Behavior-Based Personalized Pricing:
When Firms Can Share Customer Information∗
Chongwoo Choe
Department of Economics, Monash University
chongwoo.choe@monash.edu
Noriaki Matsushima†
ISER, Osaka University
nmatsush@iser.osaka-u.ac.jp
Mark J. Tremblay
Farmer School of Business, Miami University
tremblmj@miamioh.edu
April 16, 2022

Abstract
We study a two-period model of behavior-based price discrimination where firms can agree toshare customer information before the first-period competition begins, and the information canbe used for personalized pricing in the second-period competition. We show that information
sharing is individually rational for firms as it softens upfront competition when information
is gathered, consumers are worse off as a result, but total surplus can increase thanks to theimproved quality of matching between firms and consumers. These findings are robust to firm
asymmetries and varying discount factors for consumers and firms.
Keywords: Information sharing, behavior-based price discrimination, personalized pricing.
JEL Classification Number: D43, L13∗

We are thankful to the Editor, two anonymous referees, Keizo Mizuno, Yusuke Zennyo, and the participantsat ARSC2020 (Kanazawa University), CORE (Université catholique de Louvain), and Japan Association for Applied Economics 2020 Spring Meeting, for helpful comments. We gratefully acknowledge financial support fromthe Australian Research Council (grant number DP210102015), the JSPS KAKENHI (grant numbers JP15H05728,
JP17H00984, JP18H00847, JP18K01593, JP19H01483, JP20H05631, and JP21K01452), the International Joint
Research Promotion Program at Osaka University, and the program of the Joint Usage/Research Center for “Behavioral Economics” at the ISER, Osaka University. Although Matsushima serves as a member of the Competition
Policy Research Center (CPRC) at the Japan Fair Trade Commission (JFTC), the views expressed in this paper
are solely ours and should not be attributed to the JFTC. The usual disclaimer applies.
†
The corresponding author. Institute of Social and Economic Research, Osaka University, 6-1 Mihogaoka,
Ibaraki, Osaka 567-0047, Japan. E-mail: nmatsush@iser.osaka-u.ac.jp1

1

Introduction

Over the past several decades, the remarkable advances in digital technologies have allowed firms
access to a vast amount of consumer data at the granular level. The availability of such data inconjunction with powerful machine-learning tools can be a potential source of competitive advantage.1 While there are many ways firms can gather such data, one important channel in various
service industries such as banking and finance, retail, and travel has been customers’ past purchase histories.2 Such information can provide firms with the opportunities for behavior-based,or history-dependent, price discrimination (Chen, 2005, Fudenberg and Villas-Boas, 2006). In
the crudest form, firms can exercise third-degree price discrimination with two market segments,
existing and new customers (Chen, 1997, Fudenberg and Tirole, 2000). As the quality of information improves, the segmentation of existing customers can be further refined (Liu and Serfes,
2004), leading to personalized pricing in the limit. While personalized pricing may be in limited
use in practice, it is becoming more prevalent in some industries thanks to the availability of big
data and finer-grained analysis, and has been drawing attention from policy circles.3
As data collection and usage often occur among competing firms, opportunities to shareconsumer data exist. For example, the airline and tourism industry relies on code-sharing to
exchange data across firms. Firms intending to share data can also utilize a third party for which
participants voluntarily provide their data, which is then aggregated.4 Information sharing also
exists in the banking industry in the form of open banking, where participating banks can shareand leverage customer data to promote the development of new apps and services.5 While it
1“When data creates competitive advantage”, Harvard Business Review, January-February, 2020.

2

Relevant information can be gathered using loyalty programs or payment records. A rich set of data can bealso collected online by tracking customers’ search and browsing histories. See, for example, “How companies learn
your secrets”, The New York Times, February 16, 2012; “Little brother”, The Economist, September 11, 2014.
3

For the examples of personalized pricing used by airlines, grocery chains, online travel portals, see “Different

customers, different prices, thanks to big data,” Forbes, March 26, 2014; “How retailers use personalized prices totest what you’re willing to pay”, Harvard Business Review, October 20, 2017. Ezrachi and Stucke (2016) provide
more examples. For relevant policy discussions, see CEA (2015) or “Personalized pricing in the digital era”, OECD,
November 28, 2018.
4

For example, STR, formerly known as Smith Travel Research, provides such a service for the hospitality

industry. Other examples are Nallan, a third-party platform that facilitates data sharing by suppliers of air freight
services, and the agrirouter, a universal data exchange platform for farmers and agricultural contractors. Feasey
and de Streel (2020) provides comprehensive discussions on data sharing in practice and related legal and regulatory
issues. Firms may also join database co-ops where they can pool their databases. See Liu and Serfes (2006) for
more discussions on database co-ops.
5

In Section 5.7, we provide more discussions on open banking.

2

seems intuitive that information sharing may increase competition (Kim and Choi, 2010, Chenet al., 2022), its full effect on firm behavior is more subtle. In particular, the expectation of
intensified competition due to information sharing will affect firms’ incentives to invest in andgather customer information in the first place.
This paper studies a dynamic model of behavior-based price discrimination to address how thepossibility of information sharing affects competition both at the stage of information gatheringand at the stage when information is shared for common use. Information sharing does nothave bite if competiting firms have the same information set. This is the case in models of
behavior-based price discrimination such as Fudenberg and Tirole (2000) where firms compete inthird-degree price discrimination. Thus our model builds on Choe et al. (2018) where competition
is in personalized pricing, but extends it in two important directions. First, we allow firms tocommit to information sharing before they compete in price. The ensuing stages are then as
follows: in the first period, firms compete à la Hotelling, at the end of which each firm acquires
full information on all of its own customers; in the second period, they compete using a mixof personalized and uniform prices. If they agreed on information sharing, then both firms use
personalized prices for all consumers based on the same, full information; otherwise, each firm
sets personalized prices only for its own previous customers and a uniform price for the rest.
Second, unlike most existing studies on behavior-based personalized pricing that assume firms
with symmetric costs, we consider firms that may differ in their production costs.
Our main findings can be summarized as follows. First, information sharing is an equilibriumoutcome in that each firm’s discounted sum of profits is larger under information sharing than thatin all equilibria without information sharing. The main driver of beneficial information sharing issoftened competition in the first period. Although information sharing intensifies competition in
the second period by allowing both firms to use personalized pricing for all consumers, the effectis relatively small since, even without information sharing, firms use personalized pricing for theirown first-period customers. In sum, the benefits from softened competition in the first period
outweigh the costs of intensified competition in the second period. Second, as a robustness check,we consider the case where firms may have different marginal costs of production. We show thatthe cost asymmetry does not have any effect on our main conclusion; it only determines whichfirm becomes more aggressive in the first period. However, the cost asymmetry introduces a
discontinuity in the set of equilibria in the subgame without information sharing. When the costdifference is small, there continue to exist two asymmetric equilibria as in Choe et al. (2018).
But the equilibrium is unique when the cost difference is above a certain threshold. In thisequilibrium, the less efficient firm chooses aggressive pricing in the first period and, as a result,3

there is one-way customer poaching by the more efficient firm in the second period. These results
hold for any discount factors for firms and consumers.
While firms are better off with information sharing, consumers are worse off in that the discounted sum of consumer surpluses is smaller when firms share information. The intuition is
as follows. Information sharing affects consumer surplus through two channels: prices and thequality of matching between firms and consumers, as reflected in the transportation cost in our
Hotelling model. Information sharing increases the quality of matching with less customer poaching in the second period than without information sharing, which benefits consumers. The flipside is that information sharing creates a negative effect for consumers by softening competitionin the first period. Given that firms benefit from information sharing, we expect the negative
effect to dominate the positive quality-of-matching effect. At the same time, because prices reflect
only the division of surplus between firms and consumers, information sharing can increase total
surplus thanks to the positive quality-of-matching effect.
We also analyze several further extensions of our model. First, when firms share customer
information, competition in third-degree price discrimination leads to larger profits and consumer
surplus, but smaller total surplus than when competition is in personalized pricing. Second, we
consider the case where the market is only partially covered in the first period. Because thecompetition-softening benefits of information sharing in the first period are reduced in this case,
we find that firms choose not to share information. Third, when consumers’ preferences changeover time so that customer information gathered in the first period is imperfectly correlatedwith that in the second period, information sharing continues to be an equilibrium outcome. It
is because sharing information with imperfect preference correlation makes competition in thesecond period less intense but competition in the first period more intense than when preferences
are perfectly correlated. Fourth, when firms make information sharing decisions at the end of thefirst period, we show that they choose not to share information. The cases with partial market
coverage and alternative timing of information sharing highlight the main mechanism at workin our model. Namely, the pre-commitment to sharing information before information gatheringand the large benefits from softening up-front competition are crucial for our results. It is because
the main benefits from information sharing materialize when the agreement to share information
softens competition at the stage when firms gather customer information.
Our work makes contributions to the literature in several important ways. First, we enrich
the existing literature on behavior-based price discrimination by incorporating firms’ decisions on
information sharing. Second, the existing literature on information sharing reviewed in the next
section shows that customer information sharing can be an equilibrium outcome only if there4are sufficient asymmetries in brand loyalties, product differentiation, or consumer preferences.
In contrast, we show that information sharing emerges under a robust space of parameters if
firms can commit to information sharing before gathering information. This may be taken as an
explanation for the prevalence of institutions such as database co-ops or open banking. Third, we
extend the literature by allowing firm asymmetries and show how the set of equilibria depends on
cost asymmetry. In particular, we provide a precise condition on when multiple equilibria collapse
to a unique equilibrium and fully characterize these equilibria. Finally, our welfare analysis
shows a clear trade-off between consumer surplus and total surplus that results from information
sharing. This can shed light on possible regulations that govern customer information sharing
among competing firms. Of course, this is subject to a caveat that our focus is on the use ofcustomer information for pricing purposes only and, therefore, we do not consider other effects
of information sharing.
The rest of the paper is organized as follows. The next section provides a review of the related
literature. Section 3 presents our baseline model, which is analyzed in Section 4. We provide
additional discussions and extensions to the model in Section 5 and conclude the paper in Section
6. All deferred proofs are contained in Appendix.

2

Related Literature

Our work is most closely related to two strands of literature. First, the literature on behaviorbased price discrimination employs a dynamic model in which firms learn customer informationfrom past purchases, which they use for price discrimination in subsequent purchases. The generalfindings are that behavior-based price discrimination hurts firms by intensifying competition
unless there are sufficient heterogeneities at the firm- or consumer level. This is true whether
competition is in third-degree price discrimination (Chen, 1997, Villas-Boas, 1999, Fudenberg
and Tirole, 2000, Pazgal and Soberman, 2008, Esteves, 2009a) or in personalized pricing (Zhang,2011, Choe et al., 2018, Garella et al., 2021).6 This literature generally assumes symmetric firms
and imposes restrictions on the discount factors for tractability. We add to this literature in two
ways. First, we allow firms the possibility to share customer information before price competition.
Second, our model allows asymmetric firms (in Section 5.4) as well as general discount factors
6

For a survey of the literature, see Chen (2005), Fudenberg and Villas-Boas (2006), or Esteves (2009b).

Behavior-based price discrimination can benefit firms when there are sufficient heterogeneities at the consumer
level (Chen and Zhang, 2009, Shin and Sudhir, 2010, Colombo, 2018) or at the firm level (Bing, 2017, Rhee andThomadsen, 2017). In a static, but general oligopoly model, Rhodes and Zhou (2021) shows that competition inpersonalized pricing can benefit firms when the market is not fully covered under uniform pricing.

5that may differ between consumers and firms.
Our analysis of the case without information sharing builds on Choe et al. (2018).7 They
study a two-period model of behavior-based price discrimination with symmetric firms when
the second-period competition is in personalized pricing. Their main results are that there are
two asymmetric equilibria, a more aggressive firm in the first period can select its preferred
equilibrium, and profits are lower compared to when the second-period competition is in thirddegree price discrimination. We extend Choe et al. (2018) by allowing firms to share customer
information and also considering the case where firms may have asymmetric costs. As we showin Sections 5.3 and 5.4, multiple equilibria in Choe et al. (2018) collapse to a unique equilibrium
if consumer preferences can vary across periods or as the cost asymmetry increases.
Somewhat related to the above, there is a growing body of literature that studies how product information provided to consumers affects competition and welfare in static settings (Ivanov,
2013, Hwang et al., 2019, Armstrong and Zhou, 2022). For example, Armstrong and Zhou (2022)
formalizes the trade-off that more information can reduce preference mismatch but soften competition by amplifying perceived product differentiation. To focus on our main objective of studying
firms’ incentives to share information, we employ a model that is different in several ways. First,
our model is dynamic where product differentiation is exogenously given and commonly known.
Second, consumers have full information about their preferences. Third, our focus is on consumer
information held by firms, rather than product information that can be provided to consumers.
We also contribute to the literature on information sharing in oligopoly. The earlier literature
considered information sharing about demand or cost conditions (e.g., Gal-Or, 1985, Shapiro,
1986, Li, 2002, Shaffer and Zettelmeyer, 2002, Armantier and Richard, 2003). The main focus inthese studies is how information sharing can allow firms to make better output or pricing decisions
under cost or demand uncertainties. Instead, the focus in our paper is on sharing customer
information that can be used for personalized pricing and how it can alter firms’ incentives togather information, as well as the dynamics of ensuing price competition.8
Several papers are similar to ours in studying information sharing as it relates to behavior7

Chen et al. (2020) extends Choe et al. (2018) to the case of personalized pricing in the presence of consumers’

identity management. Chen et al. (2022) extends Choe et al. (2018) to the case of personalized pricing that is madepossible by data-driven mergers. Garella et al. (2021) extends Choe et al. (2018) by allowing asymmetric firms ina vertically differentiated duopoly but does not consider information sharing.
8

Awaya and Krishna (2020) shows that information sharing can benefit firms by improving monitoring andfacilitating coordination. We also find that firms benefit from information sharing since committing to information
sharing softens upfront competition at the information acquisition stage. The main difference is that we consider
behavior-based price discrimination while Awaya and Krishna (2020) considers unit pricing.

6

based price discrimination. Liu and Serfes (2006) is the closest to our work. They consider
a two-period model where consumer information is obtained first, after which firms can share
information before competing in personalized pricing (where relevant) in the second period. Theyfind that information sharing can increase industry profits only when there are large asymmetries
in loyal customer base. In addition, profitable information sharing is only one-way. Our work
differs from Liu and Serfes (2006) in several respects. First, we allow firms to pre-commit to
information sharing before information is gathered and show that information sharing occurs
in equilibrium at all levels of firm asymmetries including the case of symmetric firms. Second,
information sharing is individually rational; hence we do not need an additional agreement on
profit sharing that is needed to support information sharing in Liu and Serfes (2006). Finally,
information sharing is two-way in our case in that firms pool their databases for common use.
Among other related studies, Kim and Choi (2010) analyzes when information sharing canbe beneficial in a two-period model with consumer heterogeneity (goods are substitutes for someconsumers and complements for others). de Nijs (2017) considers a two-period model of behaviorbased price discrimination with three asymmetric firms and competition in third-degree pricediscrimination in the second period. Finally, Chen et al. (2001), Shaffer and Zhang (2002),
Jentzsch et al. (2013), Shy and Stenbacka (2013), Belleflamme et al. (2020) all use a static model
to identify various conditions under which information sharing can benefit firms. But information
is exogenously given in these studies. Thus they cannot address how the possibility of information
sharing can soften competition at the stage when firms gather information.9

3

The Model

There is a linear city with unit length where firms A and B are located at points 0 and 1,
respectively. Both firms have constant marginal cost of production, which is normalized to zero.10
Consumers are distributed uniformly over the unit interval, live for two periods (indexed τ = 1, 2),
and have unit demand in each of the two periods. We call the consumer located at x ∈ [0, 1]
simply consumer x. The utility of consumer x that purchases from firm i in period τ is given byuτi (x) = v − pτi (x) − t(x − xi )2 ,9

(1)

The literature on information gathering/sharing is also expanding into other areas, for example, information

sharing among bidders (Asker et al., 2020), how the coarseness of information collection impacts monopoly profits(Laussel et al., 2020), and how data intermediaries act as data providers to competing firms (Bounie et al., 2021).
10

In Section 5.4, we consider the case where firms have different marginal costs and show that our main resulton the benefits of information sharing continues to hold.

7

where v is the gross surplus from the product, pτi (x) is firm i’s price for consumer x in period τ ,t is a positive transportation cost that captures the extent of product differentiation, and xi isthe location of firm i, i.e., xA = 0, xB = 1.11 We assume that v is sufficiently large so that themarket is fully covered in equilibrium.12
Firms obtain information on their first-period customers. By “information,” we specificallymean the consumer’s location, which is assumed to stay the same over time.13 Since firms do nothave any information in τ = 1, they can only offer a single price to all consumers. Thus pτi (x)in (1) reduces to p1i in τ = 1. But in τ = 2, firms know the exact locations of all their τ = 1
customers. Thus they can offer personalized prices to these consumers and a uniform price toall other consumers. For example, firm A chooses p2A (x) for its τ = 1 customer x while firm B
chooses p2B (x0 ) for its τ = 1 customer x0 .
To consider information sharing agreements, we add τ = 0 before τ = 1, when firms decide
whether or not to share the customer information that they gather in τ = 1.14 We consider asimple mechanism for information sharing: firms agree to establish an information bank where
they can deposit their customer information for common use. More specifically, firms play a
non-cooperative game where each firm chooses between ‘share’ and ‘not share’ subject to thecondition that the information bank will be set up if and only if both firms choose ‘share’, whichbecomes a binding commitment.15 Commitment to information sharing is commonplace in someindustries, the financial sector being a prime example, as it is mandated by regulations.16
We also assume that firms do not choose weakly dominated strategies when making information sharing decisions. Notice that unilateral information sharing is never optimal in our model11

We assume a quadratic transportation cost to stay consistent with Choe et al. (2018). This allows us todirectly draw from their results when firms have symmetric costs, hence simplifies the discussion of the casewithout information sharing. But it is easy to see that our results are robust to the linear transportation cost
structure because the consumer’s utility comparison is the same with quadratic or linear transportation costs.
12

In Section 5.2, we relax the assumption of full market coverage by considering the case where v < t.

13

Section 5.3 studies the case where preferences change over time in that the second-period location is imperfectly

correlated with the first-period location.
14

In Section 5.5, we consider an alternative timing in which firms make information sharing decisions at theend of τ = 1 but before τ = 2.
15

We do not consider a cooperative agreement with side payments, as it can lead to a situation where information

sharing can work as a collusive device.
16

See our discussions in Section 5.7. Also, deviation from the commitment can be easily detected since, in

our duopoly model, information sharing means each firm must have full information in τ = 2. This facilitates
enforcement of commitment.

8because it creates competition where one firm has superior information in τ = 2.17 This disadvantages the firm that unilaterally shares information.18 Thus, there remain only two possibilities:
both firms share or neither firm shares. As we show later, ‘not share’ is weakly dominated by‘share’. If firms agree to establish an information bank, then the customer information gatheredin τ = 1 can be used by both firms in τ = 2. In this case, both firms have the same, full
information in τ = 2 because of our assumption of full market coverage.
The formal timeline of the game is as follows. In τ = 0, firms decide whether or not toshare customer information. In τ = 1, firms compete à la Hotelling by selecting their uniform
prices; consumers make purchase decisions and firms acquire information on their customers. In
τ = 2, price competition proceeds in two stages. First, as usual in the literature on personalized
pricing (e.g., Thisse and Vives, 1988, Shaffer and Zhang, 2002, Liu and Serfes, 2006, Braulin andValletti, 2016, Choe et al., 2018, Chen et al., 2020), firms simultaneously and independently offer
their uniform prices only to those consumers whose information is not available to the respective
firm. After observing the uniform prices, each firm offers personalized prices to each consumer it
recognizes. The sequential timing in pricing decisions not only reflects the flexibility in choosing
personalized prices, but also allows us to solve for the subgame perfect Nash equilibrium in purestrategies.19
The discount factor is denoted by δc ∈ [0, 1] for consumers and δf ∈ [0, 1] for firms. We denotethe discounted sum of firm i’s profits as Πi ≡ πi1 + δf πi2 , where the superscripts represent theperiods. Also, we denote the discounted sum of consumer x’s utility as u1 (x) + δc u2 (x), whereuτ (x) is the utility level of consumer x in period τ . In the main text that follows, we focus on
the case where δc = δf = 1. This is for ease of exposition and clarity of explanations. But our
results hold for general values of δc , δf ∈ [0, 1], as we show in the proof of our main propositionsin Appendix.
17

For example, suppose only firm B shares its information [z, 1] where z is the marginal consumer in τ = 1.

Then, in τ = 2, firm A competes with full information while firm B has information on only [z, 1]. Because firm
A can choose personalized prices on [z, 1] that can be set lower than its uniform price, firm B is worse off by such
unilateral information sharing.
18

If a firm can choose the amount of information to share, that is, a subset of information it has, then there

are possibilities of beneficial, unilateral information sharing (Choe et al., 2021).
19

When firms simultaneously choose uniform and personalized prices, no pure-strategy equilibrium exists inthe subgames where only one firm has information (Liu and Serfes, 2004). Chen et al. (2020) (Section 5.5) further
shows that all equilibria in the subgames without information sharing are in mixed strategies except when z = 1/2.

9

4

Analysis

We solve the game backward, starting from the subgame that follows the information sharing
game in τ = 0. Let A (B, resp.) denote the set of consumers that firm A (firm B, resp.) has
information on in τ = 2. With information sharing, we have A = B = [0, 1] thanks to theassumption of full market coverage. Thus firms compete in τ = 2 under full information and offer
personalized prices to all consumers. Without information sharing, we have A ∪ B = [0, 1] but
A ∩ B = ∅. Thus each firm offers personalized prices only to its τ = 1 customers, but a uniform‘poaching’ price to its rival’s τ = 1 customers. That is, firm A’s price in τ = 2, denoted by p2A (x),is personalized for all x ∈ A, but uniform for x ∈ B. Likewise, firm B’s price in τ = 2, denotedby p2B (x), is personalized for x ∈ B, but uniform for x ∈ A. In τ = 2, firm A’s τ = 1 customerx ∈ A chooses between firm A’s personalized price and firm B’s uniform price, while firm B’s
τ = 1 customer x ∈ B chooses between firm B’s personalized price and firm A’s uniform price.
In τ = 1, firms compete by choosing uniform prices, which we denote by p1A and p1B .

4.1

Equilibrium of the subgame with information sharing

Consider the subgame where information sharing occurs. We solve for the equilibrium using
backward induction. In τ = 2, regardless of the τ = 1 outcome, both firms can offer personalized
prices to all consumers. This leads to competition in personalized prices as in Thisse and Vives(1988). In τ = 1, consumers anticipate that the τ = 1 outcome does not affect the τ = 2 outcome
since information sharing renders any difference in firms’ τ = 1 market shares irrelevant to τ = 2
competition. Thus consumers delink their τ = 1 purchasing decisions from τ = 2 decisions. This
leads to the Hotelling outcome in τ = 1. Put together, we have the following.
Lemma 1. If firms agree to share information, then equilibrium prices, profits, and consumer
surplus in τ = 2 are given by
p2a
A (x)
p2a
B (x)



t(1 − 2x) for x ∈ A = [0, 1/2],
0
for x ∈ B = [1/2, 1],0
for x ∈ A = [0, 1/2],
t(2x − 1) for x ∈ B = [1/2, 1],

=
=

2a
2a
πA
= πB
= t/4, CS 2a = v − (7t)/12,(2)

where the superscript ‘a’ indicates the agreement on information sharing. In τ = 1, they are
given by
1a
1a
1a
1a
p1a
= v − (13t)/12.
A = pB = t, πA = πB = t/2, CS

10

(3)

Proof: See Appendix.

4.2

Equilibrium of the subgame without information sharing

For the case where information sharing does not occur, we follow Choe et al. (2018). They showthat there are two asymmetric equilibria, one being a mirror image of the other. Without loss ofgenerality, we focus on the equilibrium where firm B has a larger market share in τ = 1. In thiscase, based on Proposition 1 in Choe et al. (2018) and noting that δc = δf = 1, we can derive thefollowing.
Lemma 2. Suppose firms choose not to share information. Then, in the equilibrium where firm
B has a larger market share in τ = 1, prices, profits, and consumer surplus in τ = 2 are given by

p2d
A (x)
p2d
B (x)



t(1 − 2x) for x ∈ A = [0, 5/14],
t/7
for x ∈ B = [5/14, 1],0
for x ∈ [0, 3/7],t(14x − 6)/7 for x ∈ [3/7, 1],

=
=

2d
2d
πA
= (47t)/196, πB= (16t)/49, CS 2d = v − (55t)/84,(4)

where the superscript ‘d’ represents the disagreement on information sharing. In τ = 1, they are
given by
1d
1d
1d
1d
p1d
= v − (19t)/84.
A = (3t)/14, pB = t/14, πA = (15t)/196, πB = (9t)/196, CS(5)As explained previously, firm B prices more aggressively in τ = 1 and secures a larger market
share, 9/14 to be exact. Although the aggressive pricing results in profit smaller than firm A’s inτ = 1, firm B’s profit is larger in τ = 2, which more than offsets the smaller τ = 1 profit, givenδf = 1. Thus, the above equilibrium in consistent with the general insight in Choe et al. (2018)that the more aggressive firm in τ = 1 can force the game to be played to its advantage.

4.3

Equilibrium

We now turn to firms’ information sharing decisions in τ = 0. As explained previously, we consider
a simple scenario where information is shared if and only if both firms agree, i.e., information
sharing is individually rational for each firm. This requires us to compare equilibrium profits
across the two subgames analyzed above. The following table summarizes the results in (2), (3),(4), and (5).
11

Table 1: Profits and consumer surplus with or without information sharing

Information sharing
No information sharing

1
πA

2
πA

1
πB

2
πB

CS 1

CS 2

t/2
(15t)/196

t/4(47t)/196

t/2(9t)/196t/4(16t)/49v − (13t)/12v − (19t)/84v − (7t)/12v − (55t)/84

As is clear from Table 1, information sharing softens competition in τ = 1, resulting in
1a = t/2 > π 1d = (15t)/196 and π 1a = t/2 > π 1d =larger profits for both firms in τ = 1: πAAB
B(9t)/196. Indeed, the softened competition manifests itself in higher prices, as shown in (3) and(5). However, information sharing intensifies competition in τ = 2 by allowing both firms tooffer personalized prices to all consumers instead of only to one’s τ = 1 customers. As a result,
2a = t/4 < π 2d = (16t)/49. But firm
firm B is worse off than without information sharing: πB
B

A is better off because the equilibrium without information sharing we focus on favors firm B:
2a = t/4 > π 2d = (47t)/196. For both firms, the positive effect of softened competition in τ = 1
πAA

is large enough, which results in larger profits than when they do no share information. We canverify this by comparing the discounted sum of profits for each firm. Given δf = 1, we have
1a + π 2a = (3t)/4 > Πd = π 1d + π 2d = (31t)/98 and Πa = π 1a + π 2a = (3t)/4 > Πd =
ΠaA = πA
B
B
B
B
A
A
A
A
1d + π 2d = (73t)/196. Thus, both firms are better off under information sharing. AlthoughπBB

the above discussion was based on the case δc = δf = 1, the following proposition holds for all
discount factors δc , δf ∈ [0, 1], as shown in the proof.
Proposition 1. For all values of δc , δf ∈ [0, 1], we have Πai ≥ Πdi for i = A, B so that the uniqueequilibrium of the whole game is as follows: in τ = 0, firms agree to share information, which isfollowed by the Hotelling outcome in τ = 1 and the Thisse-Vives outcome in τ = 2.
Proof: See Appendix.
The main reason for the beneficial information sharing is that the commitment to information
sharing softens competition at the stage of information acquisition. Without the commitment,each firm strives to gain a larger market share in τ = 1 since a larger market share translates tomore customer information, which the firm can leverage in τ = 2 when employing personalized
pricing. This intensifies competition in τ = 1 which is escalated since prices are strategic complements. Although information sharing intensifies competition in personalized pricing in τ = 2,
the effect is relatively small because firms already compete using personalized pricing for theirown τ = 1 customers even without information sharing. As we can see from Table 1, the negative
effect of information sharing on the τ = 2 profits is relatively small compared to the positive12effect on the τ = 1 profits. To summarize, the commitment to share information generates thebenefits of softened competition in τ = 1 that outweigh the relatively small costs of intensifiedcompetition in τ = 2.

4.4

WelfareGiven that information sharing occurs in equilibrium, our next question is how information sharing affects welfare. We start with consumer surplus denoting consumer surplus under information sharing by CS a = CS 1a + δc CS 2a and consumer surplus without information sharing by
CS d = CS 1d + δc CS 2d . In general, information sharing should hurt consumers in τ = 1 but
benefit them in τ = 2, precisely because of its differing effect on competition in each period.
More specifically, information sharing affects consumer surplus through two channels: prices andtransportation costs. The price effect on consumer surplus is negative. As we have seen above,firms benefit from softened competition in τ = 1, which more than offsets the adverse effect ofincreased competition in τ = 2. On the other hand, the average transportation cost decreases
with information sharing. Given that firms are located at 0 and 1, the average transportation costis minimized when the marginal consumer’s location is at 1/2, which is indeed the case in both
periods when firms share information. Without information sharing, the marginal consumer’s
location is at 1/2 if and only if δf = 0. As we show below, however, the negative price effectdominates the positive transportation cost effect. For the case δc = 1, we can calculate CS a andCS d from Table 1: CS a = v − (5t)/3 < CS d = v − (37t)/42. As before, the negative effect of
information sharing on consumer surplus holds for general values of δc and δf .
Lemma 3. With information sharing, consumer surplus is smaller in τ = 1 but larger in τ = 2
than without information sharing. For all values of δc and δf , the discounted sum of consumer
surpluses is lower with information sharing: CS 1a < CS 1d , CS 2a > CS 2d , CS a < CS d .
Proof: See Appendix.
The effect of information sharing on total surplus is straightforward. Given that the market
is fully covered, total surplus depends only on the average transportation cost. Since information
sharing leads to the equilibrium where the average transportation cost is minimized, it follows
that total surplus is higher when firms share information. Simply put, the positive effect of information sharing on total surplus is driven by reduced preference mismatch enabled by information
sharing.20 We summarize the discussions so far in the following proposition.
20

In Armstrong and Zhou (2022), preference mismatch is reduced when firms optimally choose to disclose

13

Proposition 2. For all values of δc and δf , the discounted sum of consumer surpluses is smaller,
but total surplus in each period is larger, when firms share customer information.
Propositions 1 and 2 highlight the costs and benefits of information sharing from a welfare
perspective. Information sharing benefits firms at the cost of consumers, as it softens competition.
But softened competition reduces socially inefficient poaching of rival’s customers, raising total
welfare.

5

Extensions and Discussions

5.1

The degrees of price discrimination

Suppose firms cannot exercise personalized pricing for reasons such as privacy concerns or lackof detailed information. Instead, they rely on third-degree price discrimination by choosing two
uniform prices as in Fudenberg and Tirole (2000), one for their own τ = 1 customers and theother for rival’s τ = 1 customers. In this case, firms in τ = 2 have the same information set,so that information sharing becomes irrelevant. Thus the equilibrium remains the same with orwithout information sharing. Given this, the following observations are immediate.
First, the discounted sum of profits for each firm under third-degree price discrimination isΠ = (3+δc )t/6+δf (5t/18). It is easy to see that it is larger than the discounted sum of profits foreach firm when firms exercise personalized pricing under information sharing. Thus, even whenfirms share customer information, they are better off when competition in τ = 2 is in third-degree
price discrimination than in personalized pricing. This is consistent with the standard result thatfirms are better off when price competition is based on coarser levels of customer information.
Second, consumer surplus in Fudenberg and Tirole (2000) is v − (13 + 4δc )t/12 in τ = 1 andv − (25t)/36 in τ = 2. It is straightforward to check that consumer surplus in each period islarger than when firms employ personalized pricing under information sharing. Finally, total
surplus in Fudenberg and Tirole (2000) is smaller than that under information sharing in ourmodel, simply because there is two-way customer poaching in τ = 2 in Fudenberg and Tirole(2000), resulting in a larger average transportation cost than when the marginal consumer’s
location is at 1/2.
Proposition 3. When firms share customer information, competition in personalized pricing
leads to larger total surplus, but smaller profits and consumer surplus, than when competition is
product information to consumers, which amplifies perceived product differentiation and softens competition. In
our model, the effect of information sharing on match quality is driven entirely by price competition because
product differentiation is fixed exogenously and commonly known.

14

in third-degree price discrimination.

5.2

Partial market coverage

Our baseline model assumed large enough v, which ensures that all consumers are served inτ = 1. What happens if the market is not fully covered in τ = 1? As our analysis has shown, thebenefits of information sharing are derived from softening competition in τ = 1. Partial market
coverage reduces such benefits because some consumers do not purchase in τ = 1, which makes
information sharing less attractive than when the market is fully covered.21 We analyze thiscase below. First, we assume v < t because the market is fully covered if and only if v ≥ t in
the Hotelling duopoly. Second, we assume a linear transportation cost and δc = 0. It is mainly
to simplify analysis because solving the case with partial market coverage is quite complicatedwith many different outcomes to consider in our two-period model. Assuming δc = 0 shuts down
one channel of complication by delinking consumers’ problems over the two periods. Even withthis assumption, the case with partial market coverage leads to several different outcomes, as we
describe below.
Suppose [zA , zB ] is not served in τ = 1. Then, for any v < t, we have zA < 1/2 < zB
with or without information sharing as shown in the proof of Proposition 4, and the outcome inτ = 2 can be divided largely into three cases. First, [zA , zB ] is fully covered and the marginal
consumer is in the interior of [zA , zB ] and has strictly positive net utility, which we call interior
duopoly. Second, [zA , zB ] is fully covered and the marginal consumer is in the interior of [zA , zB ]but has zero net utility, which we call corner monopoly. Third, [zA , zB ] is not fully covered andeach firm serves a fraction of [zA , zB ], which we call local monopoly. As v decreases from t, theoutcome changes from interior duopoly to local monopoly with or without information sharing.
The following proposition shows that, for all τ = 2 outcomes described above, both firms preferno information sharing to information sharing.
Proposition 4. Suppose δc = 0 and assume a linear transpiration cost. Then, for all v < t,the τ = 1 market is not fully covered with or without information sharing, and neither firm
strictly prefers information sharing to no information sharing. Thus, no information sharing is
an equilibrium outcome.
Proof: See Appendix.
21

Related to this, Rhodes and Zhou (2021) shows that, when the market is partially covered under uniform

pricing, competition in personalized pricing benefits firms by enabling them to serve low-value customers who would
otherwise be excluded.

15

The general intuition for the above result can be provided as follows. First, as explained
previously, partial market coverage reduces the benefits of information sharing in τ = 1. In
τ = 2, firms compete à la Hotelling on [zA , zB ] with or without information sharing. These
Hotelling prices constrain each firm’s personalized prices under no information sharing. With
information sharing, each firm’s personalized price for the customer it serves is constrained by
the rival’s personalized price offered to that customer. This means that, compared to the casewith full market coverage, competition in τ = 2 is not as intense because of the ‘buffer’ zone,[zA , zB ], which is true with or without information sharing. Put together, we can conclude that
information sharing is less valuable under partial market coverage because the benefits of softenedcompetition in τ = 1 are smaller and its effect in τ = 2 is less pronounced because partial market
coverage softens competition in τ = 2 even without information sharing.
However, the above discussion only explains that partial market coverage reduces the benefitsof information sharing, but not why firms choose not to share information. For this, observe that
consumers’ participation constraints impose a cap of 2v − t on p1A + p2A . This means that, as v
becomes smaller, competition becomes more intense. When v = t, although the market is fully
covered, competition is intense in that the Hotelling prices are p1A = p1B = t/2 < t, the latter being
the Hotelling prices in our baseline model where we assumed v is sufficiently large, or v > (3t)/2
to be precise.22 Thus, when v = t, Hotelling competition is already quite intense so that there is
not much to gain by achieving this outcome through the information sharing agreement.

5.3

Imperfect correlation of consumer preferences

In our baseline model, we assumed that preferences stay the same in both periods. We now
consider the case where preferences are imperfectly correlated across the two periods. For example, some consumers may have their preferences changing over time. In this case, information
gathered in τ = 1 is less useful for price discrimination in τ = 2. Thus, compared to the casewith perfectly correlated preferences, competition in τ = 2 softens when firms do not share information. However, the anticipation of softened competition in τ = 2 can intensify competition inτ = 1. It is because each firm expects to retain much of its τ = 1 market share in τ = 2 thanks
to the softened competition. Put together, the case with imperfectly correlated preferences leads
to intense competition in τ = 1 but softened competition in τ = 2 when firms do not share
information. Given that the main benefits of information sharing are from softening competitionin τ = 1, while the downside of intense competition in τ = 2 exists with or without information
sharing, we expect information sharing to be preferred by both firms.
22

See Chen and Riordan (2008) or Cowan and Yin (2008) for related points.

16

We formalize the above by considering a simple model of imperfectly correlated preferences
following (Armstrong and Vickers, 2010, pp. 52-53). To be precise, we consider a model wherea consumer’s τ = 1 location is imperfectly correlated with her τ = 2 preference. Suppose thata fraction η ∈ (0, 1] of consumers have preferences changing over time in that, in τ = 2, theirpreferences are drawn from a new uniform distribution on [0, 1]. That is, these consumers moveto new locations in the beginning of τ = 2. The remaining fraction of consumers have the same
preferences in both periods. For a consumer whose location changes, we assume that firms canobserve her new location if they gathered her information in τ = 1 or acquired it through information sharing. This assumption not only renders personalized prices precise meaning but also
simplifies analysis.23 To further simplify analysis, we assume δc = 0 and a linear transportation
cost, as in Section 5.2.
Proposition 5. Suppose a fraction η ∈ [0, 1] of consumers have their τ = 2 preferences drawn
from a uniform distribution on [0, 1] independently of their τ = 1 preferences, but the remaining
consumers have the same preferences in both periods. Suppose δc = 0 and assume a linear
transpiration cost. Then, for all η ∈ (0, 1],• the subgame without information sharing has a symmetric equilibrium where the τ = 1
prices are p1A = p1B = t − δf (8 − η)(t/16), and the discounted sum of profits is ΠA = ΠB =t/2 + δf (2 − η)(t/8).
• the subgame with information sharing has the same equilibrium as the case with perfectly
correlated preferences where the τ = 1 prices are p1A = p1B = t, and the discounted sum of
profits is ΠA = ΠB = t/2 + δf (t/4).
• both firms prefer information sharing to no information sharing.
Proof: See Appendix.
When firms do not share information, the symmetric equilibrium in Proposition 5 is in contrast
to the asymmetric equilibria in Choe et al. (2018). It is because the existence of consumers whose
preferences change substantially alters uniform poaching prices in τ = 2. Suppose preferences
stay the same in both periods as in Choe et al. (2018), and consider the case where firm B’s
τ = 1 market share is larger than 1/2, i.e., z < 1/2. Then firm B’s uniform price is zero, where it
23

When competition is in uniform price as in Armstrong and Vickers (2010), only the aggregate information,

not the consumer’s precise new location, matters. But the location information matters when competition is inpersonalized pricing as in our case.

17remains as z decreases further to 0. But as z decreases, firm A’s poaching price increases, which
benefits firm B by allowing it to increase its personalized prices. Given that this outcome is theresult of firm B’s aggressive pricing that gives firm B a larger market share in τ = 1, firm B
does not have incentives to deviate in τ = 1, and nor does firm A. This sustains the asymmetricequilibrium in Choe et al. (2018). Suppose now there are some consumers whose preferenceschange, and consider again the case where z < 1/2. Then, as shown in the proof of Proposition5, firm B’s uniform price is t/2 rather than 0, where it remains as z decreases further to 0. In
contrast to the case where preferences stay fixed, firm B chooses a positive uniform price evenwhen z < 1/2. It is because, when there are consumers with changing preferences, there are someconsumers firm B can serve even if their τ = 1 locations were closer to firm A. Although firm A’s
uniform price is also t/2 when z is close to 1/2, as z decreases further, firm A lowers its uniform
price to attract firm B’s τ = 1 customers whose preferences do not change. This hurts firm B
because its personalized prices need to be decreased in response to firm A’s lower uniform price.
Therefore, firm B does not benefit much from competing for a larger market share in τ = 1, andthe same is true for firm A. This leads to the symmetric equilibrium in Proposition 5.

5.4

Asymmetric costs

This section extends analysis to the case where firms may have different marginal costs. Specifically, we assume that firm A’s marginal cost is zero but firm B’s marginal cost is c ≥ 0. This
nests our baseline model as a special case where c = 0. This asymmetric cost case yields two
main results, which are analyzed fully in an earlier version of this paper. Thus, we present only
the key results here and refer to Choe et al. (2020) for formal analysis and proofs.
In the subgame without information sharing, the structure of equilibria depends on the costdifference c. When c is below a certain threshold, there continue to exist two pure-strategy
equilibria as in Choe et al. (2018). In one equilibrium, the less efficient firm, firm B by ourassumption, prices aggressively in τ = 1, as a result of which firm A poaches firm B’s τ = 1
customers in τ = 2. We call this the firm A poaching equilibrium. In the other equilibrium, firm
B poaches firm A’s τ = 1 customers in τ = 2, which we call the firm B poaching equilibrium.
When c is above the threshold, the firm A poaching equilibrium remains as the unique equilibrium.
More specifically, we have the following proposition for the case δc = 0, δf = 1, and t = 1.24
Proposition 6. Suppose δc = 0, δf = 1, and t = 1. In the subgame where firms do not share
information, there exists a constant k ≈ 0.04 such that
24

This corresponds to Proposition 1 in Choe et al. (2020). But the proposition holds for general values of δc ,

δf and c, as proved in Choe et al. (2020).

18

• there is a unique firm A poaching equilibrium if and only if k < c, in which firm A’s market
share in τ = 1 is given by zI = (11 + 7c)/26,• if c ≤ k, then a firm B poaching equilibrium coexists with the firm A poaching equilibrium,in which firm A’s τ = 1 market share is given by zII = (15 + 7c)/26.
We can illustrate the above using figures. In Figure 1, the (blue) solid lines represent firm
A’s best response function with pBJ indicating its discontinuity point, and the (red) dashed lines
represent firm B’s best response function with pAJ indicating its discontinuity point. In Figure
1, the best response functions intersect twice, hence we have multiple equilibria. In the current
example, this corresponds to the case where c ≤ k ≈ 0.04. For example, when c = 0, the firm
A poaching equilibrium is given by (pA , pB ) = (10/13, 8/13) with zI = 11/26, and the otherequilibrium is its mirror image, as in Choe et al. (2018).
— Insert Figure 1 about here. —Suppose now c increases. Then firm A becomes less aggressive so that pBJ increases, while firm
B becomes more aggressive so that pAJ decreases. As can be seen from Figure 1, this makes theintersection of pAII and pBII less likely, which will eventually leave only the intersection between
pAI and pBI as the unique equilibrium. This is shown in Figure 2. For example, when c = 1/2, theunique equilibrium is the firm A poaching equilibrium, which is given by (pA , pB ) = (12/13, 27/26)
with zI = 29/52.
— Insert Figure 2 about here. —Despite the cost difference, the main insight from the symmetric cost case continues to be valid.
Namely, for both firms, the benefits from softened competition at the information acquisition stage
outweigh the costs of intensified competition when information is used for price discrimination.
As a result, information sharing continues to be individually rational. The following is the main
result in Choe et al. (2020) that generalizes Proposition 1.
Proposition 7. For all values of δc , δf , and c, the unique equilibrium of the whole game is asfollows: in τ = 0, firms agree to share information, which is followed by the Hotelling outcome inτ = 1 and the Thisse-Vives outcome in τ = 2. The discounted sum of consumer surpluses underinformation sharing is smaller than that in either equilibrium without information sharing.

19

5.5

Alternative timing

The point in time when the agreement to share information occurs is important in our framework.
Suppose firms make decisions to share information at the end of τ = 1 but before τ = 2. Other
than this, all other features of our baseline model stay the same. In particular, information
sharing occurs if and only if both firms agree to do so. This alternative timing results in no
information sharing in equilibrium, as we show below.
Consider τ = 2. With information sharing, we have the Thisse-Vives outcome. Without
information sharing, the total industry profit in any equilibrium is bounded below by the totalindustry profit in the Thisse-Vives equilibrium, which follows from Proposition 2 in Chen et al.
(2020). This implies that at least one firm has higher profit than the Thisse-Vives level in any
equilibrium without information sharing, and hence will choose not to share information. Given
the above and our assumption that information sharing occurs if and only if both firms agree,
we can conclude that firms do not reach an agreement to share information at the end of τ = 1.
Then, in τ = 1, we have the equilibria as in Choe et al. (2018).
This highlights the mechanism behind our main result. The pre-commitment to information
sharing prior to the acquisition of information is crucial because the main benefits from information sharing are to soften competition at the stage when information is gathered. Such benefits
disappear when the information sharing agreement follows the stage when firms compete for customer information. Which timing is more plausible in practice depends on different mechanisms
for information sharing. For example, when banks apply for the accreditation to participate inopen banking, they do so in anticipation of sharing information gathered after their accreditation,rather than sharing information they already have. This is discussed in more detail in Section 5.7.
On the other hand, firms may join a database co-op with a view to gaining access to information
other members already have.

5.6

Longer time horizon

Our analysis has identified a clear trade-off in information sharing. The benefits come fromsoftened competition in τ = 1 when firms compete to gather customer information, while thecosts are due to intensified competition in τ = 2 when firms use information for price discrimination. Given this trade-off, a natural question is whether information sharing continues to bean equilibrium outcome if there are multiple future periods when firms compete using the shared
information, which can increase the costs of information sharing.
To address this question and consider the possibility of ongoing information sharing, we follow
Rhee and Thomadsen (2017) to expand the range of the discount factors beyond the traditional
20

range of zero to one. In particular, we allow δc , δf ∈ [0, 3/2] so that the case with δc , δf ∈ (1, 3/2]
offers a way of modelling multiple continuation periods in reduced form. We restrict analysis tothe case where δc , δf ≤ 3/2, which ensures an interior solution for the τ = 1 marginal consumer’s
location, i.e., z ∈ (0, 1). Otherwise, one of the firms monopolizes the market in τ = 1 so that
information sharing becomes irrelevant.
Given the expanded range of discount factors, we can show that our qualitative results staythe same. That is, each firm prefers information sharing to no information sharing for all valuesof δc , δf ∈ [0, 3/2], and that the discounted sum of consumer surpluses is smaller when firms share
information.25

5.7

Information sharing in practice

Earlier in the paper, we presented several examples of information sharing by firms such as
information exchange in the airline industry, database co-ops, and open banking. In this section,
we provide some more details on information sharing in practice. We then discuss legal andregulatory issues related to information sharing in general.
Information sharing among competitors is mandated by government regulations in several
industries. In Europe, for example, information sharing is imposed in automotive, banking andfinance, electronic communications, energy, and postal services (Feasey and de Streel, 2020). As
discussed previously, information sharing in banking can take the form of open banking, which
is mandated in Australia (Consumer Data Right or CDR), and the UK and EU (UK OpenBanking Standard, and Payment Services Directive Two).26 In Australia, in particular, the CDR
Register and Accreditation Application Platform provides a portal where businesses can apply tobe accredited, and create a trusted data environment where encrypted data is shared only amongaccredited participants. This application and accreditation process can be taken to reflect thestage τ = 0 in our model. Although our stylized model does not capture important features ofbanking such as the interaction between deposit and lending markets, screening and monitoring,
evidence suggests that open banking leads to more personalized offers and services in banking,27
the latter being the main role of information in our model.
25

The details are available from the authors.

26

Australia goes even further to mandate data sharing beyond the financial sector. The banking sector is thefirst industry where the CDR applies, followed by the energy sector, with the telecommunications sector expected
to follow (https://www.accc.gov.au/focus-areas/consumer-data-right-cdr-0).
27

For evidence, see, for example, https://fintechmagazine.com/financial-services-finserv/rise-open-banking-how-

big-data-changing-fintech. Vives and Ye (2022) provides a spatial model of bank competition that explicitly takes
into account the effects of information technology.

21

In addition to the mandated information sharing mentioned above, there is evidence ofbusiness-to-business (B2B) information sharing in other industries as well. As an example, Arnaut
et al. (2018) reports results from a survey conducted in 2017-2018 covering 129 companies across
31 countries in the European Economic Area. The survey covers firms with various sizes from six
business sectors: data-generating driving (i.e., automotive, transport and logistics), smart agriculture, smart manufacturing, telecom operators, smart living environments (i.e., home automation,
sensors, robotics, or wearable technology), and smart grids & meters. Although the report does
not say whether firms use shared information for pricing purposes, it finds that most B2B information sharing is within the same business sector and that firms choose to share information
depending on their business strategies.
Whether or not information sharing among competitors can potentially breach competition
laws depends on the type of information that is shared. Some information sharing can be vital for
innovations leading to new products and services, while sharing other information can facilitatecollusion. The key issue is then weighing the beneficial effects of information sharing against
the adverse effects on competition. In the EU, for example, Article 101(1) of the Treaty on the
Functioning of the European Union (TFEU) can limit information sharing among competitors if
it restricts competition that cannot be justified under Article 101(3) as having beneficial effects
that outweigh anticompetitive effects (Feasey and de Streel, 2020, pp. 40-41). Lundqvist (2018,p. 150) classifies information roughly into three types: (i) pricing and output information, (ii)consumers’ and general market information, and (iii) more technology- or know-how-oriented
information. Sharing the first type of information is most likely harmful but sharing the third
type is most likely innocuous. The second type of information falls in the grey area, whichis relevant to our paper where the primary purpose of customer information sharing is pricediscrimination. While some legal scholars seem to have concerns about information sharing thatcan facilitate price discrimination (Lundqvist, 2018, p. 152), whether it is pro- or anti-competitive
depends on market environments. A dominant firm exercising price discrimination can generally
harm consumers. However, as is well-known and also shown in the analysis of τ = 2 pricing
game in this paper, information sharing in oligopoly can intensify competition when its primary
use is for price discrimination. Rather than price discrimination per se, it is the anticipationof information sharing that can restrict competition at the stage when firms compete to gaincustomer information. Thus, whether information sharing can be pro- or anti-competitive needs
to be understood in a dynamic context within a clearly defined market environment.

22

6Conclusion

This paper has studied a model of behavior-based price discrimination where firms can agree toshare customer information that can be used for personalized pricing. Our main findings are
summarized as follows. First, firms are better off sharing customer information as it softens
upfront competition when they gather information, which more than offsets the adverse effectof intensified competition when the information is later used for price discrimination. Second,
consumers are worse off as a result of information sharing. Third, information sharing can increase
total surplus thanks to the improved quality of matching between firms and consumers. These
results hold for all discount factors for consumers and firms and are robust to a variety of cost
asymmetries across firms. An additional finding is how the set of equilibria changes as cost
asymmetries change. Specifically, there are multiple equilibria as in Choe et al. (2018) when thecost difference is small, but the equilibrium is unique when the cost difference is above a certain
threshold.
We have considered several other extensions of our baseline model to discuss whether information sharing continues to be an equilibrium outcome. We find that firms prefer information
sharing to no information sharing when some consumers have preferences changing over time, or
when the time horizon is extended so that shared information has more lasting effect of intensifying competition. On the other hand, firms choose not to share information when the market
is not fully covered at the stage where information is gathered, or when the agreement to share
information follows the information gathering stage. These extensions reconfirm the key mechanism at work. The pre-commitment to sharing information before information gathering is crucial
because the main benefits from information sharing are to soften competition at the stage when
information is gathered.
We conclude the paper with an important caveat. Our results are driven by our focus on theuse of customer information for pricing purposes only. There are other potential benefits frominformation sharing that we did not consider in this paper. For example, information sharing canbenefit consumers through the reduction in switching costs, and the development of new apps andmore personalized services. In addition, information gathering in this paper is a by-product offirst-period price competition, rather than a stand-alone management decision. In practice, firms
commit significant resources to investments in customer information. These and other aspects of
information sharing need to be kept in mind for a richer understanding of information sharing
among competing firms.

23

Appendix
In the main text, we focused mostly on the case where δc = δf = 1. In this appendix, we stateand prove the results for general values of δc , δf ∈ [0, 1], whenever relevant.
Proof of Lemma 1: In τ = 2, regardless of the τ = 1 outcome, both firms can offer personalized
prices to all consumers as in Thisse and Vives (1988). Thus the equilibrium prices are given byt(1 − x)2 − tx2 = t(1 − 2x) for x ≤ 1/2,
2apA (x) =0
for x ≥ 1/2,
0
for x ≤ 1/2,
p2a
B (x) =
tx2 − t(1 − x)2 = t(2x − 1) for x ≥ 1/2.
From the above, we can calculate equilibrium profits as
Z 1
Z 1/2
t
t
2a
2a
t(2x − 1)dx = .
πA =t(1 − 2x)dx = , πB =
4
4
1/2
0
The consumer surplus in τ = 2 is then
Z 1/2
Z 1
7t
CS 2a =(v − paA (x) − tx2 )dx +(v − paB (x) − t(1 − x)2 )dx = v − .
120
1/2
In τ = 1, the Hotelling equilibrium prices and profits are straightforward. The consumer surplus
R1
R 1/2
is then CS 1a = 0 (v − t − tx2 )dx + 1/2 (v − t − t(1 − x)2 )dx = v − (13t)/12.
Proof of Proposition 1: Without information sharing, the equilibrium that favors firm B is as
given in Proposition 1 in Choe et al. (2018). Based on this, we can calculate the profits in eachperiod as follows:
1d
πA
=
1d
πB
=
2d
πA
=
2d
πB
=

(4 − 2δc + δf )(12 − 6δc − δf )(6 − 3δc − 2δf )t,4(12 − 6δc + δf )2
3(4 − 2δc + δf )((6(2 − δc )2 − 3(2 − δc )δf − 2δf2 )t4(12 − 6δc + δf )2(36(2 − δc )2 + 12(2 − δc )δf − δf2 )t4(12 − 6δc + δf )2,,(6 − 3δc + δf )2 t.
(12 − 6δc + δf )2

Since Πki = πi1k + δf πi2k for i = A, B and k = a, d, we haveΠaA − ΠdA =(36(2 − δc )2 δc + 12(4 − δc )(2 − δc )δf + (24 − 11δc )δf2 − 2δf3 )t4(12 − 6δc + δf )2
24

+

δf2 t
2(12 − 6δc + δf )2> 0,

ΠaB − ΠdB =(36(2 − δc )2 δc + 24(2 − δc )δf + (44 − 21δc )δf2 + 6δf3 )t4(12 − 6δc + δf )2−

3δf (8 − 4δc + δf )t> 0.
4(12 − 6δc + δf )2

Thus both firms choose information sharing. The rest of the proposition follows from the discussions in Section 4.1.
Proof of Lemma 3: With information sharing, consumer surplus in each period is given in(2) and (3). Without information sharing and for general values of δc and δf , we can calculate
consumer surplus in each period as follows:
36(2 − δc )2 (13 − 6δc ) − 12(2 − δc )(5 − 3δc )δf − (179 − 96δc )δf2 − 12δf3 t
CS 1d = v −,12(12 − 6δc + δf )2(42(2 − δc ) + 13δf ) t.
CS 2d = v −12(12 − 6δc + δf )From the above, we obtaintδf> 0,
2(6(2 − δc ) + δf )t 18(2 − δc )2 δc + 3(6 − δc )(2 − δc )δf + 8(2 − δc )δf2 + δf3
CS 1a − CS 1d = −< 0,(6(2 − δc ) + δf )2
CS 2a − CS 2d =CS a − (CS 1d + δc CS 2d )t 36(2 − δc )2 δc + 12(3 − δc )(2 − δc )δf + (32 − 17δc )δf2 + 2δf3=−
< 0.
2(6(2 − δc ) + δf )2

Proof of Proposition 4: Suppose [zA , zB ] is not served in τ = 1 where 0 < zA < 1/2 < zB < 1with or without information sharing. We show below that this condition holds if v < t. In
the following, we consider only the case where the τ = 2 outcome is interior duopoly. But the
proposition holds for all other τ = 2 outcomes, and the proof is available from the authors.
The subgame without information sharing
We solve the game backwards, starting with τ = 2. Competition on [zA , zB ] is à la Hotelling,leading to the following prices and the location of the marginal consumer from this segment:p2∗
A =(1 − 4zA + 2zB )t(−1 − 2zA + 4zB )t
1 + 2(zA + zB )
2∗
, pB
=
, x∗ =.
3
3
6

For [zA , zB ] to be fully covered in τ = 2, the net utility of consumer x∗ must be positive. That is,v − tx∗ − p2∗
A =v−(1 − 2zA + 2zB )t
> 0.
2
25

(6)

Profits from this segment are
2c∗
πA
=

(1 − 4zA + 2zB )2 t(−1 − 2zA + 4zB )2 t
2c∗
, πB
=
.
18
18

Consider next [0, zA ] where firm A chooses personalized prices and [zB , 1] where firm B chooses
2∗
personalized prices. Using p2∗
A and pB , we can derive the location of consumer x̃A whose net utility

is zero if she chooses firm B and pays price p2∗
B , and similarly, x̃B whose net utility is zero if shechooses firm A and pays price p2∗
A:
x̃A =

3v − (1 − 4zA + 2zB )t2(1 − zA + 2zB )t − 3v
, x̃B =.
3t
3t

Then firm A chooses personalized price v − tx for consumer x ∈ [0, x̃A ] and t(1 − 2x) + p2∗
B for
consumer x ∈ (x̃A , zA ]. Similarly, firm B chooses personalized price v − t(1 − x) for consumerx ∈ [x̃B , 1] and t(2x − 1) + p2∗
A for consumer x ∈ [zB , x̃B ). Then profits from these segments canbe calculated as
2 + 10(1 + 2z )z − 2(1 + 2z )2 )t2 + 12(1 − z + 2z )tv − 9v 22(−17zA
B A
B
A
B
,
18t
2 + 4(1 + 5z )z − (5 − 4z + 8z 2 ))t2 + 12(2 − 2z + z )tv − 9v 22(−17zB
A B
A
A
B
A
.
18t

2t∗
πA
=
2t∗
πB
=

Because the above personalized prices cannot result in negative net utility for consumers zA andzB , we must have2∗
v − t(1 − zA ) − p2∗
B > 0 and v − tzB − pA > 0.

(7)

Consider now τ = 1. Given δc = 0, we have zA = (v−p1A )/t and zB = (t−v+p1B )/t. Thus, total
2t∗
2c∗
1
2t∗ + π 2c∗ ) and Π
profits for the two firms are ΠAn = p1A zA + δf (πA
Bn = pB (1 − zB ) + δf (πB + πB ).
A

Solving the first-order conditions for profit maximization gives us
1∗p1∗
A = pB =3((1 + 4δf )v − 2δf t)(3 − 2δf )v + 6δf t∗∗, zA= 1 − zB=.
6 + 10δf2(3 + 5δf )t∗ < 1/2 < z ∗ for any v < t. The resulting total profits are
From this, we can verify zA
BΠ∗An = Π∗Bn =(3 + δf )(3 − 2δf (9 + 11δf ))v 2 + 72δf (1 + δf )(2 + δf )vt − 18δf (1 + δ)(3 + δf )t2.
4(3 + 5δf )2 t

For the above equilibrium to be possible, we need conditions (6) and (7). One can verify thatthese two conditions are satisfied if and only ifv>(3 + δf )t≡ vn .
2(2 + δf )26

(8)

The subgame with information sharing
The analysis is similar to the subgame without information sharing except one difference that,in τ = 2, competition on [0, zA ] and [zB , 1] is more intense because firms choose zero personalized
price for consumers they cannot serve. Thus, we omit the details and only state total equilibrium
profits and the condition needed to support the equilibrium, similar to the condition in (8).
Total equilibrium profits with information sharing are given byΠ∗As = Π∗Bs =(9 − 15δf + 12δf2 − 2δf3 )v 2 + 2δf (9 − 2δf )(1 − δf )vt + δf2 (5 − δf )t2
4(3 − δf )2 t,

which is supported if and only ifv>(9 − δf )t≡ vs .
2(6 − δf )(9)

Equilibrium of the information sharing game
We compare profits, Π∗in and Π∗is for i = A, B. Given that firms have the same profits, weonly compare Π∗An and Π∗As . Direct calculation gives us∆Π∗ (v) ≡ Π∗An − Π∗As =−4δf (162 + 81δf − 72δf2 + 48δf3 − 7δf4 )v 24(3 − δf )2 (3 + 5δf )2 t+−

2δf (567 + 369δf − 165δf2 + 107δf3 − 14δf4 )vt
4(3 − δf )2 (3 + 5δf )2 t
(486 + 369δf − 75δf2 + 59δf3 − 7δf4 )4(3 − δf )2 (3 + 5δf )2 t.

We need conditions (8), (9), and v < t, hence max{vn , vs } < v < t. First, notice that ∆Π∗ (v) isstrictly concave in v. Second, we can verify ∆Π∗ (v)|v=max{vn ,vs } > 0 and ∆Π∗ (v)|v=t > 0. Thisshows ∆Π(v) > 0 for all v that satisfies max{vn , vs } < v < t because ∆Π∗ (v) is strictly concave.
Thus firms choose not to share information.
Proof of Proposition 5: The subgame following the information sharing agreement has the sameoutcome as the case with perfectly correlated preferences. Thus, each firm earns the discounted
sum of profits equal to t/2 + δf (t/4). In the following, we solve for the equilibrium of the subgame
without information sharing.
We start with τ = 2. Let z be the marginal consumer in τ = 1. We will call A = [0, z],firm A’s turf and B = [z, 1], firm B’s turf. First, consider firm A’s turf. Firm B anticipates thatfirm A can offer zero personalized prices to protect its turf. Thus the marginal consumer on [0, z]
given firm B’s uniform price p2B is xA = (t + p2B )/(2t). Then the demand facing firm B iszη(1 − xA ) + (1 − η)(z − xA ) if xA < z and z > 1/2,2dB =zη(1 − xA )if xA ≥ z or z ≤ 1/2.
27

2
Firm B chooses p2B to maximize its profit from A given by πB,A
= p2B d2B . Solving the maximization

problem, we have1(1 − 2z)2t
if z ≤ or η >for z ∈ (1/2, 3/4),

2
2
1−z
p2∗
=
B
((2 − η)z − (1 − η))t3
(1 − 2z)2
if z ≥ or η ≤for z ∈ (1/2, 3/4),
2(1 − η + ηz)
4
1−z

1
(1 − 2z)23
if z ≤ or η >for z ∈ (1/2, 3/4),

4
2
1−z
∗
xA =
(2 + η)z + (1 − η)
3
(1 − 2z)2
if z ≥ or η ≤for z ∈ (1/2, 3/4),
4(1 − η + ηz)
4
1−z

1
(1 − 2z)2tηz
if z ≤ or η >for z ∈ (1/2, 3/4),

8
2
1−z
2∗
πB,A
=
((2 − η)z − (1 − η))2 t
3(1 − 2z)2
if z ≥ or η ≤for z ∈ (1/2, 3/4).
8(1 − η + ηz)4
1−z∗Then, firm A chooses its personalized price, pA (x) = p2∗
B + t(1 − 2x) for x ≤ xA . Thus firm A’s

profit from A isz(3(8 − 5η) − 16(1 − η)z)t



16
2∗
πA,A
=
((2
+
η)z
+
(1
− η))2 t
16(1 − η + ηz)1(1 − 2z)2or η >
for z ∈ (1/2, 3/4),
21−z
3(1 − 2z)2
if z ≥ or η ≤for z ∈ (1/2, 3/4).
4
1−z
if z ≤

Next, consider firm B’s turf, B. Following similar steps, we find that firm A faces demand(1 − z)ηxB + (1 − η)(xB − z) if xB > z and z < 1/2,2
dA =(1 − z)ηxB
if xB ≥ z or z ≥ 1/2
where xB is the marginal consumer’s location in B. Solving firm A’s profit maximization problem,
we obtain

p2∗
A

x∗B

2∗
πA,B


t
1
(2z − 1)2

if z ≥ or η >for z ∈ (1/4, 1/2),

2
2
z
=
(1 − 2z + ηz)t1
(2z − 1)2

if z ≤ or η ≤for z ∈ (1/4, 1/2),
2(1 − ηz)4z
1
1
(1 − 2z)2
if z ≤ or η >for z ∈ (1/4, 1/2),

4
2
1−z
=
3
(1 − 2z)2
1 + 2z − 3ηz
if z ≥ or η ≤for z ∈ (1/4, 1/2),
4(1 − ηz)41−zt(1 − z)η1(2z − 1)2

if z ≥ or η >for z ∈ (1/4, 1/2),

8
2
z
=
(1 − 2z + ηz)2 t
1(2z − 1)2

if z ≤ or η ≤for z ∈ (1/4, 1/2),
8(1 − ηz)
4
z
28

∗
Given the above, firm B chooses its personalized price, pB (x) = p2∗
A − t(1 − 2x) for x ≥ xB , andearns profit from B given byt(1 − z)(8 + η + 16(1 − η)z



16
2∗
πB,B
=
2t
(3
−
2z
−
ηz)



16(1 − ηz)1(2z − 1)2or η >
for z ∈ (1/4, 1/2),2z
1(2z − 1)2
if z ≤ or η ≤for z ∈ (1/4, 1/2),
4z
if z ≥

Based on the above, we can divide possible τ = 2 outcomes into three cases: Combining thep
two discussions, we classify the outcomes into the three cases: (i) z < (4 + η − η(8 + η))/8; (ii)ppp
(4 + η − η(8 + η))/8 ≤ z ≤ (4 − η + η(8 + η))/8; (iii) (4 − η + η(8 + η))/8 < z. Cases (i)and (iii) can result in asymmetric equilibria while case (ii) can lead to a symmetric equilibrium.
Consider now τ = 1. Since δc = 0, the marginal consumer’s location is given by z = (t −12∗ + π 2∗ ), and firm B
pA + p1B )/(2t). Then firm A chooses p1A to maximize ΠA = p1A z + δf (πA,AA,B
2∗ + π 2∗ ). We proceed as follows. First, wechooses p1B to maximize ΠB = p1B (1 − z) + δf (πB,AB,B
focus on case (ii) and solve for each firm’s local optimum. This gives us a symmetric candidate
equilibrium where
p1A = p1B = t −δf (8 − η)tδf (2 − η)tt, ΠA = ΠB = +
.
16
2
8

Next, we check if either firm has incentives to deviate by choosing price that leads to cases (i) or(iii). One can verify that no firm has incentives to deviate.
Comparing the above profits with the profits under information sharing, t/2 + δf (t/4), we canconclude that both firms prefer information sharing to no information sharing.

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33

𝑝𝑝𝐴𝐴
𝑝𝑝𝐵𝐵𝐵𝐵𝑝𝑝𝐴𝐴𝐴𝐴

𝑝𝑝𝐴𝐴𝐴𝐴𝐴𝐴𝑝𝑝𝐴𝐴𝐴𝐴

2 − 𝑐𝑐52 − 𝑐𝑐7

𝑝𝑝𝐵𝐵𝐵𝐵𝐵𝐵

2 + 5𝑐𝑐7

2 + 3𝑐𝑐
5

𝑝𝑝𝐵𝐵𝐵𝐵

Figure 1: First-period multiple equilibria when 𝒄𝒄 ≤ 𝒌𝒌

𝑝𝑝𝐵𝐵

2−
5
2−
7

2+5
7

2+3
5

Figure 2: First-period unique equilibrium when>