5.1 The British rule in the allocation of litigation costs

Each party bears his own litigation costs regardless of the trial’s outcome under
the American fee rule, which has been assumed throughout the paper. Under the
alternative British rule, contrastingly, the losing party bears all the litigation costs.

The change in the governing rule in the allocation of litigation costs affects on the

A

2” Recall, if the injunctive relief is not granted, the plaintiff will drop the suit.

79

R"...

players’ payoffs, which in turn has an impact on the decisions of the settlement offers
and the motion for requesting a preliminary injunction.

More specifically, a plaintiff who goes directly to trial without filing for an in-
junction does not need to pay his litigation cost cp if he wins the case, whereas
he additionally bears the defendant’s litigation cost cd with his loss at trial. That
is, the rule change—from American rule to British rule—has the net impact of
nR(—6cp) + (1 — nR)(6cd) on the expected payoff of going to trial, where R E {G', D}.
The likelihood of a filing for a preliminary injunction and the likelihood of a settle-
ment hinge upon the relative magnitude of litigation costs, the prior and posterior
beliefs, which do not allow us to have a clear-cut way to describe the effect of the rule

change for legal cost allocation.

5.2 Optimistic- and pessimistic bias

In our models we assume that both parties share the same prior belief about a case,
i.e., 7r 2 up = 7rd. However, when a party has private information containing some in-
formation to infer the distribution of 7r differently from the other party, the prior may
differ across the agents. In addition, when we consider the optimistic or pessimistic
bias toward the quality of a case when a particular message is received through the
rule on the preliminary injunction, the posteriors may become different across agents.
That is, we can think of the case such that 7r;2 75 a? for i,j = d, p , i 75 j, and
R E {G , D}. Fortunately, in even such a case, our model can be easily modified to

see how these changes affect the likelihood of the motion for a preliminary injunction,

80

the settlement amount, and litigation decisions, by just distinguishing the defendant’s
beliefs and the plaintiff’s beliefs with the use of subscripts. Of course, this modifica-
tion yields a lot of possibilities depending on the relative magnitude of each party’s

prior.

5.3 The judgment favoring social efficiency

So far in our models we have assumed that the court’s discretion is based on only the
state in which the case resides: if the state is valid, the court in principle must be
favor of the plaintiff; otherwise, it must be favor of the defendant. Another interesting
point is that the court (or, judge) may consider the public interest and total efficiency

21 One way of

as important factors for judgment in addition to the case merits.
approaching this is that the court’s judgment can be described as a function of the
defendant’s gain and the plaintiff’s damage. Specifically, we may think of a function
7T6 = 7rc(g — w) with Tr’C < 0. Then, for the case with high damages and low gains,
the court is more likely to be in favor of the plaintiff, while for the opposite case with
low damages and high gains, the court will more likely be in favor of the defendant.
Roughly speaking, this consideration may increase our social welfare because then
the plaintiff’s damage is better protected and possible nuisance suits are less likely

to happen. Of course, once again the relative magnitude of the plaintiff’s and the

defendant’s litigation costs will affect how such consideration impacts social welfare.

 

21For instance, the Judge Sydney H. Stein in the Plavix case wrote in his ruling that “Although
there are competing and substantial public interests at stake on both sides of this litigation, the
balance of those competing public interests slightly favors Sanofi. The public interest in lower-
priced drugs is balanced by a significant public interest in encouraging the massive investment in
research and development that is required before a new drug can be developed and brought to
market.”

81

 

6 Concluding Remarks

In this article, the court’s ruling on a motion for a preliminary injunction is viewed as
a unique (noisy) informative message concerning the likely final judgment in addition
to being the only channel through which the plaintiff’s irreparable damage can be pre-
vented. In this sense, the plaintiff’s motion for preliminary injunctive relief is in part
an information gathering activity. In this sense, we seek a new role for understanding
preliminary injunctions as methods of information transmission, which complements
the work of Lanjouw and Lerner (2001) in which the preliminary injunction is a device

of raising rivals’ costs.

82

References

[1]

[2]

[3]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

Bebchuk, L. “Litigation and Settlement under Imperfect Information.” Rand
Journal of Economics, Vol. 15 (1984), pp. 404—415.

Bizjak, John M. and Jeffrey L. Coles, “The Effect of Private Antitrust Litigation
on the Stock-Market Valuation of the Firm,” The American Economic Review,
Vol. 85, No. 3. (Jun., 1995), pp. 436-461.

Boyce, John R. and Aidan Hollis, "Preliminary Injunctions and Damage Rules
in Patent Law," Journal of Economics 59’ Management Strategy, Vol. 16 (2),
Summer 2007, 385-405.

Briggs, H. C., Huryn, K.D. and McBride, M.E. “Treble damages and the in-
centive to sue and settle” RAND Journal of Economics, Vol. 27, No.4, (Winter
1996) pp. 770-786.

Che, Y-K. and Yi, J .G. “The Role Precedents in Repeated Litigation,” Journal
of Law, Economics 63 Organization, Vol. 9, No. 2. (Oct., 1993), pp. 399-424.

Choi, Jay Pil, "Patent Litigation as an Information-Transmission Mechanism,"
The American Economic Review, Vol. 88, No. 5. (Dec., 1998), pp. 1249-1263.

Hirshliefier, Jack and John G. Riley, The Analytics of Uncertainty and Informa-
tion, Cambridge University Press, 1992.

Lanjouw, Jean O. and Josh Lerner, “Tilting The Table? The Use of Preliminary
Injunctions,” Journal of Law and Economics, Vol. XLIV (October 2001), pp.
573-603.

Meurer, Michael J ., “The settlement of patent litigation,” Rand Journal of Eco-
nomics, Vol. 20 (1989), pp. 77-91.

Nalebuff, B. “Credible Pretrial Negotiation.” Rand Journal of Economics, Vol.
18 (1987), pp. 198—210.

P’ng, 1. “Strategic Behavior in Suit, Settlement, and Trial.” Bell Journal of
Economics, Vol. 14 (1983), pp. 539-550.

Reinganum J. and Wilde, L. “Settlement, Litigation, and the Allocation of Legal
Costs.” Rand Journal of Economics, Vol. 17 (1986), pp. 557—566.

83

 

Chapter 3. The Strategic Tying with Consumer Switching Costs

In this chapter, I study a new rationale for the tying practice between complementary goods
in the presence of switching costs. I find that the monopolist may strategically commit to
tying in order to capture the dynamic rents associated with those who have relatively high
switching costs, especially if the monopolist has an inferior complementary product to the
rival firm’s complementary one. I also show that the monopolist’s tying decreases both
consumer surplus and social welfare relative to the decision of no tying, because switching

costs are endogenously incurred and the consumers end up using an inferior good.

1. Introduction
Because of Microsoft's behavior and a series of the associated court cases, a dominant
firm's tying’ strategy has gained considerable attention in and out of economics. In recent
lawsuits against Microsoft’s tying between its almost monopolized Windows operating
system and other application software such as Internet Explorer, Window Media Player,
and Window messenger, tying allegedly impairs competition on the merits because it
makes consumers bear additional costs to search, download, install, and learn other prod-

ucts. Unfortunately, however, little attention been has given to this issue. This paper stud-

 

’ Tying refers to the behavior of selling one product (the tying product) conditional on the pur-
chase of another product (the tied product). J. Tirole (2005, p.7) distinguishes tying and bundling
as follows: “. .. the tied product is available on a stand-alone basis under tying, but not under
bundling.” Here both terms are interchangeable because this distinction is irrelevant if a tied-good

is valueless without a tying-good.

84

 

ies how the monopolist can use tying strategically in the presence of consumer switching
(learning, or installation) costs, and its effect on consumers and competing firms.

In a simple two-period model, I find that the monopolist may strategically commit to ty-
ing his two complementary goods especially if his own non—monopolized product is infe-
rior to alternatives. The monopolist must offer a more attractive price to sell his own infe-
rior non-monopolized good on a stand-alone basis because he needs to compensate for
expectedly higher switching costs as well as for product inferiority. As a result, if the
price afier the monetary compensation falls into negative, then tying becomes the only
effective way for the monopolist to sell its products in earlier marketing.

By doing so, the monopolist can earn more profits from those who have relatively high
switching costs in repeated sales. If the dynamic rents from these “loyal” consumers2 ex-
ceeds the loss from not allowing a superior complementary product used together, the
monopolist will have the incentive to tying its products.

In addition, I show that the tying decision may decrease both consumer surplus and social
welfare because it endogenously raises switching costs and makes the consumers use an in-
ferior good. Of course, we must be extremely cautious in interpreting this result because
such prediction is from the specific framework posited in this paper: it involves several
crucial assumptions and controls for many other factors possibly driving the tying deci-
sion. However, ceteris paribus, this study provides a theoretical support for the concern

about the negative effects of tying on the rivals and consumers with switching costs.

 

2 “Switchers” are in a sense penalized relative to “loyal” consumers, those who repeatedly pur-
chase from the same firm. See Chen (1997) and Klemperer (1987a, 1987b, 1995), etc. for refer-

CUCES.

85

 

«new

In fact, there have been various justifications for why a firm wants to tie its products:
for examples, tying may increase efficiency and assure quality better; a firm may use ty-
ing to evade price controls or to exercise price discrimination. Nevertheless, tying has
been one of the most controversial strategic actions that a dominant firm can take to ma-
nipulate the competitive environment in its favor. This has been mainly due to the “lever-
age theory,” which contends that a monopolist in one market can use its monopoly power
to monopolize other markets as well. This logic has played against monopolists in the
history of US. antitrust cases.3

However, a group of economists known as the Chicago School4 successfully showed
that such an argument is logically vulnerable. Their intuition is that a monopolist cannot
have more profits with tying because it can already extract the entire monopoly rent
through adjusting the price of its monopolized primary product.5

To this criticism, Whinston (1990) showed that a monopolist can increase its profit
with the commitment to tying for independent, differentiated goods in oligopoly market
structure. The commitment to tying leads to the more intensified competition in the tied
good market, because with tying the monopolist cannot sell the monopolized tying-good
on a stand-alone without the non-monopolized tied-good. Therefore, the potential entrant

would rather choose not to enter the market because of the decreased post-entry profit.

This mechanism has been known as strategic foreclosure.

 

3 Such cases include United States vs. Terminal Railroad Association of St. Lewis, 224 US. 383
(1912); International Business Machines vs. United States, 298 US. 131 (1936); Standard Oil vs.
United States, 337 US. 293(1949).

4 As well-known references, see Director and Levi (1956), Bowman (1957), Posner (1976), and
Bork (1978), etc.

5 This argument has also been known as “one monopoly profit theory.”

86

 

It is noteworthy that the intuition of the strategic foreclosure does not directly invali-
date the Chicago School’s logic. As emphasized in Whinston (1990), the Chicago
School’s criticism generally holds for complementary goods if the monopolized good is
essential for all uses of the non-monopolized good.6 Certainly, if there is any use for the
non-monopolized good without the monopolized good, tying once again can emerge as a

profitable strategy even for complementary goods.

 

F.
For such examples, Whinston suggested two situations: when there exists an inferior
and competitively supplied alternative primary component in the market, when there is a
second use for the non-monopolized product such as replacement parts market. He
showed that the monopolist once again might prefer strategic foreclosure in such circum- *9

stances.

This paper contributes to this literature by providing another situation where tying can
be a profitable strategy even for complementary goods. Remarkably, however, tying in
this paper does not necessarily result in strategic foreclosure. In other words, the rival
firm can sell its product in period two even under tying regime.7 In this sense, this paper
complements other studies showing the incentive to tying without resorting to strategic

foreclosure.

 

6 Carlton and Waldman (2005) show that this is not true for durable-goods where product up-
grades can be important issue. Interestingly, they show consumer switching costs amplify the in-
centive to tying. This paper and theirs have something in common in that both study the tying in-
centive for complementary goods in the present of consumer switching costs.

7 If the monopolist is the sole producer in the primary market in both periods, then it is only twice
repetition of the one-stage game where the Chicago School’s one monopoly profit theory exactly
fits. That is, if the rival firm cannot produce the primary component in period two, the monopolist

will not tie its products.

14-1—1

87

Choi (2004) showed that we can see tying as a strategic commitment to a more aggres-
sive R&D investment, which reduces rivals' R&D incentives in the tied good market. The
monopolist can make a higher overall profit because of a higher dynamic rent in the tied-
good market in spite of the loss from initially intensified price competition.

Church and Gandal (2000) studied the possibility of a profitable vertical integration in
the hardware-software system market. In their model, vertical integration and the finn's
decision to make its software incompatible with its rival's hardware can occur without
monopolizing the hardware market. They showed that if hardware technologies are suffi-
ciently differentiated and the marginal value of a software variety is small enough, the ri-
val hardware firm has a positive market share because of the consumers who have rela-
tively strong preference for its differentiated hardware. Since we can regard the irreversi-
ble tying as a firm's vertical integration with a subsequent incompatibility decision, their
study provides another case of a profitable tying without excluding rivals.8

The remainder of this paper proceeds as follows. Section 2 describes the model. Sec—
tion 3 analyzes the market equilibrium with tying and without it. Then, Section 3 explains
why and when the monopolist has the incentive to the commitment to tying, and how ty-
ing affects on the rival. Section 5 offers the welfare analysis and discusses related impli-
cations. Lastly, Section 6 closes the paper. Proofs of lemmas and propositions are in Ap-

pendix.

 

8 Note that the same term “foreclosure” has different meaning in their paper. They defined that
foreclosure occurs when an integrated firm — a merged hardware-software firm — makes its soft-
ware incompatible with a rival hardware. In contrast, in this paper “foreclosure” means the situa-

tion where one firm is excluded from the market because of its low profitability.

88

‘- nn'fin" '-" " Ii”

 

2. The Model

Consider two products, A and B, which must be used together as a system in one-to-one

 

proportion. There are two periods. A continuum of consumers, whose measure is one, has
a unit demand for each component in each period: each consumes either one or zero unit
of the system good. That is, each consumer faces a repeated purchase in period two.

In period one, there is a sole producer in market A; two firms compete in prices in market W
B. In period two, however, the rival firm in market B enters market A.9 The monopolist
in market A and the other firm are denoted as firm 1 and firm 2, respectively. As natural

notations, A1 and A2 refer to the primary component produced by firm 1 and firm 2, re-

 

spectively. Similarly, B1 and B2 refer to the complementary component of firm 1 and 5'

firm 2, respectively. Assume that both firms have the same constant unit-production cost
CA and CE for each component.

Assume that Al and B1 are inferior to A2 and B2 by the monetary value of AA (20)10
and A3 (20), respectively. Each consumer derives a value V from consuming A1 and B1
together. Obviously, he/she enjoys a higher value V+AB, V +AA, or V +AA+A3 from the
consumption of A1+B2, A2+B1, or A2+B2, respectively. The value V is sufficiently high

to ensure that every consumer ends up consuming at least one system in equilibrium.

 

9 We can think of the case in which the monopolist’s primary good is protected by patents that
expire at the beginning of the second period. Unlike Carlton and Waldman (2002), the entry and
exit of a rival primary good producer are not issue in this model.

’0 The qualitative result of this paper is robust to relaxing the superiority of A2 over A1. I make

this assumption for more general description of the model and the ease of explaining the intuition.

"11

89

Each consumer faces an individual switching costs, uniformly distributed over [0, 1],
when he/she uses the product that was not used previously. 1’ I assume that each con-
sumer has the same switching cost for both components, A and B. That is, if a consumer
switches both components in the second period, he/she needs to bear the switching cost
twice.12 Following the switching-cost literature, the consumers realize their switching

costs only after the first period.’3 This assumption implies that all the consumers are iden-

 

tical in period one; they become heterogeneous in the repeat—purchase according to their
personal switching costs.

The timing of the game is as follows. At the beginning of period one, the monopolist

 

makes a decision whether to tie its products irreversibly through technological arrange-
ments in the production process or in product design. That is, with tying the consumer

cannot use B2 with A1 together. After tying decision, two firms engage in price competi-

 

” For instance, it is costly to try different software and attain a similar level of skill as for the pre-
vious one. For example, a consumer having previously used MS Word and MS Excel will pay
some costs in switching to Word Perfect and Lotus. This cost may vary across consumers (or us-
ers) because of they differ in the rate and effort level in learning process. See Klemperer (1995)
for abundant examples and various interpretations for switching costs.

'2 More generally, switching costs for each product can be independent so that we can think of the
total switching cost as SA+S3, where SA, SB 6 [0, 1]. Then, the demand for each consumer must be
represented two-dimension in the space of SA and 33, which drives the analysis much complicated.
In my opinion, the simple specification in the model serves to avoid such complexity with the key
intuition still alive.

’3 For references, Chen (1997), Gehrig and Stenbacka (2004), Klemperer (1987), etc. In fact, if
consumers are aware of their own switching cost before the first transaction, the analysis becomes
severely complicated. This is because firms’ choice of tying and pricing are affected by the con-
sumers’ strategic motives, which in turn has influence upon consumers’ choices. Aside from
these analytical complications, consumers may not know their ex post switching costs due to the

presence of uncertain factors in the learning process.

90

 

tion. In period two, once again the firms compete with prices under the same tying deci-
sion made in period one. This assumption reflects that tying decision is a long-term con-
sideration compared to the sales in each period. Finally, consumers and firms have the

same discounting factor normalized to one. As a rule, the analysis proceeds backwardly

for the subgame-perfect Nash equilibrium.

3. The Equilibrium Analysis: with tying and without tying
3. 1 Tying regime

To begin with, let me analyze the case in which the monopolist commits to an irreversible

 

tying between A1 and BI so that every consumer buys the system (A1+B1) in period one.
Assuming that tying decision is effective throughout both periods, neither A1 nor B1 is
available on a stand-alone basis even when consumers make a repeat purchase. Thus,

each consumer faces two choices in period two: buying the same bundle (A1+B1) from
firm 1 or buying (A2+B2) from firm 2.

Consumers can avoid their switching costs if they use the same system as in period
one, while by doing so they end up using the inferior system. The marginal type of con-
sumer, denoted by E , who is indifferent between the two choices must satisfy the follow-
ing equation

V—P1=V+AA+AB—P2-2§ (1)

91 I

where P,- denotes the total price of a system composed of two components produced by
firm i, for i=1, 2.” The left-hand side in equation (1) measures the net utility from the
choice of (A1+B1), while the right-hand side is for switching to the choice of (A2+B2)
that yields better quality with doubled switching costs. By solving the equation (1) for '5 ,
the threshold consumer '5 is given by

AA+AB+PI_P2

ll‘
2 (2)

 

§=

Since the consumers with s S '5 will prefer switching to the choice of (A2+BZ), the de-

mands for firm 1 and firm 2 are 1— 3' and E , respectively. Substituting these demand

 

functions into each firm’s profit expression, then maximizing with respect to each firm’s _,,,
bundle price yields the following reaction functions

:2—AA-AB+CA+CB+P2 PzzAA+AB+CA+CB+P1.

2 2 (3)

 

P1

 

By simultaneously solving two response functions, we get the equilibrium prices as

PI=CA+CB+4—_é—43—:A—B fi2=CA+CB+-2—+駗f—Ai, (4)15
For such equilibrium prices, the marginal consumer is
A A
§ = l + L11 (5)
3 6

 

’4 P2 is equivalent to the sum of the price of A2 and that of 82, i.e., pAz + p32 = P2. Two compo-
nents virtually constitute a unit of bundled-product because consumers always need both to con-
sume one system.

’5 Variables with a tilde denote the tying regime.

““1!

92

where the interiority of the solution is ensured with the condition A A + A B < 4. As ex-

pected, 3' increases in AA and AB: more consumers will switch to the highly superior sys-
tem.

Finally, we can compute the second period profit for each firm as

.. (4—AA—AB)2 1 (2+AA+AB)2
72' 2 72'2: .
18 18

 

(6)

 

which shows the intuitive result that firm 1’s profit decreases in AA and A3, but firm 2’s
profit increases in either A, or A3, or both.

The monopolist, firm 1, can exploit the entire surplus from the consumers in period 1
and earns the profit of ( V — c, — c8 ), because we consider two complementary products.
Consequently, firm 2 earns no profit in period one because it cannot offer the component
A until the second period. Summing the profits over both periods, the total profits for

each firm are given by

(7)

 

 

2
1:12 : (2+AA +AB) .
18 18
3. 2 No Tying Regime
Now let me study the case in which the monopolist did not commit to tying arrangement.

Then, consumers can freely consume any available combination in both periods.

3. 2. 1 The subgame with B1 sold in period one
Suppose that the monopolist sold his inferior product B1 in period one. Then, a consumer
facing the repeated transaction will have three choices: repeating the same consumption,

(A1+B1); changing either product A or product B, (A1+B2) or (A2+Bl); or changing

93

 

 

 

both brands, (A2+B2). Let me assume A3 2 AA in order to reduce the number of cases to
analyze. Then, consumers will prefer (A2+Bl) to (A1+B2) because they never switch to
an inferior system at the same switching cost.

Once again, we can characterize the threshold types by comparing the utilities for each
choice. The consumer who is indifferent between (A2+B2) and (A1+B2), denoted by § ,
satisfies the following equation F-

V+AA+AB—pA2-p82_2§=V+AB"PA1’PBZ—§- (8)
The left-hand-side of equation (8) is the net surplus when a consumer switches to

(A2+BZ) from (A1+B1), while the right-hand-side captures the net surplus when a con-

 

sumer switches to (A1+BZ). Similarly, the consumer who is indifferent between (A1+BZ)
and (A1+B1), denoted by s , is characterized by the equation
V+AB-PA1-P32-§=V-PAi-Pm- (9)

From (8) and (9), two thresholds are

91)

:AA+ pA1_pA2 §=AB+pBl—PBZ° (10)
Assuming s S s that is indeed satisfied in equilibrium, we can derive the demands of
the consumers in period two: those with s _<_ s choose (A2+B2) by changing both compo-
nents, those with s < s s s choose (A1+B2) by changing only the complementary com-
ponent, and those with s > 5 do not change either product because of their relatively high

costs of switching.

3. 2. 2 The subgame with 82 sold in period one
Suppose the consumers bought the superior product B2 in period one. Then, they can

make any choice in period two: repeating the same choice (A1+BZ), buying (A2+B2)

94

with changing the primary component, the choice of (A1+B1) by switching back to the
inferior B l , or changing both brands with doubled switching costs into (A2+B1). How-
ever, the option of(A1+B1) is never chosen with the condition AB 2 1, and the choice of
(A2+B1) is also dominated by other choices in equilibrium.’6 Since these two options are

not interesting — besides, the analysis becomes much simple -— hereafter we restrict our

 

attention to the first two cases, assuming AB 2 1. q]
The consumer who is indifferent between (A1+B2) and (A2+BZ), denoted by 3‘, satis- 7—

fies the condition of

 

V+AB—pAl_PBZ=V+AA+AB-PA2_PBZ—S*° (11) if
The left-hand-side in equation (10) measures the net surplus of repeating the choice of
(A1+B2), and the right-hand-side captures the net surplus of switching the primary com-
ponent to A2. The marginal consumer, sf, is given by
S*=AA+PA1'PA2- (12)
Since those with s S St will choose (A2+B2), the demands for firm 1 and firm 2 are 1— s’

and s' , respectively. The left- and right panels in Figure 3-1 show the choices of the con-

sumers when B1 and B2 are sold in period one, respectively.

 

’6 Specifically, in equilibrium no consumer would switch back to the inferior combination
(A1+B1) if and only if A321. The explanation for this outcome is as follows. Note that the mo-

nopolist is still a “dormant” seller in market B who can produce Bl at cost c3, even if BZ sold in

period one. The consumer who is indifferent between keep buying BZ and switching to B1 is the

type p 32 — CB -— A B in terms of its switching cost. Thus, the demand for B2 is
1- p 32 + A B + c B . The profit maximization problem for this case yields the equilibrium price

for B2 as c B + (1 + A B ) / 2 , the according marginal type is (1 - A B ) / 2 . Consequently, no con-

.5 l”

sumer will switch to Bl if and only if A B 2 1.

With Bl sold With B2 sold

A *
0 s S 1 0 IS 1
l -

A2/B2 Al/B2 Al/Bl A2/B2 Al/B2

1

Figure 3-1. Consumer choices in period two

3. 2. 3 The prices and profits in equilibrium
Now we are ready to derive the equilibrium prices in period two. Let 0' denote the share
of consumers who bought B1 from firm 1, the monopolist in market A in period one. The

second-period profit expression for firm 1 follows as

7’1 = U[(PAI —CA)(1-§)+(PBI ‘03)(1—§)l+(1-0)(PA1 ’CA)(l-S*)- (13)
Firm 1 will sell his primary component A1 to those with s > 3" who bought B1 previously,
while he will sell A1 to those with s > 3' who did not buy B1 in period one.17 In addition,
firm 1 earns the profit by selling his B1 to those with s > 3" who bought B1 in period one.
In a similar manner, firm 2’s profit expression when the monopolist did not commit to ty-
ing is given by

”2 = U[(PAZ ‘CA)§+ (P32 ‘CB)§)l+(1 ’0')I(PA2 *6/03” +(P32 “Csll- (14)

Substituting demand functions into each firm’s profit function, then maximizing with

respect to each firm’s prices, we have following reaction functions for the primary prices

_l—AA+PA2+CA
2

 

 

'A + +0
10.42: A pAl A, (15)

PAI 2

 

’7 As shown in (19), § and 3‘ become equal. Thus, the expression (13) can be simplified into
7’1=(PA1—CA)(1-§)+0(P31‘63)(1-5).

96

'\ v
”a
O
:-

 

 

 

which are independent of o. By solving response functions, we can find the Nash equilib-

rium prices as

(16)

 

 

2—A 1+A
A 10:12=CA+ A

* =c +
PA] A 3 3

Recall that all the consumers are ex ante homogeneous so that there would be either 0 = 1

or o = 0, unless both firms post the same price for the complementary product in period

 

 

I!-
one.’8 For the case of o=1, we can derive the response functions for the complementary
Ii“
prices as
l—A +p +c A +p +c ,"s
P31: B 232 B .032: B 231 B (17) -,_
s

 

The equilibrium prices are easily derived and given by

Z-AB l+AB

3 (18)

 

at:
P32 =63 +

 

at:
P31 = 03 +
Let me assume A A s 2 and A B s 2 so that the profit margin is nonnegative in (16) and

(18). The thresholds in equilibrium are identified as

S*=l—-+—AA §=I+AA §=I+AB. (19)

3 3 3

 

 

Finally, the equilibrium profit for the case of o=1 are derived as

 

(20)

 

_ 2 _ 2 * 2 2
7r"'=(2 AA) +(2 As) ”2:(1+AA) +(1+AB)
9 9 9 9

where the single asterisk is for the case of 6:1.

 

’8 This is because firms are asymmetric in period one in that firm 1 is the monopolist in market A.
This differs from other articles that analyze a symmetric interior solution for the market share in
period one, i.e., oe[0, 1]. See e.g. Caminal and Matutes (1990), Chen (1997), Gehrig and Sten-
backa (2004), Klemperer (1987a, 1987b), Marinoso (2001), and Fudenberg and Tirole (2000) for

two symmetric firms.

97

Similarly, for the case of 6:0 we can derive the following equilibrium prices

** *1: 1+A
P31 =03 P32 =63 + 2 B- (21)

 

For these equilibrium prices, each firm has the profit as followings:

 

2 2
”r*:(2 AA) ”**:(I+AA) +I+AB

22
9 2 9 2 ()

where the double asterisk denotes the case of o=0.

3. 2. 4 Total profits without tying

To identify when the monopolist has the incentive to tying, we need to compare the over-

 

all profits in two-period total with and without tying. Note that the monopolist can always
claim the entire surplus in period one through the price of his monopolized good. That is,
the intensified price competition in market B does not make the monopolist worse off. ’9
However, the monopolist cannot capture the surplus A3 generated by the superiority of
82 if he sells the inferior product B1. Remarkably, I deliberately assume that the mo-
nopolist can capture the entire surplus A3 generated by the presence of B2 in order to
make the most disadvantageous situation for the monopolist’s tying decision.

Using the previous derivations, we can specify the overall profits of firm 1 when B1

and B2 are sold in period one respectively as

 

’9 This result is quite different from the outcome of standard switching cost literature in that the
monopolist firm does not compete away his surplus in the form of a low price in the initial com-

petition.

7"}

98

 

(2—AA)2+(2—AB)2
9 9

n’,’ =(V—cA —c3)+(
2
n?*=(V—cA—c3)+AB+[QZ§L]. (23)

Firm 2 cannot earn any profit in period one under the assumption that the monopolist

 

captures the entire surplus, even if it successfully sold B2 product. However, firm 2 can
sell its BZ to the entire consumer in period two, which was not the case if B] sold in the

previous sales. The overall profits of firm 2 when B1 and B2 are sold in period one is re-

 

 

 

spectively given by
2 2 2
H3=[<1+3A) +(1+:3) ] “3*:[<1+:\A> +1393] (24,

4. The Incentive to tie and its effect on the competitor
The monopolist had no reason for tying its complementary products if there had been
only one transaction, which is the Chicago School’s argument. With tying, the monopo-
list only loses the benefit from a superior complementary product used together with his
monopolized good A1. However, we cannot apply this logic to a two-period setting with
consumer switching costs where the early sales of Bl may cause the consumers who have
relatively high switching costs to choose Bl over B2 in repeat transactions. That is, now
the monopolist can earn some benefits from inducing the consumers to buy his inferior

complementary good B 1.
More specifically, the monopolist additionally earns 7r; — 72'1“ = (2 — A B)2 / 9 in period

two if he sells B1 in period one. Since, for this case, the monopolist cannot capture the

surplus A3 generated by the superiority of B2 in period one, the monopolist would like to

99 F

sell his own complementary product B1 unless A3 — the cost of tying — is enough large,

which is summarized in the following lemma.

Lemma 1. The monopolist has a higher profit by selling his own inferior product B1 in
period one than when the rival firm sells B2, if and only if A 3 3 AB = (13 — 3Jfiy2

z0.315.

It is noteworthy that the monopolist’s willingness to sell his product B1 does not neces-
sarily imply that he can do so. It is the consumers who decide to buy which firm’s com-
plementary product with no tying. Accordingly, the monopolist must compensate for any
utility loss associated with the inferiority of his product B1 to induce the consumers to
choose B1 over B2.

If the consumers are myopic (naive, or short—sighted) in the sense that their purchase
decision is based on the first period utility only, the monopolist could induce them to buy
Bl with a price cut of A3 relative to the rival. On the other hand, if the consumers are ra-
tional (sophisticated) so that they consider the effect of the switching costs on later
choices, he needs to compensate for expectedly higher switching costs as well as for
product inferiority.

In order to compute how much the monopolist has to lower its price of B2 relative to
the price of B 1 , let me compare the expected total payment per consumer for two distinct

subgames.

100

 

If a consumer purchased B1, he/she will switch to B2 with probability of (1 + A B ) / 3
but buy B1 repeatedly with probability (2 — A B ) / 3 . Thus, the expected (second period)

total payment is given by

MP)? + Z-AB]+(1+AB)[[CB +1—+A—B)+E1+AB)/3s ds—AB]. (25)

 

3 3 3 3

 

The first term (including the parenthesized term) in expression (27) represents the ex- 1
pected payment for the repeat purchase of B 1 , the product of the probability for that case 3..

and the equilibrium price of B 1. The second term measures the expected payment when a

 

consumer switches to B2. For this event, we must consider three factors: the price of 82, y: j
the first term in the bracket; the expected switching cost, the second integrated term; and i L
the quality difference, the last term. Note that we need to subtract A3 to assess the effec-
tive payment for B2 since a consumer switching to B2 can use a superior product.

In contrast, if a consumer purchases B2 in period one, recall that he/she will not switch

back to Bl with the assumption of A B 21. For this case, the total payment is

I+AB
2

 

CB+ —AB (26)

where we subtract A 3 for the same reason explained above. With some algebra, we can

compute the difference between (22) and (23) as (A33 — 33% + 4) / 54 denoted by z hereaf-

ter for notational brevity. We can interpret Z as the additional compensation needed for
inducing the sophisticated consumers to choose B1 over B2. In summary, the monopolist
must set the price of B1 lower than that of BZ by at least Z+A3 to sell his inferior com-

plementary product initially on a stand-alone basis.

10]

 

Lemma 2. The monopolist will sell his inferior product B1 if q] < 42 — Z — A B where q,-

denotes the price of Bi in period one for i = 1, 2.

The next question that arises naturally is what pricing strategy firm 2 will take for its

complementary product. Recall that firm 2 will have the higher profit by

Azrz = 7r? — 7r; = ( 5A B — 2A123 + 7)/ 18 in period two by selling its B2 product in period
one. As a result, firm 2 is willing to offer up to the price c B — A7r2 for BZ. This implies
that the monopolist must lower the price of B1 even below the level of

(A3B-9A129+69AB + 25)
54

 

(cB—Aa2)—Z—AB=CB— (27)

to become the first-period complementary seller.

Interestingly and importantly, the price of B1 needed for the sales of B1 in period one
may fall into a negative level. This means that if we do not allow negative pricingzo, then
the monopolist may not be able to sell his Bl without resorting to tying practice.

This result explains the real-world behavior of the monopolist. As easily noticed, if
firm 2 can decrease the price of BZ at near-zero or zero (give-away), the monopolist has

no choice but to provide his inferior complementary good for free in order to sell it with-

out tying. In reality, Microsofi’s web-browser Internet Explorer has been provided at zero

price. If the give-away is not enough, the monopolist may offer other benefits to capture

 

2° The assumption that prices must be non-negative has been widely adopted. For examples, Far-

rell and Gallini (1988) justify the non-negativity assumption by mentioning the problem of oppor-

tunism that people could take products at a negative price and use them for landfill. As for more
closely related literature, Carlton and Waldman (2005) also analyze the monopolist’s incentive to

use tying in durable goods with non-negative prices assumed.

102

 

 

the initial market share. Therefore, we can predict that the monopolist will resort to tying
that allows him to sell B1 effectively in period one.
As a special case in the analysis, let me consider the case where the marginal produc-

tion cost is zero, i.e., CB 2 0 , which fits to computer software industry. Then, we can eas-

ily see that the value in (24) is always negative for any 1 S AB S 2. By the continuity ar-
gument, the monopolist’s price-cutting cannot make any sales of B1 for a sufficiently low

Q; without tying.

Lemma 3. For a sufficiently low production cost of CB, tying is the only effective way to

sell both products A1 and B1 to all consumers in the first period.

The reason is that the rival firm will decrease its price enough to make the consumers
choose BZ over B1, even if B1 is a give-away product. Of course, in reality we often pay
for superior goods and services even if there are give-away ones.

Based on the lemmas we have discussed, we can derive the following result.

Proposition 1. (a) The monopolist has no reason for tying its products if he can sell its
Bl without commitment to tying. (b) If the monopolist cannot sell B1 without tying be-

cause of the non-negativity constraint, then tying can be more profitable than no tying:

 

precisely, if and only if A B <13 — A A — JZAE, — 26A A +161 (which is the solution for

fil > 11'1").

The part (a) in the above proposition tells us that the monopolist will not use a tying strat-
egy if he can sell his Bl product without tying. This is because tying is a commitment to

103

 

'n'u.

 

 

more aggressive competition so that the firm who decides to tie its products also suffers
from the intensified competition. As part (b) says, however, the monopolist will use a ty-
ing strategy if consumers do not choose his inferior product B1 even at a near-zero or
zero price because there exists an alternative BZ which could be also available at a low or
zero price.

How does the tying decision affect firm 2? This question can be easily addressed with

, ~ *4:
the comparison of 112 and 112 .

Proposition 2. The rivial, firm 2, prefers no tying to tying regardless of the size of the

quality superiorities.

Under tying regime, firm 2 faces more aggressive bundle vs. bundle competition in the
second period and at the same time it loses the opportunity to sell its superior product B2
in period one. Therefore, firm 2’s profit always decreases with tying.

So far, the entry-deterrence issue has been purposely suppressed because this paper
shows another mechanism for a profitable tying without the exclusion of rival firms
unlike Whinston (1990), Choi and Stefanadis (2001), and Carlton and Waldman (2002).
It is noteworthy, however, that the monopolist strategically also uses tying to stifle the
potential entry of the rivals in market A. In other words, the strategic foreclosure revives
in this model with switching costs.

Suppose that firm 2 needs to bear a cost of K for entry in market A due to possibly

R&D investment. If the cost of entry is sufficiently high to the extent of K > Hz, tying

would emerge as an entry-deterrence device. In that case, the monopolist will enjoy mo-

nopoly rent in both periods.

104

 

 

5. The Welfare Analysis

In this section, I study the effect of tying on consumer surplus and social welfare. To say
the conclusion first, the model set up in this paper predicts the negative effects of tying
on consumers and society as a whole. Intuitively, this is because tying forces the consum-
ers to use an inferior product and thus leads to the higher switching costs.

With or without bundling, the consumer surplus in period one is zero because the mo-
nopolist in the primary market will exploit the entire surplus, assuming there is no wait-
ing option for the consumers in this model.

Since we consider the case where the market is fully covered, the consumer surplus

 

with tying is calculated from the following expression
~ 5 ~ _ 1 ~
C =L(V+AA+AB—P2—ZS)dS+J:(V-P1)dS. (25)
S

where the bundle prices and the marginal type '5 follow the analysis in the subsection 3.1.
The first integration term measures the consumer surplus of those switching to firm 2’s

system in period two, while the second term is for those attached to firm 1’s system.

 

In a similar manner, we can compute the consumer surplus for no tying with the sales
of B2 in period one as follows.

**

8* * M l :1: M
C =L (V+AA +AB—PA2 “P32—S)dS+ jS.(V+A3 -PA1—P32)dS

(26)
where the prices and the thresholds follow the analysis in the subsection 3.2. The first in-
tegration term measures the consumer surplus of those who switch from (A1+B2) to

(A2+B2). The second term captures that of those repeating the same consumption pattern

105 E

(A1+B2).

The economic total welfare is the sum of the consumer surplus and the firms’ profits.

With some algebra, I present the consumer surplus and the social welfare for each case in

Table 3-1.

Table 3- 1. Consumer surplus and social welfare with and without tying

 

 

 

 

 

 

 

Without tying With tying
.. - 71
C =V-CA-CB CzV—cA—CB )1

CS 1 2 1 2

+1—8—(A,+8AA+9AB—20) +—3-g[(A,+A,) +16(A,,+AB)—44] _
sw s”=2(V—c,—c,) §=2(V—c,—c,)

1

+-1—§(5A2A +43, +363, —1) +§lg[5(d, +A,,)2 +8(A,, +A,)—4]

~ .. 1[ 2 2 ]
C—C g—AA+AB+2AAAB—2AB—4
S ’5 if 53’, +532, +10AAAB —64AB —2]

 

 

By examining the signs of the differences in consumer surplus and social welfare under
. . ~ 13* ~ ** .
two regimes, i.e., C — C and S — S , we can see how tymg affects consumer surplus

and total welfare.

Proposition 3. The monopolist’s tying decreases both consumer surplus and social wel-

fare.

106 H

Of course, we must be extremely cautious in interpreting this result because such predic-
tion is from the specific framework posited in this paper: it involves several crucial as-
sumptions and controls for many other factors possibly driving the tying decision. In fact,
tying can save consumers the transaction costs associated with shopping twice for two
separate products and assembling them. As manufacturers often emphasize, the reliability
of a bundled package may be relatively higher. However, ceteris paribus, this study pro-
vides a theoretical support for the concern about the negative effects of tying on the rivals
and consumers with switching costs. Keeping that in mind, in my opinion, this study sup-
ports the concern about the negative effects of tying on the rivals and consumers with

switching costs.

6. Concluding Remarks
The firms who can wield the market power take a variety of strategic actions to influence
the competitive environment in their favor. Tying is the most controversial one among
them in antitrust history and economics. This paper studies a new rationale for the tying
practice between complementary goods in the presence of switching costs.

I find that the monopolist may strategically commit to tying in order to capture the dy-
namic rents associated with those who have relatively high switching costs, especially if the
monopolist has an inferior complementary product to the rival firm’s complementary one. I
also show that the tying decision decreases both consumer surplus and social welfare.

I believe that we can extend this simple model in several directions. One extension is
to consider independent switching costs for each component. To highlight key intuition in

the simplest manner, I have assumed that all the consumers have identical switching costs

107

 

in both products. However, it would be more realistic and interesting to study the case
where some consumers have a very high switching cost in one product but a relatively
low one in the other product.

Remarkably, the welfare analysis was quite simple because I assume that a consumer
has a unit demand for each product. Thus, it is a natural extension to consider a down-
ward-sloping demand and see how the welfare result changes.

It may also be interesting to interpret the present framework in the context of co-
branding (or co-marketing). We can reasonably interpret the level of switching costs as
the degree of brand loyalty that varies across consumers. In this vein, we may see tying as
a firm’s strategic behavior to raise the loyalty level. Since the co-branding literature has
been paid little attention by researchers compared to its widespread pervasiveness in the
business and marketing realm, I expect this paper to stimulate more research in this direc-

tion.

108

 

 

Appendix
Proof of Lemma 1.

Compare the cost of tying, AB, and its benefit 7:: — 7r," = (2 — A1,)2 / 9 . Solving the inequality

(2—AB)2/92A3,we can easily derive the condition AB SXB = (13—3x/1—7)/2 zO.315.

Proof of Proposition 1 .

2
(a) The comparison of 1'1l and IT: shows 1']: — IIl = (—A—‘—18-A—’i 2 O . This implies that the mo-

nopolist’s bundling is not a profitable strategy when it can sell both products separately.

(b) If the monopolist cannot sell its Bl, the relevant comparison is between fl, and HT. Solving

the inequality of fl, > H," with respect to A B, we can find the condition of

 

A, <i3—A, —,/2Ai, —26AA +161.
Proof of Proposition 2.

In order to compare firm 2’s profit fi 2 and H; , let me study such a condition that satisfying

 

.. = (2+A,+A,)2 _ [may +1+A8

2 0. We can rearrange this expression as
18 9 2

fi {— (AA — A3)2 + 2(AB — 1)2 — AB - 9}, which always proves to be negative for 0 5 AA 5 2 and

ISABSZ.

Proof of Proposition 3.
The welfare analysis can be done by studying the sign of 5 — C” and S — S ” in Table 1. Let me

prove this proposition by illustrating the relevant areas graphically for easier understanding.
Firstly, we can present the areas where 5 -— C" 2 (<)0 and S — S ” 2 (<)0 in the space of A .4 and

AB. Then, for the area in which the assumptions we made for the analysis are satisfied, we can

see 5 < C .. and S < S". That is, the following Figure 3-A-l shows that tying decreases con-

sumer surplus and social welfare”.

 

2' Detailed mathematical proofs are available upon a request to the author.

109

 

 

 

 

 

 

 

Figure 3-A-l. The welfare comparison with and without tying

110

 

'3
g

 

 

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112

 

 

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