Discussion Paper No. 1023

COMPETITIVE PERSONALIZED PRICING

Zhijun Chen
Chongwoo Choe
Noriaki Matsushima

March 2018

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Competitive Personalized Pricing∗
Zhijun Chen†
Department of Economics, Monash University
chenzj1219@gmail.com
Chongwoo Choe
Department of Economics, Monash University
ISER, Osaka University
chongwoo.choe@monash.edu
Noriaki Matsushima
ISER, Osaka University
nmatsush@iser.osaka-u.ac.jp
March 9, 2018

Abstract
We study a duopoly model where each firm chooses personalized prices for its targeted consumers, who can be active or passive in identity management. Active
consumers can bypass price discrimination and have access to the price oﬀered to
non-targeted consumers, which passive consumers cannot. When all consumers are
passive, personalized pricing leads to intense competition and total industry profit
lower than that under the Hotelling equilibrium. But market is always fully covered.
Active consumers raise the firm’s cost of serving non-targeted consumers, whichsoftens competition. When firms have suﬃciently large and non-overlapping target
segments, active consumers enable firms to extract full surplus from their targeted
consumers through perfect price discrimination. With active consumers, firms alsochoose not to serve the entire market when the commonly non-targeted market segment is small. Thus active identity management can lead to lower consumer surplus
and lower social welfare. We also discuss the regulatory implications for the use of
consumer information by firms as well as the implications for management.
Key words: Personalized pricing, identity management, customer targeting
JEL Classification: D43, D8, L13, L5∗

We are thankful to the seminar audience at various institutions for constructive comments and suggestions. We are especially thankful to Masaki Aoyagi, Yoshiyasu Ono, Patrick Rey, Wing Suen, Chengsi
Wang for many helpful discussions, and Peter Lambert for excellent research assistance. We gratefully acknowledge the financial support from the Japan Society for the Promotion of Science (JSPS), KAKENHI
Grant Numbers JP15H03349, JP15H05728, and JP17H00984, and the Murata Science Foundation. The
second author thanks Osaka University for its International Joint Research Promotion Program. The
usual disclaimer applies.
†
The corresponding author. Department of Economics, Monash University, Wellington Road, Clayton, VIC 3800, Australia. Email: chenzj1219@gmail.com

1

1

Introduction

Firms in various service industries can collect a huge volume of individual-level consumer information at unprecedented levels of variety and velocity, commonly dubbed big
data, thanks to ubiquitous online search and transactions, interactions on various social
networking websites, etc. Much of the relevant information is collected and distributedby data brokers ranging from established companies such as Acxiom and Bloomberg, tomore recently established ones such as BlueKai (Oracle), and Teradata.1 According to
TRUSTe, a technology compliance and security company, the 100 most widely used websites are monitored by more than 1,300 firms (“Getting to know you”, The Economist,
September 11, 2014). Firms also collect information through their customers’ past purchases, often utilizing various loyalty programs and payment records. The rapid development in information and communication technologies allows firms to collect big data
at increasingly lower costs. It is now common for a typical firm to have a dedicated teamfor data analytics and, in many cases, a position titled as chief data oﬃcer (“Just using
big data isn’t enough any more”, Harvard Business Review, February 9, 2016).
The availability of consumer information allows firms to divide the market into different segments and make a tailored oﬀer to each segment. A classic example is discountcoupons targeted at price-sensitive consumers (Shaﬀer and Zhang, 1995). As the quality
and quantity of information improves, firms can aﬀord a finer market segmentation andmore personalized oﬀers. For example, more information makes even coupons more personalized and targeted: Coupons.com, an online platform oﬀering digital coupons, uses
its proprietary data on consumer behavior to personalize and target coupons (Ezrachi
and Stucke, 2016, p. 91). Other examples abound: Safeway’s Just for U program uses
complex algorithms to process customers’ purchase data, based on which to send personalized oﬀers online or through mobile apps (“Supermarkets oﬀer personalized pricing”,
Bloomberg, November 16, 2013); Uber’s “route-based pricing” charges customers basedon their predicted willingness to pay (“Uber starts charging what it thinks you’re willing to pay”, Bloomberg, May 19, 2017). These are just a few examples that herald thepossible arrival of even real-time personalization (Esteves and Resende, 2016).2
As firms gain access to more consumer information, consumers are becoming increasingly aware that their online activities are being monitored and their personal information being collected and possibly shared. With privacy concerns added to such awareness,
1

These firms collect data from various sources, including their own data collection technologies,
arrangements with website owners for installing tracking tools such as cookies, public information, datafrom public authorities and third-party companies such as banks. The industry is estimated to turn over$156 billion annually (“The dark market for personal data”, The New York Times, October 16, 2014).
2
There are many other examples of personalized pricing used by airlines, grocery chains, online travel
portals, etc. For example, see “Dynamic pricing: which customers are worth the most? Amazon, Delta
Airlines, and Staples weigh in”, Forbes, April 17, 2015; “How retailers use personalized prices to test
what you’re willing to pay”, Harvard Business Review, October 20, 2017. Ezrachi and Stucke (2016,
Chapter 10) provide more discussions and examples of personalized pricing.

2some consumers take proactive measures to protect themselves and thwart firms’ attempt
to use personalized pricing. Such actions can include using virtual private networks foronline activities, erasing or blocking browser cookies, creating a new account for new
transactions, maintaining several online identities, and using diﬀerent credit cards fordiﬀerent transactions, etc. These actions are not confined to online transactions only.
In industries such as retail banking and insurance, telecommunications, cable TV services, and power and utilities, firms often oﬀer new-customer-only special discounts. In
that case, an existing customer may search for a better oﬀer, based on which to directly
haggle with the firm.3 She may also cancel the existing account and create a new one if
doing so is not too costly. Such proactive measures by consumers, which we collectively
call identity management (Acquisti 2008), incur various transactions costs such as time,
eﬀort, and even money.
In this paper, we study personalized pricing in an oligopolistic environment in which
consumers may engage in identity management. It is well known that more consumer
information can intensify price competition and hurt profitability unless there are suﬃcient heterogeneities at the firm level.4 But this result is based on the assumption that
consumers cannot engage in identity management. Several recent studies reviewed in
Section 2 incorporate diﬀerent types of identity management, but mostly for the caseof monopoly. Thus our study fills the gap in the literature by incorporating identity
management in a competitive setting. By doing so, we also address important policy
issues that relate to the use of consumer information for price discrimination. For example, the US Council of Economic Advisers (2015) proposed giving consumers greater
access to and control over their information, arguing that increased transparency into
how companies use consumer information would promote more competition and better
informed consumer choice. As we show in this paper, whether more transparency will
promote competition hinges crucially on how it aﬀects identity management. Specifically, if more transparency leads to more active identity management, then we showthat competition is softened, which reduces consumer surplus and, in some cases, evenreduces social welfare.
Formally, we consider a Hotelling linear city with two firms at each end. Each firm
has a target segment on which it has complete information about consumer preferences
and can oﬀer personalized prices. For consumers outside its target segment, each firm cancharge only a uniform price. In our static duopoly model, we assume firms are endowed
3

According to a 2013 survey of 2,000 American adults conducted by the Consumer Reports National Research Center, 33% of customers negotiated with their existing mobile phone
providers. Of these, 76% reported being successful at least once with the average annual saving of $80. Similar findings are reported for banks, credit-cards, and cable TV services. See
http://www.consumerreports.org/cro/magazine/2013/08/how-to-bargain/index.htm. In Appendix B,
we provide more detailed evidence based on the data collected from various internet portals.
4This literature is reviewed in Section 2. For example, Choe et al. (2017) show that a symmetricduopoly results in increasingly smaller industry profit when competition shifts from that in uniform
pricing to third degree price discrimination, and to personalized pricing.

3with relevant consumer information, possibly through purchase from data brokers, andfocus on pricing equilibria for all possible market segmentations. Our key modelling
ingredient is the possibility of identity management by consumers. We consider two
types of consumers. An active consumer can costlessly engage in identity management,
implying that, in addition to the personalized price oﬀered by the targeting firm, she
can also choose the uniform price set by the firm for non-targeted consumers. Thus anactive consumer can potentially choose from three prices: a personalized price from thetargeting firm and two uniform prices. But a passive consumer faces prohibitively highcosts in identity management and cannot choose the uniform price set by the targetingfirm. Thus a passive consumer faces at most two prices, a personalized price from thetargeting firm and the uniform price from the rival firm.
Before summarizing our main findings, we start with two observations. First, personalized pricing allows firms to defend their target segments more aggressively thanwhen they can charge prices at higher levels of aggregation. Because personalized prices
are oﬀered privately to targeted consumers, a firm can reduce a personalized price fora targeted consumer without reducing personalized prices for other targeted consumers.
Thus firms can defend their targeted consumers individually and, if necessary, cut theprice for the marginal consumer down to zero. Second, firms become more aggressive inpoaching the rival’s targeted consumers when their own targeted consumers are passive
than when they are active. It is because passive targeted consumers cannot choose thefirm’s uniform poaching price, which allows the firm to delink its personalized prices
from the poaching price. But this is not possible when the firm’s targeted consumers areactive since a low poaching price will also attract the firm’s targeted consumers. This
raises the cost of poaching, which softens competition.
The above observations imply that both the poaching and defending sides will behave
aggressively when they face passive consumers. This intensifies competition, leading to
the following results when all consumers are passive. First, when each firm targets all its
loyal consumers and there is some overlapping target segment, competition is the mostintense in that the equilibrium outcome is that in Thisse and Vives (1988). Second,firms are collectively better oﬀ when there is a market segment that is not targeted byeither firm. Firms compete à la Hotelling on the commonly non-targeted segment, whichworks as a cushion and softens competition on each firm’s target segment. Needlessto say, the Hotelling equilibrium obtains when the entire market is non-targeted byeither firm. Third, in equilibrium for any given market segmentation, the total industry
profit is bounded above by the Hotelling profit, and below by the profit from the Thisse
and Vives outcome. Thus more consumer information unambiguously lowers industry
profitability when it is used for price discrimination. Nonetheless all consumers areserved in any equilibrium since firms can separate competition on the targeted and nontargeted segments. Given our model assumption, such full market coverage implies that
there is no deadweight loss.
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The results change drastically when consumers are active because firms become lessaggressive in poaching in this case. Since personalized prices and the poaching pricecannot be considered in separation, there are many diﬀerent types of equilibria dependingon market segmentation. One salient equilibrium is where each firm exercises perfectprice discrimination and extracts full consumer surplus from all of its targeted consumers.
This equilibrium is possible when the market is fully targeted and firms have suﬃciently
large and non-overlapping target segments. In this case, neither firm has incentives topoach the rival’s targeted consumers and, as a result, both set high uniform prices thatare not accepted on the equilibrium path. This allows them to exercise perfect pricediscrimination for all of their targeted consumers. Thus a collusive outcome is obtainedin the one-shot game without implicit or explicit collusion. This is in stark contrast to
the case with passive consumers: for the same market segmentation that supports perfectprice discrimination when consumers are active, the equilibrium with passive consumers
can result in the most intense competition as in Thisse and Vives. Another noteworthy
equilibrium is when there is a small market segment that is not targeted by either firm.
This can lead to firms exercising perfect price discrimination for their targeted consumers
while choosing not to serve the non-targeted segment, which creates a deadweight loss.
The insight that competition is softened when consumers are active holds more generally
for all other types of equilibria. Indeed we show that, for any market segmentation, thetotal industry profit in equilibrium is larger when consumers are active than when they
are passive.
Our analysis also reveals a prisoner’s dilemma that consumers face in identity management. Each individual consumer can benefit from being active. But consumers arecollectively worse oﬀ when more consumers become active because of the negative externality that each active consumer imposes on others. We show this by looking at thecase where a fraction of consumers are active and analyze the equilibrium as the fraction
increases. The comparative statics leads to a number of results: as more consumers
become active, the equilibrium with deadweight loss obtains for a wider range of market
segmentation; the equilibrium with perfect price discrimination is also more likely fora wider range of market segmentation; and more consumer information is required tointensify competition. The last point can be also related to privacy and consumer welfare. The equilibrium with the largest consumer surplus is the one with the most intensecompetition, i.e., the Thisse and Vives outcome. When all consumers are passive, anymarket segmentation in which each firm has information about only its loyal consumers
leads to this outcome. When all consumers are active, however, the same outcome obtains if and only if when both firms have full information about all consumers. Thatis, no privacy can lead to the equilibrium with the largest consumer surplus when all
consumers are active. We discuss this point further in Section 7.
Our paper extends the existing literature on competitive price discrimination in an
important way and provides new insight towards understanding price discrimination
5

when consumers can take measures to bypass firms’ attempt to price discriminate. In
the age of big data, behavioral targeting, and personalized pricing, more technologies
and tools are becoming available for identity management by consumers. By incorporating identity management explicitly, we show that the results from the existing literatureare completely overturned when all consumers are active in identity management. Even
when only a fraction of consumers are active, our general insight carries through in thatcompetitive price discrimination benefits firms as more consumers become active. We
also contribute to the debate on the regulation of the collection and use of consumer
information by firms. Strict privacy rules that prevent firms from using consumer information for price discrimination can soften competition and benefit firms when consumers
are passive. In addition, policies that improve the transparency in and the disclosure of
the use of consumer information may soften competition and benefit firms, if they also
induce consumers to become more active in identity management.
The rest of the paper is organized as follows. Section 2 reviews the related literature.
Section 3 presents the model. Section 4 analyzes the case where all consumers are passive
and Section 5, the case where all consumers are active. In Section 6, we consider the
hybrid case and provide comparative statics results with respect to the fraction of active
consumers. Section 7 provides various discussions including the regulatory implications
for collection/use of personal data and the implications for management. Section 8
concludes the paper. Appendix A contains all the proofs while Appendix B provides
some evidence on identity management by consumers.

2

Related literature

There is a large literature on competitive price discrimination.5 Two general findings
from the literature can be summarized as follows. First, price discrimination can intensify
competition and hurt firm profitability compared to the non-discrimination benchmark
unless there are suﬃcient heterogeneities at the firm- or consumer-levels. This is true
whether firms compete in third-degree price discrimination (Shaﬀer and Zhang, 1995;
Chen, 1997; Villas-Boas, 1999; Fudenberg and Tirole, 2000; Pazgal and Soberman, 2008;
Esteves, 2010) or in personalized pricing (Thisse and Vives, 1988; Zhang, 2011; Chen andIyer, 2002; Choe et al., 2017). Second, competition becomes more intense when firms
compete in personalized pricing than in third-degree price discrimination (Thisse andVives, 1988; Fudenberg and Tirole, 2000; Choe et al., 2017). The intuition behind theseresults is that more customer information makes firms more aggressive in pricing. For
example, when firms compete in personalized pricing, they compete for each consumer
individually without having to change prices set for other consumers. This gives them5

See Stole (2007) for a comprehensive survey and, for surveys of the literature where competitionis based on behavior-based price discrimination, see Chen (2005) or Fudenberg and Villas-Boas (2006,2012).

6

a (false) sense of their capability to protect their turf, making competition more intensethan when they compete with less customer information. But these results hold only
when all consumers are passive in the way we have defined the term in this paper. With
active consumers, we show both results are overturned.
Although our model is essentially static, it is nonetheless related to the literature
on behavior-based price discrimination where consumers can take actions to remain
anonymous, dubbed identity management (Acquisti, 2008). Our basic assumption isthat active consumers can choose identity management strategies to prevent firms fromusing their information for price discrimination. We may group these studies based onwhen consumers choose to do so. First, Taylor (2004), Villas-Boas (2004), and Acquisti
and Varian (2005) consider the case where consumers can prevent the firm from tracking
their purchase record that can be used for price discrimination. For example, consumers
can do so by delaying purchase or refusing to accept cookies. We may call this ex ante
identity management as it prevents firms from gathering consumer information in thefirst place. Not surprisingly, they show that a monopolist is worse oﬀ under ex ante
identity management. The second type, which we call interim identity management,
refers to the case where consumers can anonymize themselves after the initial purchase
but before firms choose prices for repeat purchase. This case was studied by Conitzer
et al. (2012) and Belleflamme and Vergote (2016), both in the monopoly setting. Theyfind that the firm is better oﬀ under interim identity management, as it renders themonopolist the commitment power not to price discriminate in repeat purchase. Third,
consumers can act as if they are new customers after observing the prices firms choose for
repeat purchase. We call this ex post identity management, which is the case studied in
our paper. We think ex post identity management is more realistic than interim identity
management since, if consumers can choose to become anonymous, it makes sense to do
so only when it is in their interest to do so. In addition, all the above studies are couchedin the monopoly setting whereas we consider the duopoly case.6
The fact that active consumers can choose the lowest of their firms’ oﬀers is reminiscent of a most-favored customer clause (MFCC), which is a contractual provisionthat a firm oﬀers to its customer that no other customers will be oﬀered a lower price.
As the MFCC raises the cost of poaching, it signals a firm’s intention not to poach therival’s customers. The competition-softening eﬀect of the MFCC has been studied bymany (e.g., Cooper, 1986; Schnitzer, 1994).7 There are several important diﬀerences
between our work and these studies. First, the MFCC is a strategic decision while wetake consumer identity management as exogenous and focus on firms’ pricing strategies
given all possible types of market segmentation. Second, the MFCC is extended to all6

Acquisti and Varian (2005) briefly touch upon the duopoly case with two consumer types.
In some cases, the MFCC can be ruled anti-competitive, Du Pont and Ethyl being the best-known
example. More recently a similar decision was made in Germany against online hotel portals (Heinz,2016).
7

7

existing customers while the poaching price in our model applies only to active, targeted
consumers. Third, the MFCC is shown to facilitate tacit collusion in a dynamic setting
whereas we show such outcome is possible in a one-shot game when consumers are active
and the market is fully targeted without an overlap.

3

The Model and Preliminaries

3.1

The model

There are two firms, A and B, selling competing brands of a consumer good. The
good is produced at a constant marginal cost that is normalized to zero. There is acontinuum of consumers, each demanding one unit of the good. Consumers are heterogeneous in their preferences, or brand loyalty denoted by l. Following Fudenberg
and Tirole (2000) and Shaﬀer and Zhang (2002), we define a consumer’s brand loyalty
as the minimum price diﬀerential necessary to induce that consumer to purchase herless preferred brand. Specifically a consumer with brand loyalty l derives a gross value
VA (l) := v + l/2 from buying brand A and derives a gross value VB (l) := v − l/2 frompurchasing brand B where l ∈ [−lB , lA ]. Thus a consumer with brand loyalty l will buy
brand B if and only if firm A’s price exceeds firm B’s price by more than l. To present
our results in most clear and parsimonious way, we assume v = 1 and that l is distributed
uniformly on [−1/2, 1/2], hence the total population of consumers is normalized to one.
As we show later, this simplification also ensures that the market is fully covered if it wasserved by a monopoly. Our main insight and the qualitative results from our analysis
carry through for general values of v, lA and lB insofar as lA , lB > 0 and v is large enoughto ensure full market coverage under monopoly.
Each firm has a target segment of the market, in which it has full information about
the exact preferences of all consumers. For example, firms can gather customer information either by purchasing it from other firms such as data brokers or by collecting iton their own through the use of various tracking technologies.8 Each firm can choose
personalized prices for its targeted consumers. For non-targeted consumers, each firm
charges a uniform price. We consider a natural case in which each firm’s target segment
is a connected set and includes consumers that are more loyal to the firm than to its rival.
Let [−1/2, b] be firm B’s target segment and [a, 1/2] be firm A’s target segment. Let
pA (x) be the personalized price firm A chooses for its targeted consumer x ∈ [a, 1/2], andqA be the uniform price firm A chooses for all its non-targeted consumers. Likewise, letpB (y) be the personalized price firm B chooses for its targeted consumer y ∈ [−1/2, b],
and qB be the uniform price it chooses for the rest. We assume that the values of a and8Gathering customer information necessary for market segmentation is costly. In this paper, we
assume away such costs and focus on pricing equilibria taking various configurations of market segmentation as given. For studies that consider endogenous information gathering, see Chen and Iyer (2002)
or Bergemann and Bonatti (2015).

8

b are publicly known.
The timing of the game is as follows, which is standard in the literature (Thisse andVives, 1988; Choudhary et al. 2005; Matsumura and Matsushima, 2015; Choe et al.
2017). In the first stage, firms oﬀer uniform prices to the non-targeted consumers, which
are publicly observed. In the second stage, they charge personalized prices to their targeted consumers. By definition, each personalized price is observed only by the targeted
consumer. Finally, each consumer makes a purchase decision after observing the uniform prices and the relevant personalized price. This two-stage pricing structure reflects
the fact that the uniform prices are ‘public’ to the non-targeted consumers whereas the
personalized prices are private. This is consistent with the commonly held view thata firm’s choice of publicly observable prices is a higher-level managerial decision and isrelatively slower to adjust in practice than a firm’s choice of personalized prices that are
oﬀered privately.
Although uniform prices are publicly observed, firms may set some hurdles thatprevent their targeted consumers from having access to the uniform prices, and bypassingthese hurdles may incur various transactions costs. Our key modelling assumption isthat some consumers can bypass the hurdles for price discrimination by utilizing various
identity management strategies, as discussed in the introduction. We assume there are
two types of consumers. A passive consumer faces prohibitively high transactions costs in
identity management and cannot have access to the uniform price oﬀered to non-targeted
consumers by the firm targeting that consumer. Thus a passive consumer x targeted byfirm A can choose between the personalized price pA (x) and the uniform price oﬀered by
the rival firm qB . Likewise a passive consumer y targeted by firm B can choose betweenpB (y) and qA . In contrast, an active consumer does not face any transactions costs in
identity management and can thus choose an additional uniform price oﬀered by thefirm targeting that consumer. Consequently, active consumer x targeted by firm A canchoose from pA (x), qB , and qA , and active consumer y targeted by firm B can choose
from pB (y), qA , and qB .
As discussed in Section 2, we consider ex post identity management. This is diﬀerent
from ex ante identity management, which prevents firms from exercising price discrimination in the first place. It is also diﬀerent from interim identity management, which
does not have bite in our static model. For example, an interim active consumer x targeted by firm A can decide between pA (x) and qA , but before observing these prices.
That is, her only choice is to remain targeted or non-targeted. Our assumption of ex
post identity management reflects the fact that it becomes increasingly diﬃcult for consumers to hide personal information ex ante, due to the advances in technologies and theproliferation of data brokers. In addition, active consumers have no reason to manage
their identity ex ante if they are confident they can do so ex post after having observed
all the options available to them. In Appendix B, we provide evidence supporting thistype of active consumers.
93.2

Benchmark results

For future reference, we document the results from four benchmark models adapted
to our setup. In all these models, we keep the standard assumption that all consumers
are passive.
First, the standard Hotelling model corresponds to the case a = −b = 1/2. Given qA
and qB , the marginal consumer z is determined by z = qA − qB . Thus firm A’s profit
is equal to πA = qA (1/2 − qA + qB ), and firm B’s profit is πB = qB (qA − qB + 1/2).
Solving for the Hotelling equilibrium then gives us qA = qB = 1/2, and each firm earns
profit equal to 1/4, hence the total industry profit of 1/2.
Second, in Fudenberg and Tirole (2000), firms compete using third degree pricediscrimination where each firm targets all its loyal consumers: a = b = 0.9 Let pi be theprice firm i chooses for its target segment and qi be the price for the rival’s target segment.
As in Fudenberg and Tirole, we assume firms choose these prices simultaneously. Thenon [−1/2, 0], consumers face two prices, pB and qA , hence the marginal consumer isgiven by z = qA − pB . Thus profits from this segment are πA = qA (pB − qA ) and
πB = pB (qA − pB + 1/2). This leads to pB = 1/3, qA = 1/6 and z = −1/6. The
other segment [0, 1/2] is symmetric, leading to pA = 1/3, qB = 1/6 and the marginal
consumer’s location at 1/6. As a result, firm A serves [−1/6, 0] ∪ [1/6, 1/2] and firm B
serves [−1/2, −1/6] ∪ [0, 1/6], and each firm has profit equal to 5/36, hence the totalindustry profit equal to 5/18.
The third case is Thisse and Vives (1988) where all consumers are targeted by both
firms (a = −b = −1/2) and firms compete in personalized pricing. Then firm A chooses
personalized prices pA (x) = x serving all its loyal consumers on [0, 1/2] and firm B
chooses pB (y) = −y serving all its loyal consumers on [−1/2, 0]. Each firm’s profit isthen 1/8 and so the total industry profit is 1/4. Comparing these three cases showsthat firms are worst oﬀ when they compete in personalized prices and best oﬀ in the
Hotelling equilibrium. It is in this sense that more consumer information that can beused for price competition intensifies competition and hurts profitability.
Finally, consider the case with a non-discriminating monopolist. Without loss ofgenerality, suppose the market is monopolized by firm A. Given the monopoly priceqA , the marginal consumer z is given by 1 + z/2 = qA . Thus the firm’s profit is πA =(1 + z/2)(1/2 − z). Maximizing it leads to z = −3/4 < −1/2, hence the market is fully
covered. The monopoly price is then qA = 5/8, which is also equal to the firm’s profit.

3.3

Non-contestable consumers

Personalized pricing allows firms to defend their target segment aggressively. Since
personalized prices are oﬀered privately to the targeted consumers, a firm can reduce a
9

We only report the second-period outcome from Fudenberg and Tirole (2000) since competition isin third degree price discrimination only in the second period of their model.

10personalized price for a particular consumer without changing the oﬀers to other targeted
consumers. In other words, a firm can defend each of its targeted consumers individuallywith personalized pricing and, if necessary, reduce the price for the marginal consumer
down to zero.
To see this, suppose firm B chooses a uniform price qB with a view to poachingsome of firm A’s targeted consumers. Then firm A’s targeted consumer x ∈ [a, 1/2]
chooses between two prices: the personalized price pA (x) oﬀered by firm A and theuniform price qB posted by firm B. Thus consumer x will choose firm A if and only
if x ≥ pA (x) − qB , implying that firm A’s optimal personalized price for consumer x ispA (x) = max{qB + x, 0}.10 If firm B aims to poach firm A’s targeted consumers, themost aggressive price it can oﬀer is qB = 0. In this case, the personalized price firm A
can choose to defend its targeted consumer x becomes pA (x) = max{x, 0}. Thus, for
any qB ≥ 0, firm A can use personalized pricing to profitably defend all its targeted
consumers as long as a ≥ 0.
We say firm A’s targeted consumer x is non-contestable by firm B if, for any qB ≥0, firm A can find pA (x) ≥ 0 that consumer x will choose over qB . Firm A’s noncontestable segment consists of all firm A’s targeted consumers who are non-contestableby firm B. Firm B’s non-contestable segment is defined in a similar way. Based on
the argument above, it is straightforward to see that firm A’s non-contestable segment
is given by NA ≡ [max{0, a}, 1/2], and firm B’s non-contestable segment is given by
NB ≡ [−1/2, min{b, 0}]. We summarize this in the following lemma.
Lemma 1 When firms can charge personalized prices, firm A has a set of targeted consumers NA = [max{0, a}, 1/2] non-contestable by firm B and firm B has a set of targeted
consumers NB = [−1/2, min{b, 0}] non-contestable by firm A.
Lemma 1 has important implications. First, by definition, a firm will serve all targeted consumers in its non-contestable segment. Thus firm A does not benefit fromtrying to poach firm B’s targeted consumers if b ≤ 0 and, similarly, firm B can nevergain in trying to poach firm A’s targeted consumers when a ≥ 0. Second, each firm has
a maximum set of non-contestable consumers, [0, 1/2] for firm A and [−1/2, 0] for firm
B. If a firm has a target segment beyond this maximum set, its targeted consumers withnegative loyalty can be poached by its rival.

3.4

Equilibrium

We adopt subgame perfection as our basic equilibrium concept. But subgame perfection admits multiple equilibria when a firm chooses a uniform price in its rival’s
10

We make the following tie-breaking assumptions. First, a consumer chooses the firm that targets
her when she is indiﬀerent. Second, when a consumer is not targeted by either firm, she chooses firm A
when indiﬀerent.

11

non-contestable market segment. For example, suppose firm B chooses qB in NA . Thenfor any qB ≥ 0, firm A can successfully defend NA by choosing pA (x) = qB + x for
all x ∈ NA . Thus firm B is indiﬀerent to any qB ≥ 0. In this case, we use a refinement in the spirit of Fudenberg et al. (1988). Specifically, for a given game without
a commonly contestable market segment, we consider a perturbed game by allowing asmall segment that is contestable by both firms. For each firm, the perturbed game hasa unique uniform price in equilibrium. Then we select the equilibrium of our original
game as the limit of the equilibrium of the perturbed game as the area of contestablesegment converges to zero.11 The following lemma shows that such a refinement allows
us to select a unique uniform price in equilibrium.
Lemma 2 Suppose zi ∈ Nj for i, j = A, B. Consider an ϵ-neighborhood of zi where
both firms choose uniform price and let qi (ϵ) be the equilibrium uniform price chosen byfirm i. Then limϵ→0 qi (ϵ) = 0.
Proof : See Appendix A.

3.5

Preview of the key results

Before we proceed to the full analysis of our model in the next section, we oﬀer a brief
account of the two most striking results from the analysis. The purpose is to highlight themain diﬀerences in equilibrium that result when consumers are passive vis-à-vis active,
and provide intuition behind the diﬀerences.
Our first result shows that, when consumers are active, a small proportion of nontargeted consumers may not be served in equilibrium, resulting in a deadweight loss. In
contrast, when consumers are passive, the market is always fully covered since firms candelink their pricing policies for targeted and non-targeted consumers. As an illustration,
suppose a = −b = δ where δ > 0 is suﬃciently small, hence [−δ, δ] is not targeted byeither firm. When consumers are passive, the two firms compete à la Hotelling on [−δ, δ],and the resulting uniform prices are qA = qB = δ. Equilibrium personalized prices arethen pA (x) = x + δ for all x ∈ [δ, 1/2] and pB (y) = −y + δ for all y ∈ [−1/2, −δ],and each firm serves all its loyal consumers. With active consumers, however, serving
consumers on [−δ, δ] can be costly since the uniform price that can appeal to them should
be suﬃciently low because they have weak brand loyalty to both firms. But the low
uniform price will also attract targeted consumers. Therefore, when δ is small enough,both firms would optimally choose not to serve the segment [−δ, δ]. In equilibrium,
11This is similar to the perturbation in ϵ-equilibria (Jackson et al., 2012). Firms consider by mistakethat there is a small segment that is commonly contestable and compete using uniform price. We lookat the equilibrium as such mistakes vanish in the limit. We need such a refinement only in the analysis
when all consumers are passive. When some consumers are active, a firm’s poaching price is uniquelydetermined in all cases.

12

firms choose suﬃciently high uniform prices (qA , qB ≥ 5/4) that are not accepted by any
consumers, both targeted and non-targeted. This allows them to exercise perfect pricediscrimination for their targeted consumers: pA (x) = 1 + x/2 for all x ∈ [δ, 1/2] andpB (y) = 1 − y/2 for all y ∈ [−1/2, −δ]. In sum, non-targeted consumers are not served
by either firm, hence lower welfare compared to when all consumers are served.
Our second result shows that competition is softened when consumers are active,
which can allow firms to extract full consumer surplus through perfect price discrimination. In contrast, passive consumers toughen competition by making firms aggressive inpoaching, leading to an all-out competition à la Thisse and Vives (1988). This can beillustrated by the previous example, a = −b = δ > 0. When consumers are passive, we
showed that firms choose uniform prices, qA = qB = δ. In the limit as δ → 0, we haveqA = qB = 0, and the personalized prices converge to those in Thisse and Vives (1988):
pA (x) = x and qB (y) = −y. This outcome results in the lowest possible total industry
profit, 1/4. When consumers are active, however, firms do not serve [−δ, δ] while extracting full consumer surplus from all its targeted consumers. As δ → 0, each firm serves all
its loyal consumers, resulting in the equilibrium with perfect price discrimination andthe maximum possible total industry profit, 9/8.
The above two results highlight the downside when consumers are active or any
policy intended in that direction. Namely, active identity management by consumers
can soften competition and lead to lower consumer surplus and lower social welfare. In
what follows, we show that the general intuition extends in other cases or even when
there is only a small measure of active consumers.

4

Passive Consumers

Suppose all consumers are passive. In this case, firms can separate their pricing
policies for targeted and non-targeted consumers. At first glance, such flexibility benefits firms because they can use personalized prices to protect their targeted consumers
from possible poaching. But the flip side is that competition for non-targeted consumers
intensifies. Since the rival’s poaching oﬀer limits the extent to which the firm can set personalized prices for its targeted consumers, the intensified competition for non-targeted
consumers prevents firms from extracting full surplus from targeted consumers eventhough they use personalized prices. As we will show below, firms are worse oﬀ as they
have more targeted consumers: the best outcome for firms is the Hotelling outcome whenneither has any targeted consumers.
We now characterize all possible equilibria when consumers are passive. These equilibria can be grouped into three types. Let us start with the case where all consumers
are targeted by at least one firm, a ≤ b. This may correspond to an established market
where firms are fairly well-informed about their customers and some consumers patronize
both firms.
13□ The equilibrium with one-way poaching. In this equilibrium, only one firm poaches
some consumers targeted by its rival. This equilibrium is likely when only one firm
aggressively targets consumers loyal to its competitor, i.e., either a ≤ b ≤ 0 or 0 ≤a ≤ b. Suppose a ≤ b ≤ 0. Then by Lemma 1, firm B’s target segment [−1/2, b] is
not contestable by firm A. In addition to [−1/2, b], firm B can poach some consumers
targeted by firm A, say [a, z], since consumers on [a, 0] are loyal to firm B. Firm A
will serve all remaining consumers. Since only firm B poaches some consumers targetedby firm A, we call this the equilibrium with one-way poaching by firm B. We show in
Proposition 1 below that this equilibrium can be described formally as follows. Firm B
serves [−1/2, b] with personalized prices pB (y) = −y, and [b, b/2] with qB = −b/2. Firm
A serves [b/2, 1/2] with pA (x) = x − b/2, and chooses pA (x) = 0 for [a, b/2] and qA = 0.
The total industry profit is then)( )2 ∫ b∫ 1/2 (bb
2 − 2b − b2
πA + πB =x−dx ++(−y)dy =
.
2
2
8
b/2
−1/2

(1)

The other case 0 ≤ a ≤ b is a mirror image of the above case and the equilibrium
is with one-way poaching by firm A. Figure 1 illustrates the equilibrium with one-way
poaching by firm B.
— Figure 1 goes about here. —□ The equilibrium with two-way poaching. Suppose a ≤ 0 ≤ b so that each firm
targets some of its rival’s loyal consumers. In this case, competition on [a, b] leads
to both firms choosing zero personalized price for the rival’s loyal consumers. Given
that both firms also choose zero uniform price, each firm serves all its loyal consumers,
including some of its rival’s targeted consumers. Thus we call this the equilibrium with
two-way poaching. In the equilibrium with two-way poaching, firm A serves [0, 1/2] withpA (x) = x, firm B serves [−1/2, 0] with pB (y) = −y, and both firms choose qA = qB = 0.
The total industry profit is then
∫ 1/2
πA + πB =

∫ 0
xdx +

0

1
(−y)dy = .
4
−1/2

(2)

It is easy to see that a ≤ 0 ≤ b is a necessary and suﬃcient condition for two-way
poaching to arise in equilibrium. Note that this equilibrium is independent of (a, b). This
includes the case in Thisse and Vives (1988) where the entire market is targeted by both
firms, i.e., −a = b = 1/2. Figure 2 illustrates the equilibrium with two-way poaching.
— Figure 2 goes about here. —Suppose now b < a so that consumers on [b, a] are not targeted by either firm, forwhom the two firms compete using uniform price. One possibility is that one firm serves14all consumers on [b, a] and possibly some of its rival’s targeted consumers as well. Thiscase was already covered above. So we only consider a new possibility in which [b, a] isserved by both firms as a result of Hotelling competition: there is z ∈ [b, a] such thatfirm B chooses qB to serve [b, z] and firm A chooses qA to serve [z, a]. This leads to thethird type of equilibrium.
□ The equilibrium with partial Hotelling outcome. This equilibrium is likely when thecommonly contestable segment [b, a] is large enough so that firms are better oﬀ sharing
this segment through Hotelling competition than one firm monopolizing it. If one firm
tries to monopolize the commonly contestable segment, competition in uniform priceintensifies, which in turn reduces personalized prices that each firm can choose for its
targeted consumers. In Proposition 1, we show that this equilibrium can be characterized
as follows: firm A serves [a, 1/2] with pA (x) = x + qB and [z, a] with qA ; firm B serves[−1/2, b] with pB (y) = −y + qA and [b, z] with qB where z = (a + b)/3, qA = (2a − b)/3,
and qB = (a − 2b)/3. The total industry profit is thenπA + πB = (a − z)qA +∫ 1/2(x + qB )dx + (z − b)qB +

∫ b

a

=

−1/2

(−y + qA )dy

1 8ab + 9(a − b) − 5(a2 + b2 )
+
.
4
18

(3)

Figure 3 illustrates the equilibrium with partial Hotelling outcome.
— Figure 3 goes about here. —We now provide our first main result, which describes possible equilibria for all configurations of market segmentation as represented by (a, b). For each pair of (a, b), there
is a unique equilibrium, which is one of the following three types.
Proposition 1 When all consumers are passive, there are three types of equilibria:• The equilibrium with one-way poaching - (i) one-way poaching by firm A if 0 ≤ a ≤2b with total industry profit Π = (2+2a−a2 )/8 ∈ [1/4, 11/32]; (ii) one-way poachingby firm B if 2a ≤ b ≤ 0 with total industry profit Π = (2 − 2b − b2 )/8 ∈ [1/4, 11/32].
• The equilibrium with two-way poaching if a ≤ 0 ≤ b with total industry profit
Π = 1/4.
• The equilibrium with partial Hotelling outcome if 2b ≤ a and b ≤ 2a with total()
industry profit Π = 1/4 + 8ab + 9(a − b) − 5(a2 + b2 ) /18 ∈ [1/4, 1/2].
Proof : See Appendix A.
Proposition 1 yields a number of observations that would be useful in comparison
with the case in the next section where all consumers are active. First, in all equilibria
15firms serve all consumers in the market. It is because firms can delink their uniform
price from personalized prices, which allows them to serve every non-targeted consumer
using a non-negative uniform price. Since every consumer derives a positive gross value
from either firm, eﬃciency requires full market coverage. Thus all equilibria are eﬃcientand market segmentation is welfare-neutral when all consumers are passive.
Second, firms are better oﬀ in the equilibrium with partial Hotelling outcome thanin the equilibrium with two-way poaching. This is because the Hotelling competition in
the commonly contestable segment results in non-negative uniform prices, which in turnincrease personalized prices above the level that would be set in the equilibrium with
two-way poaching. For example, suppose a = −b = δ > 0. Then the equilibrium uniform
prices are qA = qB = δ, personalized prices are adjusted upwards by δ relative to theequilibrium with two-way poaching, and the total industry profit is Π = 1/4 + δ(1 − δ).
The total industry profit increases in δ and is equal to the Hotelling profit when δ = 1/2.
The equilibrium collapses to the one with two-way poaching if δ = 0.
Third, in all equilibria, total industry profit is bounded above by 1/2, total industry
profit under the Hotelling equilibrium. In addition, the Hotelling equilibrium obtains if
and only if a = −b = 1/2, i.e., neither firm has any targeted consumer. This implies thatfirms are collectively best oﬀ when they have no consumer information, and that moreconsumer information as represented by larger target segments intensifies competitionand hurts firm profitability.
Fourth, two-way poaching is possible if and only if both firms target their rival’s
loyal consumers, leading to the smallest total industry profit of 1/4. Thus aggressive
targeting results in the worst possible outcome for the firms. But this does not require
full information, i.e., −a = b = 1/2 as in Thisse and Vives (1988). Minimal informationneeded for the Thisse-Vives outcome is a = b = 0. Any additional information beyond
this has no additional eﬀect on the equilibrium.
We summarize the above points in the next proposition.
Proposition 2 The equilibrium with passive consumers has the following properties:• The market is fully covered in all equilibria.
• In all equilibria, total industry profit is bounded above by 1/2, total industry profit
under the Hotelling equilibrium, and below by 1/4, total industry profit in the equilibrium with two-way poaching.
• The Hotelling equilibrium obtains if and only if a = −b = 1/2.

5

Active Consumers

We now consider the case where all consumers are active. Recall that an active
consumer can choose from both uniform prices in addition to the relevant personalized
16

price. Recall also that a firm’s targeted consumers are more loyal to the firm than nontargeted consumers by assumption, implying that any uniform price that is accepted bysome non-targeted consumers should necessarily be lower than personalized prices forthe targeted consumers. Thus if a firm’s uniform price is accepted by some non-targeted
consumers, then it is also accepted by all of its targeted consumers. This implies thata firm can serve its targeted consumers with personalized prices if and only if it does
not serve any non-targeted consumers. A firm can exclude all non-targeted consumers
by choosing a suﬃciently high uniform price. Given that max{Vi (l) : i = A, B; l ∈[−1/2, 1/2]} = 5/4, the lower bound on such uniform prices is 5/4. In sum, there
are only two possible pricing options for each firm, namely, serving only its targeted
consumers with personalized prices or choosing a uniform price that is accepted by all
consumers, both targeted and non-targeted.

5.1

Perfect price discrimination

If both firms choose uniform prices higher than 5/4, then there is no poaching andeach firm serves its targeted consumers only. In this case, each firm can exercise perfectprice discrimination (PPD) by setting maximum personalized prices and extract full
surplus from all of its targeted consumers. When each firm has a significantly large
target segment, the PPD outcome yields the highest possible profit for each firm forthe given market segmentation. When such an equilibrium exists, we call it a PPD
equilibrium and use it as a benchmark outcome.12
We describe the PPD equilibrium formally below. Given a and b with b ≤ a, firms
choose uniform prices qA , qB ≥ 0, which are followed by each firm choosing maximum
personalized prices for all its targeted consumers: pPAP D (x) = VA (x) = 1 + x/2 for allx ∈ [a, 1/2] and pPBP D (y) = VB (y) = 1 − y/2 for all y ∈ [−1/2, b]. When firms deviate to′ , q ′ < 5/4, subgame perfection requires that, for any deviation by its rival, each firmqA
B
optimally defends its turf with a nonnegative price that does not exceed any consumer’s
maximum willingness to pay. Thus personalized prices for each firm in this case are′ + x, 0}} and p (y) = min{1 − y/2, max{q ′ − y, 0}}. GivenpA (x) = min{1 + x/2, max{qB
B
A
these oﬀ-the-path personalized prices, a firm cannot deviate to poach its rival’s noncontestable, targeted consumers; the only reason for a deviation is to serve non-targeted
consumers and/or poach the rival’s contestable, targeted consumers. Each firm’s profit
in the PPD equilibrium is then
∫ 1/2
PPD
πA
(a) =

pPAP D (x) dx =a

9 − 16a − 4a2
,
16

(4)

Strictly speaking, a PPD equilibrium can exist only when b ≤ a, i.e., there is no overlapping target
segment. But we will also use the term when there is an overlapping target segment if firms can charge
maximum personalized prices to a subset of its targeted consumers.
12

17

and

∫ b
PPD
πB
(b) =

−1/2

9 + 16b − 4b2
.
16

(5)

9 − 8(a − b) − 2(a2 + b2 )
.
8

(6)

pPBP D (y) dy =Thus the total industry profit is equal to
PPD
PPDΠP P D = πA(a) + πB(b) =We analyze when the PPD equilibrium exists and, when it does not, find the alternative equilibrium. Following the argument similar to the case with passive consumers, we
can classify all possible equilibria into several types. In doing so, we note that, whenevera firm exercises PPD for all or part of its targeted consumers, it chooses a uniform price
above 5/4 and the oﬀ-the-path personalized prices described previously. Thus we omit
the description of these prices when it is clear from the context.
With active consumers, firms can no longer delink their personalized prices from theuniform price. This makes possible deviations from the candidate equilibrium more complicated, leading to more types of possible equilibria than when consumers are passive.
Thus we divide the analysis into two cases, first when the market is fully targeted andsecond, when the market is partially targeted.

5.2

Fully targeted market

When the market is fully targeted, i.e., a ≤ b, there are three types of possible
equilibria as described below.
□ The PPD equilibrium. This equilibrium is likely when each firm has a considerable
target segment so that neither has incentives to deviate by lowering the uniform pricebelow 5/4. It is possible only when the market is fully targeted without an overlap,
i.e., a = b. The PPD equilibrium can lead to the highest total industry profit when
P P D = π P P D = 9/16 anda = b = 0. In this case, (6) shows that each firm earns profit πAB
the total industry profit 9/8 is larger than the monopoly profit 5/8. As it was formallydefined above, we omit the details. The PPD equilibrium is illustrated in Figure 4.
— Figure 4 goes about here. —□ The PPD equilibrium with partial Thisse-Vives outcome. This equilibrium exists
when there is an overlapping target segment that includes consumers loyal to both firms,
i.e., a < 0 < b. It can be described as follows. Given (a, b), firm A exercises PPD to serve[b, 1/2] and chooses personalized prices pA (x) = x to serve [0, b]. Firm B exercises PPD
to serve [−1/2, a] and chooses personalized prices pB (y) = −y to serve [a, 0]. Thus thisequilibrium involves the Thisse and Vives outcome on the commonly targeted segment
while each firm exercises PPD for its targeted consumers who are not targeted by its

18

rival. The total industry profit is then equal to
∫ 0
PPD
PPD
πA
(b) + πB(a) +∫ b(−y)dy +

xdx =

a

0

9 + 8(a − b) + 2(a2 + b2 )
.
8

(7)

The equilibrium with partial Thisse-Vives outcome is illustrated in Figure 5. A
variant of this equilibrium is when the commonly targeted segment is served by one firm
only. This is possible when the commonly targeted segment includes consumers who are
loyal to only one firm. For example, if 0 ≤ a < b, and a and b are not large enough, thenfirm A serves [a, b] with personalized prices pA (x) = x while firm B chooses pB (y) = 0 on
this segment. In the other case with a < b ≤ 0, firm B can serve all commonly targeted
consumers insofar as a and b are not too close to −1/2.
— Figure 5 goes about here. —□ The equilibrium with one-way poaching. We noted above that a variant of the PPD
equilibrium with partial Thisse-Vives outcome involves firm A serving all commonly
targeted consumers as long as a and b are not too close to 1/2. Otherwise firm A
can profitably deviate by charging a uniform price qA and serving more consumers on[z, 1/2] for some z < b. We show in Proposition 3 that the optimal deviation involves
qA = z = 1/4. Given firm A’s deviation, firm B’s best response is as was described
previously in the definition of PPD equilibrium. Specifically, this equilibrium can be
described as follows: firm A charges pA (x) = 1/4 on [a, 1/2] and qA = 1/4, serving[1/4, 1/2]; firm B charges pB (y) = −y + 1/4 and serves [−1/2, 1/4], chooses pB (y) = 0 on
[1/4, b], and qB = 0 on [b, 1/2]. As firm A serves some of firm B’s targeted consumers, wecall this the equilibrium with one-way poaching by firm A. This equilibrium is illustrated
in Figure 6. The total industry profit in this case is1
πA + πB =+16)∫ 1/4 (111−y +dy = .
4
32
−1/2

(8)

When a < b ≤ 0, there is an equilibrium with one-way poaching by firm B thatmirrors the above equilibrium, hence qB = 1/4 and pA (x) = x + 1/4, and the same totalindustry profit as in (8). In any equilibria with one-way poaching, the poaching firmchooses a uniform price 1/4 and serves the most loyal 1/4 fraction of the market.
— Figure 6 goes about here. —Proposition 3 When all consumers are active and the market is fully targeted, there
are three types of equilibria as follows:• The PPD equilibrium if a = b ∈ [2 −given in (6).

√√6, −2 + 6] with total industry profit as19• The PPD equilibrium with partial Thisse-Vives outcome - (i) firms sharing thecommonly targeted segment if a ≤ 0 ≤ b with total industry profit as given in (7);√(ii) firm A serving the commonly targeted segment if 0 ≤ a ≤ b ≤ −2 + 2(1 + a2 )()
with total industry profit Π = 9 + 8(a − b) − 6a2 + 2b2 /8; (iii) firm B serving√
the commonly targeted segment if −2 + 2(1 + b2 ) ≤ a ≤ b ≤ 0 with total industry()
profit Π = 9 + 8(a − b) + 2a2 − 6b2 /8.
• The equilibrium with one-way poaching - (i) one-way poaching by firm A if b ≥√a ≥ 0 and b ≥ −2 + 2(1 + a2 ) with total industry profit Π = 11/32; (ii) one-way√
poaching by firm B if a ≤ b ≤ 0 and a ≤ −2 + 2(1 + b2 ) with total industry profit
Π = 11/32.
Proof : See Appendix A.

5.3

Partially targeted market

When b < a so that some consumers are not targeted by either firm, it is clear thatneither the PPD equilibrium nor the PPD equilibrium with partial Thisse-Vives outcome
exists. But the third type, the equilibrium with one-way poaching, continues to exist:
one-way poaching by firm A if b is close to 1/2 and one-way poaching by firm B is a isclose to −1/2. In addition, there are three new types of equilibrium when the market is
not fully targeted.
□ The PPD equilibrium without full market coverage. Suppose the non-targeted
segment is small and each firm has a considerable target segment. Then both firms canfind it profitable to exercise PPD on their target segments and ignore the non-targeted
segment by setting high enough uniform prices that are not accepted on the equilibrium
path. This is a variant of the PPD equilibrium but the description is precisely thesame with the only diﬀerence that this equilibrium is under the condition b < a. It is
illustrated in Figure 7.
— Figure 7 goes about here. —□ The equilibrium with PPD and a uniform price. In this equilibrium, one firm
exercises PPD and serves its targeted consumers only while the other firm uses a uniform
price to serve the rest. This equilibrium is possible when the firm exercising PPD has
a large enough target segment but the other firm choosing a uniform price has only asmall target segment. Thus the non-targeted segment is not significant enough for thefirm with a large target segment to give up its PPD, but significant enough for the firmwith a small target segment. Specifically, given (b, a) with b suﬃciently far away from
−1/2 and a close enough to 1/2, firm B exercises PPD to serve [−1/2, b] and firm A
chooses qA = pB (b) + b = 1 + b/2 to serve [b, 1/2]. Given qA = 1 + b/2, consumer b is20

indiﬀerent between staying with firm B and switching to firm A. Needless to say, firm B
chooses qB ≥ 5/4. This equilibrium is illustrated in Figure 8. The total industry profit
in this case is
(
)(
)
b
1
17 + 4b − 12b2
PPD
πA + πB = 1 +− b + πB
(b) =
.
2
2
16

(9)

This equilibrium is similar to the equilibrium with one-way poaching in that one
firm uses a uniform price and the other firm uses personalized prices on the equilibrium
path. But the diﬀerence is that, in the equilibrium with PPD and a uniform price, there
is no poaching and the personalized prices are equal to PPD prices. Note also that amirror equilibrium exists when firm A exercises PPD and firm B chooses a uniform priceqB = 1 − a/2.
— Figure 8 goes about here. —□ The Hotelling equilibrium. When both firms have relatively small target segments,
neither firm has an incentive to exercise PPD while ignoring the large, non-targeted
segment. As a result, both firms choose uniform price, in which case the equilibriumis the Hotelling outcome. Of course this is subject to the conditions that neither firm
has an incentive to deviate by reverting to personalized prices given the rival’s Hotelling
price. In sum, the Hotelling equilibrium is likely when there is a large segment nottargeted by either firm.
The following proposition shows the range of (a, b) that admits each type of equilibrium.
Proposition 4 When all consumers are active and the market is partially targeted, there
are four types of equilibria as follows:• The equilibrium with one-way poaching - (i) one-way poaching by firm A if a ≥√−2 + 6 and a > b > 1/4 with industry profit Π = 11/32; (ii) one-way poaching√by firm B if b ≤ 2 − 6 and b < a < −1/4 with total industry profit Π = 11/32.
• The PPD equilibrium without full market coverage if (i) a > b ≥ max{(−3 +√√√√7 + 32a + 8a2 )/4, (4 − 17 − 12a + 8a2 )/2} or (ii) (3 − 23)/4 ≥ a > b ≥ 2 − 6√√or (iii) (−3 + 23)/4 ≤ a < b ≤ −2 + 6 with total industry profit as given in (6).
• The equilibrium with PPD and a uniform price - (i) PPD by firm B if a > b and√√(3 − 2a − 10(1 − 2a + 2a2 ))/2 < b < (−3 + 7 + 32a + 8a2 )/4 with total industry√
profit as given in (9); (ii) PPD by firm A if a > b and (−1 + a + 5a(2 + a))/4 <√b < (4 − 17 − 12a + 8a2 )/2 with total industry profit Π = (17 − 4a − 12a2 )/16.
√√• The Hotelling equilibrium if b ≤ (1 − 2)/2 and a ≥ ( 2 − 1)/2 with total industry
profit Π = 1/2.
21

Proof : See Appendix A.

5.4

Comparing equilibria with passive or active consumers

Comparing the equilibria depending on whether consumers are passive or active, we
can formally show the results previewed in Section 3.3. Namely, active consumers canbenefit firms by softening price competition and enabling them to exercise PPD; active
consumers can also induce firms to ignore some market segment that is not commonly
targeted, resulting in an ineﬃcient outcome. Moreover, for any market segmentation(a, b), total industry profit is higher when consumer are active than when they are
passive. We discuss each of these points below.
First, consider the case where each firm’s target segment includes all its loyal consumers and there is some commonly targeted segment, i.e., a < 0 < b. Then the
PPD equilibrium with partial Thisse-Vives outcome obtains when consumers are active
whereas the equilibrium is with two-way poaching when consumers are passive. As thecommonly targeted segment vanishes, i.e., a = b = 0, firms can enjoy the full PPD
profits with active consumers, resulting in the highest possible industry profit 9/8. But
the equilibrium does not change when consumers are passive. Thus each firm is strictly
better oﬀ when consumers are active. This was illustrated in Section 3.3. In addition, forall (a, b) such that a ≤ 0 ≤ b, the equilibrium is with two-way poaching when consumers
are passive, leading to the lowest possible total industry profit 1/4. When consumers
are active, however, the total industry profit is 1/4 if and only if both firms have full
information, i.e., −a = b = 1/2. Thus more information is required to intensify competition when consumers are active. The following results are immediate from comparing
Propositions 1 and 3.
Proposition 5 (i) Suppose a = b = 0. When consumers are active, the PPD equilibrium
obtains with the highest possible total industry profit 9/8. When consumers are passive,the equilibrium results in the Thisse-Vives outcome with the lowest possible total industry
profit 1/4. (ii) The Thisse-Vives outcome obtains for all a ≤ 0 ≤ b when consumers are
passive, but if and only if −a = b = 1/2 when consumers are active.
Second, suppose there is a small, commonly non-targeted segment around l = 0. As
discussed in Section 3.3, firms may choose not to serve this segment when consumers areactive since a low uniform price that can appeal to the non-targeted consumers will bealso chosen by active, targeted consumers. This leads to the PPD equilibrium without
full market coverage. From Proposition 4, one can show that the values of a and b thatlead to the PPD equilibrium without full market coverage should necessarily satisfy a ≤√√( 17 − 4)/2 ≈ 0.06 and b ≥ (− 17 + 4)/2 ≈ −0.06. With passive consumers, however,
the market is always fully covered as firms compete à la Hotelling on the commonly nontargeted segment, no matter how small it is. Given that the social optimum requires full22

market coverage in our model, active consumers can lead to an ineﬃcient outcome. In
contrast, all equilibria are eﬃcient when consumers are passive.
√
Proposition 6 When consumers are active, there is a pair (a, b) with (− 17 + 4)/2 ≤√b < 0 < a ≤ ( 17 − 4)/2 such that consumers on the segment (a, b) are not served inequilibrium, hence an ineﬃcient outcome. When consumers are passive, the equilibrium
is with partial Hotelling competition for all b < 0 < a and the market is fully covered,hence eﬃcient.
Third, when consumers are passive, total industry profit is maximized in the Hotelling
equilibrium, which is possible if and only if neither firm has any consumer information,i.e., a = −b = 1/2. Whenever firms acquire some consumer information, equilibrium departs from the Hotelling outcome, leading to smaller total industry profit. This is consistent with the conventional result that consumer information intensifies price competitionand hurts firm profitability. When consumers are active, however, the Hotelling equilibrium obtains even when both firms have some consumer information. From Proposition√
4, the threshold values of (a, b) are given by a = −b = ( 2−1)/2 ≈ 0.21. Whenever both
firms have smaller target segments than indicated by these threshold values, equilibrium
results in the Hotelling outcome. Once again, this implies that active consumers dull thecompetition-intensifying eﬀect of consumer information. From Propositions 2 and 4, wehave the following.
Proposition 7 The Hotelling equilibrium obtains if and only if a = −b = 1/2 when√√
consumers are passive, but if and only if b ≤ (1 − 2)/2 and a ≥ ( 2 − 1)/2 when
consumers are active.
The results so far show how active consumers can benefit firms by softening pricecompetition, but only in some special cases. We show below that this holds more generally in any possible equilibria for any given market segmentation.
Proposition 8 For any (a, b), total industry profit in equilibrium with active consumers
is larger than that with passive consumers.
Proof : See Appendix A.

6

Robustness

So far we have considered the two polar cases where all consumers are either activeor passive. Our main findings are that consumers are worse oﬀ and, in some cases, social
welfare is also lower when all consumers are active. We now examine whether this insightcarries through to the more realistic case with a mix of active and passive consumers.
23

Specifically, we ask if our main findings are more likely to hold when the proportion ofactive consumers increases.
To this end, suppose now that a fraction α ∈ (0, 1) of consumers are active. We canalso interpret α as the probability a randomly drawn consumer is active. With α < 1,
it is now possible for each firm to use both personalized prices and a uniform price thatare accepted on the equilibrium path, as it expects only a proportion α of its targeted
consumers to choose the uniform price. Since the additional parameter α complicates
our analysis, we examine only the cases with either a = b or a = −b. Obviously we do
not consider market segmentation for all values of (a, b) because of this simplification.
But we do cover all possible types of market segmentation including the fully targetedmarket with an overlapping target segment (−a = b = δ > 0) or without one (a = b),
and the partially targeted market (a = −b = δ > 0).

6.1

Fully targeted market

Suppose a = b = δ ≥ 0 so that the market is fully targeted without an overlapping
target segment. The case with δ < 0 is symmetric so the same analysis can be applied.
We analyze how α aﬀects the conditions for the existence of PPD equilibrium and thelikelihood firms may deviate from the PPD equilibrium. Recall that the equilibrium iswith one-way poaching for all a = b ̸= 0 when α = 0. When α = 1, we have either the
PPD equilibrium or the equilibrium with one-way poaching.
Consider the PPD equilibrium corresponding to (a, b). From Lemma 1, all consumers
targeted by firm A are non-contestable by firm B. Thus firm B cannot benefit frompoaching them, implying that firm B does not have incentives to deviate from the PPD
equilibrium. On the other hand, firm A may try to poach some consumers on [0, δ]
targeted by firm B. Intuitively, firm A’s gain from poaching increases with δ. But
active consumers targeted by firm A can also take advantage of the low poaching price.
The cost associated with such active consumers decreases as firm A’s target segment
becomes smaller, i.e., as δ increases. Thus firm A is more likely to deviate from the PPD
equilibrium as δ increases, implying a cutoﬀ value of δ such that the PPD equilibrium
exists when δ is below the cutoﬀ.
To characterize the cutoﬀ value, suppose firm A deviates from the PPD equilibriumby choosing a uniform price qA ≤ 5/4. Since firm B’s oﬀ-the-path personalized prices
on [0, δ] are zero due to subgame perfection, the marginal consumer z upon firm A’s
deviation is given by z = qA . Thus firm A can poach firm B’s targeted consumers on[z, δ] for an extra profit qA (δ − qA ).13 On the other hand, since qA is lower than pPAP D (x)for all x ∈ [δ, 1/2], firm A expects to lose pPAP D (x) − qA when its targeted consumer x
also chooses qA instead of pPAP D (x). Given that the fraction of active consumers is α,[ PPD]firm A’s expected loss is α πA(δ) − qA (1/2 − δ) . Thus firm A’ net benefit from the13

We only focus on the case δ ≥ qA . Obviously, firm A will not deviate if this is not the case.

24

deviation is given by(
Γ (qA ; α, δ) ≡ qA (δ − qA ) + αqA)
1PPD− δ − απA
(δ).
2

(10)

Choosing qA to maximize the above net gain leads to the optimal deviation pricedqA=

α + 2δ(1 − α)
,
4

(11)

and the maximum net gain from the deviation is equal tod 2PPDΓ(δ; α) = (qA) − απA(δ).

(12)

Firm A does not deviate from the PPD equilibrium if Γ(δ; α) ≤ 0.
We now characterize the conditions for the existence of PPD equilibrium. Note thatd increases in δ and π P P D (δ) decreases in δ. Note also thatΓ(δ; α) increases in δ since qAA
Γ(0; α) < 0 and Γ(1/2; α) > 0 for any α ∈ (0, 1). Thus there exists a cutoﬀ value, δ̄(α)
solving Γ(δ̄(α), α) = 0 such that Γ(δ; α) ≤ 0 if and only if δ ≤ δ̄(α). It follows that PPD
equilibrium can be sustained if δ ≤ δ̄(α). The same analysis applies to the case δ < 0,where the PPD equilibrium can be sustained if δ ≥ −δ̄(α). Combining the two cases, weconclude that the PPD equilibrium exists if δ ∈ [−δ̄(α), δ̄(α)].
Then how does α aﬀect the range of δ that sustains the PPD equilibrium? The main
point from our analysis in the previous section is that active consumers benefit firms bysoftening competition. Thus we expect that the PPD equilibrium is more likely when α
increases. That is, as α increases, we expect δ̄(α) to increase so that the PPD equilibrium
exists for a wider range of δ. This is easy to verify: by totally diﬀerentiating Γ(δ; α) = 0,
d (1 − α) + α(1 + δ/2)]dδ − [π P P D (δ) − q d (1/2 − δ)]dα = 0. Since the terms
we obtain [qAAA
inside the brackets are positive, we have dδ/dα ≥ 0 for all α ∈ (0, 1) and δ ∈ [−1/2, 1/2].
For example, simple calculation shows δ̄(1/10) ≈ 0.294 and δ̄(1/2) ≈ 0.415. Thus
as the fraction of active consumers increases from 0.1 to 0.5, the likelihood of PPD
equilibrium increases from 60% to 83% of the parameter range. It is also easy to check√
limα→1 δ̄(α) = −2 + 6, as is consistent with Proposition 3.
When δ > δ̄(α) or δ < −δ̄(α), one of the firms deviates from the PPD equilibrium.
Thus we have an equilibrium with one-way poaching. But the diﬀerence from the casewhere all consumers are active is that the firm that chooses a uniform poaching price also
sets personalized prices so that only its active, targeted consumers choose the uniform
price instead of personalized prices. Suppose δ > δ̄(α) so that the equilibrium is the oned )2 + (1 − α)π P P D (δ).
with one-way poaching by firm A. Then its profit is πA (δ; α) = (qAA
As α increases, firm A’s uniform price in (11) increases since firm A needs to make up
for the loss from not being able to charge personalized prices to its active consumers.
But the higher uniform price means firm A can poach less from its rival. It is easy tocheck that πA (δ; α) decreases in α and is equal to 1/16 when α = 1, as shown in (8). We
25

summarize the above discussions below.
Proposition 9 Suppose a fraction α of consumers are active and the market is fullytargeted without commonly targeted segment, i.e., a = b. Then there exists a cutoﬀ δ̄(α)
that solves Γ(δ̄(α), α) = 0 where Γ(·, ·) is given in (12).
• For any δ ∈ (−δ̄(α), δ̄(α)), a unique PPD equilibrium exists.
• If δ < −δ̄(α) or δ > δ̄(α), then the equilibrium is with one-way poaching where thepoaching firm uses the uniform price that increases in α.
√• δ̄(α) is increasing in α and converges to −2 + 6 as α increases to 1. Thus the
PPD equilibrium is supported by a wider range of δ as α increases.
Suppose now −a = b = δ > 0 so that the market is fully targeted with an overlapping
target segment [−δ, δ]. Then the equilibrium results in the Thisse-Vives outcome when
α = 0, and PPD with partial Thisse-Vives outcome when α = 1. Importantly, neither
firm has any incentives to use a uniform price to poach its rival’s targeted consumers.
Since active consumers matter only when a firm uses a uniform price on the equilibrium
path, these equilibria are invariant to α when −a = b = δ > 0.

6.2

Partially targeted market

Suppose a = −b = δ > 0 so that consumers on [−δ, δ] are not targeted by either firm.
With passive consumers, we have the equilibrium with partial Hotelling outcome while,with active consumers, we have the PPD equilibrium without full market coverage when
δ is suﬃciently small.14 We consider how changes in α aﬀect the firm’s incentives todeviate from the PPD equilibrium without full market coverage.
Suppose firm A deviates from the candidate equilibrium. Since [−1/2, −δ] is firm B’s
non-contestable segment, firm A cannot poach any consumers targeted by firm B. Thus
firm A’s deviation involves serving commonly non-targeted segment [−δ, δ] by choosing
a uniform price qA . Since the market is fully covered when served by a monopoly, firm A
will optimally serve all consumers on [−δ, δ], implying that its optimal deviation price is
qA = 1 − δ/2. Then firm A earns additional profit 2δqA from [−δ, δ]. From its targeted
consumers who switch to the uniform price, firm A earns profit α(1/2 − δ)qA . On theother hand, firm A loses an α fraction of its PPD profit. Putting all together, firm A’s
net benefit from the deviation is given by[∆(δ; α) ≡ 2δ + α

(

1
−δ
2

)] (

δ
1−
2

)
PPD
− απA
(δ).

(13)

By substituting a = −b = δ > 0 into the conditions for the PPD equilibrium
without full market√
coverage in Proposition 4, one can find that the threshold value of δ is (7 − 4 3)/2 ≈ 0.036.
14

26

It is easy to check ∆(0; α) = −α/16 < 0, ∆(1/2; α) = 3/4 > 0, and ∆(δ; α) increasesin δ. Thus there is δ̂(α) ∈ [0, 1/2] such that ∆(δ̂(α), α) = 0 and ∆(δ; α) ≥ 0 if and only ifδ ≥ δ̂(α), implying that firm A does not deviate if δ ≤ δ̂(α). By symmetry, firm B does
not deviate if δ ≥ −δ̂(α). In sum, the PPD equilibrium without full market coverage issustained by δ ∈ (−δ̂(α), δ̂(α)).
To see how changes in α aﬀect the range of δ that sustains the above equilibrium, totally diﬀerentiate ∆(δ, α) = 0. This leads to [qA (2 − α) + (α + δ/2)] dδ −[ PPD]
πA (δ) − qA (1/2 − δ) dα = 0 where qA = 1 − δ/2. Again both terms inside thebrackets are positive, hence dδ/dα ≥ 0. Thus the PPD equilibrium without full market
coverage is more likely when the fraction of active consumers increases. For instance, itis easy to verify δ̂(1/2) ≈ 0.017 and δ̂(1) ≈ 0.036. This implies that 3.4% of the market
is not served when a half of consumers are active but it increases to 7.2% when all consumers are active. In sum, as more consumers become active, an ineﬃcient equilibrium
becomes more likely. This extends Proposition 6 to the case α ∈ (0, 1).
Proposition 10 Suppose a fraction α of consumers are active and the segment [−δ, δ]
is not targeted by either firm. Then there exists a cutoﬀ δ̂(α) that solves ∆(δ̂(α); α) = 0
where ∆(·, ·) is given in (13).
• For any δ ∈ (−δ̂(α), δ̂(α)), a unique PPD equilibrium without full market coverage
exists.
• δ̂(α) is increasing in α. Thus the PPD equilibrium without full market coverage is
supported by a wider range of δ as α increases.
The above PPD equilibrium without full market coverage cannot be sustained if δ
is suﬃciently large. When α = 1, Proposition 4 shows that the Hotelling equilibrium√
obtains if δ ≥ ( 2 − 1)/2 ≈ 0.21. When α = 1, however, Hotelling competition is forthe entire market, not just on the commonly non-targeted segment [−δ, δ], because firms
cannot use both the uniform and personalized prices on the equilibrium path. Withα < 1, firms can use both types of prices and they can compete à la Hotelling on [−δ, δ].
In this case, we show below that, as more consumers become active, total industry profit
increases because the (symmetric) Hotelling price increases.
To see this, suppose firms choose uniform prices qA and qB . Then firm A can attract
consumers on [qA − qB , δ], hence earns profit (δ − qA + qB )qA . In addition, firm A’s profit
from its active, targeted consumers who also choose qA is α(1/2 − δ)qA . For the rest of
its targeted consumers, firm A’s personalized prices are given by pA (x) = x + qB , hence∫ 1/2
profit equal to (1 − α) δ (x + qB )dx. Thus firm A’s total profit isπA (qA ; qB , α) = (δ − qA + qB )qA + α(1/2 − δ)qA + (1 − α)

∫ 1/2
(x + qB )dx.
δ

27

(14)

Choosing qA to maximize the above profit and solving for the symmetric equilibrium
prices, we obtainqA = qB = δ + (1/2 − δ)α.
(15)This equilibrium price is higher than the Hotelling price δ on [−δ, δ], with the term
(1/2 − δ)α reflecting the marginal benefit firms enjoy as more consumers become active.
We summarize this below.
Proposition 11 Suppose a fraction α of consumers are active and the segment [−δ, δ] is√
not targeted by either firm. If δ ≥ ( 2 − 1)/2, then there exists a symmetric equilibrium
in which both firms exercise PPD and choose a uniform price q̂ = δ + (1/2 − δ)α.
• q̂ is higher than the Hotelling equilibrium price δ on [−δ, δ].
• q̂ increases in α and, when α = 1, it is equal to the Hotelling equilibrium price 1/2
on [−1/2, 1/2].

7

Discussions

7.1

Implications for policy and consumer welfare

The use of big data for price discrimination has triggered debate in policy circles. In
the US, for example, a report by the Council of Economic Advisers (2015) raised concerns that some consumers can be made worse oﬀ without knowing why, and proposed
giving consumers greater access to and control over their information. The report also
argued that increased transparency into how companies use consumer information would
promote competition and better informed consumer choice. On February 27, 2015, President Obama announced the Consumer Privacy Bill of Rights Act, a draft bill intended
to govern the collection and dissemination of consumer data, and in October, 2016, theFederal Communications Commission (FCC) adopted new rules that require ISPs to get
consumers’ opt-in consent before collecting, selling or sharing their information.15 Opponents argued that the rules are duplicative regulation and would place an undue burden
on ISPs and that all actors in the online space should be subject to the same rules. For
instance, the Federal Trade Commission’s acting chair, Maureen Ohlhausen, said thatthe industry should largely be left to regulate itself. She also defended the practices of
personalized pricing by saying, “Information can be used to target some consumers witha higher price, but the same information can be used to target some consumers with abetter deal.”16 On March 28, 2017, the US House of Representatives voted to repeal the15
More stringent rules that go beyond ISPs are in place or being proposed elsewhere. See, for example,
the General Data Protection Regulation in the European Union (https://www.eugdpr.org/) or a reportby the Productivity Commission (2017) in Australia. Indeed the EU regulation is the default optionthat many countries around the world follow with the US being an exceptional case (“Customer data:
designing for transparency and trust”, Harvard Business Review, May 2015).
16
https://www.theguardian.com/technology/2017/mar/14/federal-trade-commission-internet-thingsregulation

28

FCC’s online privacy rules, which was signed by President Trump the following Monday(“Trump just killed Obama’s internet-privacy rules - here’s what that means for you”,
Business Insider, April 4, 2017).
Our analysis sheds light on the two related issues that are central to the above debate,
namely, privacy rules and consumer empowerment. First, to the extent that stricter privacy rules make personalized pricing more diﬃcult to implement, they have the eﬀectof softening competition. Although many questions about privacy go beyond economic
considerations, it is worth noting that laxer privacy rules are more likely to benefit
consumers by intensifying competition. This is true whether consumers are passive or
active. In the extreme case of no privacy where firms can freely use all consumer information, hence a = −b = −1/2, consumers benefit the most as competition becomes themost intense, as shown in Proposition 5-(ii). Second, consumer empowerment relates togiving consumers more control over their information and enabling them to have accessto various tools that can help them with price search and comparison. If empowered
consumers are more likely to be active in identity management, then consumer empowerment is more likely to benefit firms, as our analysis shows. Both considerations seemto favor a more liberal approach to the use of consumer information by firms when thefocus is on improving consumer welfare. Of course this is subject to the caveat that ouranalysis is based on the assumption that consumer information is used solely for pricing
purposes in the competitive setting. Either when consumer information can be used toprovide value added thereby softening competition (Acquisti and Varian, 2005) or when
it is used by a dominant firm, more liberal use of consumer information can benefit firms.

7.2

Implications for management

The general conclusion from our study is that more consumer information can intensify competition if the information is used solely for pricing purposes. But this eﬀect canbe mitigated when more consumers are active in identity management. In view of thisconclusion, we discuss below some implications for management in regards to customer
information and pricing strategies.
First, firms can rely on a set of strategies that can credibly signal their intent to soften
price competition, such as price matching guarantees or most-favored customer clauses.
By adopting a price matching guarantee, a firm commits to its own targeted consumers tomatch the rival’s poaching price. For example, if firm A has a price matching guarantee
in place, its targeted consumer x now faces a personalized price that cannot be higher
than firm B’s poaching price, i.e., pA (x) ≤ qB . When both firms adopt price matchingguarantees, the end result is softened competition and higher poaching price.17 A mostfavored customer clause is a firm’s promise to a customer that no other customers will
17

It is well known that price matching guarantees facilitate tacit collusion in a concentrated industry
with low consumer search costs, although the opposite may be the case with enough heterogeneity inconsumer search costs and brand loyalty. See, for example, Chen et al. (2001).

29

be oﬀered a lower price. Suppose firm A issues a most-favored customer clause to all its
targeted consumers. Then consumer x faces a personalized price pA (x) ≤ qA . This has
the same eﬀect as when consumer x is active in identity management. Once again, thissoftens competition as shown in our paper.
Second, the sole use of customer information in our paper was to extract consumer
surplus through personalized pricing, which is why more information can intensify competition. A natural implication is then customer information needs to be used not only
for pricing purposes but also for broader customer relationship management, of which
ultimate aim is to drive value by building one-to-one relationships with customers. For
example, a firm can provide enhanced services to its targeted consumers such as personalized product recommendations or lowered transactions costs (Acquisti and Varian,2005). It can also build a loyal customer base through various reward programs, personalized discounts, customer experience management, and so on (Kumar and Shah, 2004;
Verhoef et al. 2009). Loyal customers are less price-sensitive, which increases the cost ofpoaching by the rival, which in turn softens competition. In addition, reward programs
can also soften competition by facilitating tacit collusion (Fong and Liu, 2011).
Finally, our analysis shows that firms can benefit from consumer empowerment if itleads to more active identity management by consumers. In addition, firms can gain
invaluable customer trust by being transparent about the collection and use of customer
information, by giving customers control over their personal information, and by delivering value in return (“Customer data: designing for transparency and trust”, Harvard
Business Review, May 2015). But this requires coordinated eﬀort by all competing firms.
A firm that unilaterally adopts measures that empower its customers is likely to lose out
at least in the short term since it cannot rely on eﬀective personalized prices while its
rivals can. A better approach would be collective and coordinated support for privacy
rules that would lead to more, not less, consumer empowerment. At first glance, laxer
privacy rules may appear pro-business by reducing red tape and increasing the benefitsof data use. But this is only one side of the story. If stricter privacy rules lead to more
active identity management by consumers, then both softened competition thanks toactive identity management and additional value of customer trust can benefit firms.

8

Conclusion

This paper has studied a duopoly model where each firm has a target segment on
which it can exercise personalized pricing, and consumers can engage in identity management. We find that more consumer information can intensify price competition but
the eﬀect can be mitigated when more consumers become active in identity management. When consumers are passive in identity management, firms are collectively bestoﬀ by competing without consumer information, which leads to the Hotelling equilibrium. When consumers are active, firms are best oﬀ with information about their loyal
30

consumers only, which allows them to exercise perfect price discrimination.
These results are driven by diﬀerent mechanisms whereby firms can soften competition by refraining from choosing aggressive uniform prices. With passive consumers,
firms cannot credibly commit not to use consumer information for personalized pricing
for their targeted consumers. It is because they can choose personalized prices independent of the uniform price. This leads to Bertrand-type competition in uniform price.
Thus having no information solves the commitment problem. On the other hand, active
consumers increase the cost of choosing aggressive uniform prices, which decreases thevalue of personalized pricing. To make the most of personalized pricing, firms therefore
have incentives to set high enough uniform prices that will not be chosen by their active,
targeted consumers.
Our analysis shows that established results from the literature on competitive pricediscrimination change drastically when consumers are active in identity management.
Indeed the conventional wisdom that consumer information intensifies competition nolonger holds when consumers are active in identity management. Consumer information
can benefit competing firms and, in some case, it allows them to achieve a collusive
outcome without explicit or implicit collusion. In the age of big data and rapid advancesin technology, more consumers have access to various tools to manage their personal dataand search for better deals and lower price. This suggests that more consumers are likely
to be active in identity management, undermining firms’ attempt to price discriminate.
This aspect of consumer reaction is an important element to take into account in amore realistic model of competitive price discrimination. The analytical results fromthe enriched model can be very diﬀerent from those from the conventional model, often
leading to widely varying implications for policy and management.
Among a number of important issues we left out in the current paper, we briefly
discuss two. First, another limit to a firm’s ability to price discriminate is a behavioral
element such as consumers’ concerns for fairness, as experienced by Amazon (“Test of“dynamic pricing” angers Amazon customers”, Washington Post, October 7, 2000). Suchfairness concerns have a similar eﬀect as active identity management. For example, if
consumers feel disutility when their personalized prices are higher than the firm’s public
price, this eﬀectively limits the firm’s ability to separate personalized prices from thepublic price. This in turn will soften competition, as shown by Li and Jain (2016) albeit
in the two-period model as in Fudenberg and Tirole (2000). The key insight is that what
limits an individual firm’s ability to use consumer information for price discrimination
can be good for firms collectively, as it can soften competition.
The second issue relates to a firm’s targeting strategy. In our paper, each firm isendowed with the exogenously given target segment. We chose this approach since our
purpose was to examine various pricing equilibria for all possible market segmentations.
But the choice of target segment, or investment in consumer addressability in general, isan important management decision (Chen and Iyer, 2002). A natural extension of our31model to endogenize target segments is to add another layer of game in the beginningwhere firms choose investment in consumer information. To start with, the investment
can be identified with the choice of a and b. Then one can consider more general targeting strategies that allow any types of target segment. For example, a firm’s target
segment may not necessarily be a connected interval starting from the firm’s location.
It would be interesting to examine how the firm’s targeting strategy is aﬀected by identity management by consumers, and whether the main thrust of the current paper willcontinue to hold.

32

Appendix A: Proofs
Proof of Lemma 2. Consider the case zB ∈ NA . First, suppose zB > 0 and consider
an ϵ-neighborhood of zB given by (z, z + ϵ) where z = zB − ϵ/2. Firms compete on(z, z + ϵ) by choosing qA and qB . Let ẑ ∈ (z, z + ϵ) be such that qA = qB + ẑ, henceẑ = qA − qB . Then firm A chooses qA ≥ 0 to maximize (z + ϵ − ẑ)qA and firm B chooses
qB to maximize (ẑ − z)qB . Solving the first-order conditions leads to qB = (ϵ − z)/3 < 0.
Thus qB = 0 and qA = (z + ϵ)/2 → zB /2 as ϵ → 0. Second, suppose zB = 0. Repeating
the same step, we find qA = qB = ϵ/2 → 0 as ϵ → 0. The other case zA ∈ NB issymmetric, hence the proof is omitted.
Proof of Proposition 1.
Fully targeted market (a ≤ b). Suppose a = b > 0. First, consider [b, 1/2]. Consumers on this segment are not contestable by firm B. Thus firm B chooses qB = 0 by
Lemma 2, hence pA (x) = x for all x ∈ [b, 1/2]. Second, consider the segment [a, b] where
the two firms compete using personalized prices. Since this segment is non-contestableby firm B, firm A can serve the entire segment by choosing pA (x) = pB (x) + x. Bertrand
competition then results in pB (x) = 0 for all x ∈ [a, b], leading to pA (x) = x. Third, consider the segment [0, a]. Suppose there is z ∈ [0, a] who is indiﬀerent between choosing
either firm. Given any qA , firm B’s optimal personalized price for z is pB (z) = qA − z.
Anticipating this, firm A can lower qA until the competition for z leads to pB (z) = 0.
Then firm A can choose qA = z to serve consumers on [z, a]. Firm A chooses qA to
maximize (a − qA )qA , leading to qA = z = a/2. On [0, a], firm A thus serves [a/2, a]with qA = a/2 and firm B chooses pB (x) = 0 for all x ∈ [a/2, a]. Finally, firm B serves
the remaining consumers using personalized prices pB (y) = qA − y = a/2 − y for all∫ 1/2y ∈ [−1/2, a/2]. Then firm A’s profit is πA ≡ qA (a − a/2) + a xdx = 1/8 − a2 /4 and∫ a/2
firm B’s profit is πB ≡ −1/2 (−y + a/2)dy = (1 + 2a + a2 )/8. Thus the total industry
profit is Π ≡ (2 + 2a − a2 )/8. On the range a ∈ [0, b], the industry profit attains theminimum of 1/4 when a = 0 and the maximum of 11/32 when a = b = 1/2. This showsthat the equilibrium is with one-way poaching by firm A if a = b > 0
Using the same argument, one can show that the case a = b < 0 leads to the equilibrium with one-way poaching by firm B and the total industry profit Π ∈ [1/2, 11/32].
Consider now the remaining case a ≤ 0 ≤ b. Firm A serves the segment [b, 1/2] bychoosing pA (x) = x since Lemma 2 implies qB = 0. Similarly, firm B serves the segment[−1/2, a] using pB (y) = −y since qA = 0. On the overlapping segment [a, b], both firms
use personalized prices. For each consumer, each firm’s lowest personalized price is zero.
This implies that firm A can never profitably serve [a, 0] and firm B can never profitably
serve [0, b]. Thus the marginal consumer’s location is at zero. Consequently, firm A
serves [0, b] with pA (x) = x and firm B serves [a, 0] with pB (y) = −y. Then each firm
earn profit equal to 1/8, hence the total industry profit of 1/4. This shows that the33equilibrium is with two-way poaching if a ≤ 0 ≤ b.
Partially targeted market (b < a). Consider first the segment [a, 1/2]. Given qB ,firm A can choose pA (x) = x + qB and serve all consumers on this segment as long as
pA (x) ≥ 0 for all x ∈ [a, 1/2]. Since pA (x) is increasing in x, the suﬃcient condition
is pA (a) = a + qB ≥ 0. Similarly firm B can choose pB (y) = −y + qA and serve all
consumers on [−1/2, b] as long as pB (b) = −b + qA ≥ 0. Consider next [b, a]. It iseasy to find the Hotelling equilibrium on [b, a]: qA = (2a − b)/3, qB = (a − 2b)/3,z = (a + b)/3, and z ∈ [b, a] if and only if qA , qB ≥ 0, or 2a ≥ b and a ≥ 2b. Given these
conditions, we can check pA (a) = 2qA ≥ 0 and pB (b) = 2qB ≥ 0. Since firm A’s profit is∫ 1/2∫aπA = (a−z)qA + a (x+qB )dx and firm B’s profit is πB = (z −b)qB + −1/2 (−y +qA )dy,()
total industry profit is Π = πA + πB = 1/4 + 8ab + 9(a − b) − 5(a2 + b2 ) /18. It is easy
to check that Π attains a minimum 1/4 when a = b = 0 and a maximum 1/2 whena = −b = 1/2. This shows that the equilibrium is with partial Hotelling competition if
2a ≥ b and a ≥ 2b.
Suppose 0 ≤ a ≤ 2b. Then we have qB ≤ 0 from the Hotelling outcome. Thus firm
B chooses qB = 0. In addition, firm B chooses pB (z) = 0 if z < b, hence z = qA . Thus
firm A chooses qA to maximize (a − qA )qA , leading to qA = z = a/2 ≤ b. In this case,firm A chooses qA to serve all consumers on [b, a] and additional consumers on [a/2, b]
targeted by firm B. So this case leads to the equilibrium with one-way poaching by firm
A. Using the same argument, we can show the case 2a ≤ b ≤ 0 leads to the equilibriumwith one-way poaching by firm B.
Combining all the above cases, we have Proposition 1
Proof of Proposition 3. First, suppose a = b = δ > 0. If firm A deviates from thed < 5/4, then it serves consumers on [z, 1/2] where z =PPD equilibrium by choosing qA
d − max{q d − z, 0} = q d . Maximizing firm A’s deviation profit π d = (1/2 − q d )q d leads
qA
A
A
A
A A
d = z = 1/4 and π d = 1/16. Comparing π d with π P P D (δ), we find π P P D (δ) < 1/16
to qA
A
A
A
A
√
√
P P D (δ) < 1/16 iﬀ δ < 2 − 6. Thusiﬀ δ > −2 + 6. A symmetric argument shows πB√√
the PPD equilibrium exists iﬀ δ ∈ [2 − 6, −2 + 6].
√
d = 1/4,
If δ > −2 + 6, then firm A deviates from the PPD equilibrium by setting qA
serving those on [1/4, 1/2]. To this, firm B’s best response is to choose personalized prices
d − y for all y ∈ [−1/2, 1/4] and q ≥ max{q − y : y ∈ [−1/2, 1/4]} = 3/4.
pB (y) = qA
B
A√
The other case δ < −2 + 6 is symmetric. Summarizing the case a = b, the PPD√√
equilibrium exists for all a = b ∈ [2 − 6, −2 + 6]; the equilibrium is with one-way√
poaching by firm A if a = b > −2 + 6; the equilibrium is with one-way poaching by√firm B if a = b < 2 − 6.
Consider now the case with an overlapping target zone, i.e., a < b. First, supposea < 0 < b. Then on [a, b], competition in personalized prices leads to the Thisse andVives outcome: pB (y) = y for all y ∈ [a, 0], = 0 for all y ∈ [0, b], and similarly forpA (x). Thus the candidate equilibrium is the PPD equilibrium with partial Thisse-Vives34

outcome. If one firm deviates from this, then its deviation profit is 1/16 as shown above.
Since the equilibrium profit in the candidate equilibrium is bounded below by 1/8, theprofit from the Thisse and Vives outcome (when −a = b = 1/2), neither firm has anincentive to deviate. Thus if a ≤ 0 ≤ b, the unique equilibrium is the PPD equilibriumwith partial Thisse-Vives outcome where the two firms share the commonly targeted
segment.
Second, suppose 0 ≤ a < b. Then on [a, b], firm B charges pB (y) = 0, hencepA (x) = x. Suppose firm A exercises PPD on [b, 1/2] and firm B exercises PPD on[−1/2, a]. For this to be an equilibrium outcome, we only need to consider firm A’s
possible deviation since firm B does not benefit from any deviation. In the candidate∫b
P P D (b) = (4b2 − 16b + 9 − 8a2 )/16. Thereequilibrium, firm A’s profit is a xdx + πA
are two possible ways firm A can deviate from the candidate equilibrium. First, it can
d = 1 + b/2 and serve [b, 1/2]. But this is clearly worse than the candidate
choose qA
equilibrium where firm A exercises PPD on [b, 1/2]. Thus we only need to consider thed = 1/4 and serves [1/4, 1/2] with the deviation profit 1/16.
case where firm A chooses qA√
If (4b2 − 16b − 8a2 + 9)/16 ≥ 1/16 or b ≤ 2 − 2(1 + a2 ), then firm A does not deviate.
√
In sum, if 0 ≤ a < b ≤ 2 − 2(1 + a2 ), then we have the PPD equilibrium with partial
Thisse-Vives outcome where firm A serves the commonly targeted segment.
√d = 1/4 serving [1/4, 1/2] andIf b ≥ 2 − 2(1 + a2 ), then firm A deviates to qA
firm B chooses pB (y) = qA − y serving y ∈ [−1/2, 1/4]. This leads to the equilibriumwith one-way poaching by firm A. Thus the range of (a, b) supporting this equilibrium√is (a, b) ∈ {(a, b)|0 ≤ a < b, b ≥ 2 − 2(1 + a2 )}. Note that this covers the case√a = b ≥ −2 + 6 as a limiting case when a = b.
The other case a < b ≤ 0 is symmetric. So we omit the details.
Proof of Proposition 4. We analyze the case b < 0 < a and identify the conditions
for the existence of diﬀerent types of equilibria. After that, we discuss any diﬀerence inthe conditions for the other cases, i.e., b < a ≤ 0 and 0 ≤ b < a.
Let us start with the PPD equilibrium without full market coverage. If firm A
d to serve [z, 1/2] where
deviates from this equilibrium, then it chooses a uniform price qA
d − 1) if z ∈ [b, a], or z = b if q d = 1 + b/2. It is because, in the PPD
z = 2(qAA
equilibrium, consumers on (b, a) are not being served while consumer b receives the PPD
d = 1 + b/2,
price 1 − b/2 from firm B. Maximizing the deviation profit leads to qA
d = (1/2 − b)(1 + b/2) = (2 − 3b − 2b2 )/4. Thus firm A does not deviate if
hence πA√P P D (a) ≥ π d , or b ≥ (−3 + 7 + 32a + 8a2 )/4. Similarly, firm B’s optimal deviation isπAAd = 1 − a/2 and the deviation profit π d = (2 + 3a − 2a2 )/4. Firm B does not
given by qB
B√d > π P P D (b), or b ≥ (4 − 17 − 12a + 8a2 )/2. Thus the PPD equilibrium
deviate if πBB
without full market coverage exists if both of these conditions are satisfied along withb < 0 < a.
Consider next the PPD equilibrium with a uniform price where firm B exercises
35

PPD and firm A chooses qA = 1 + b/2, serving [b, 1/2]. Firm A’s profit is equal tothe deviation profit from the previous case. Thus firm A does not deviate to PPD if√b ≤ (−3 + 7 + 32a + 8a2 )/4. On the other hand, firm B’s deviation involves choosingd = q − a = (2 + b − 2a)/2, with which firm B can serve [−1/2, a]. Itsa uniform price qBA()
d = (a + 1/2)q d = 2 + b + 2(1 + b)a − 4a2 /4. Thus firm B
deviation profit is then πBB√
P P D (b) ≥ π d or b ≥ (3 − 2a −10(1 − 2a + 2a2 ))/2.
does not deviate if πB
B
Consider next the PPD equilibrium with a uniform price where firm A exercises PPD
and firm B chooses qB = 1−a/2. Proceeding similarly as in the second case, we can show√√that neither firm deviates if (−1 + a + 5a(2 + a))/4 < b < (4 − 17 − 12a + 8a2 )/2.
The calculation of total industry profit is straightforward and is omitted.
Consider now the Hotelling equilibrium: qA = qB = 1/2 and πA = πB = 1/4.
Firm A’s deviation involves serving only its targeted consumers only using personalized∫
d = 1/2 (x + 1/2)dx =prices pdA (x) = qB + x for all x ∈ [a, 1/2]. Its profit is then πA√ad or a ≥ ( 2 − 1)/2. Similarly(3 − 4a − 4a2 )/8. Thus firm A does not deviate if 1/4 ≥ πA√
firm B does not deviate if b ≤ (1 − 2)/2. Thus the Hotelling equilibrium exists if and√√only if a ≥ ( 2 − 1)/2 and b ≤ (1 − 2)/2.
Finally, the equilibrium one-way poaching does not exist in the current case b < 0 < asince this equilibrium is possible only if b < a < −1/4 or 1/4 < b < a.
Let us now turn to the case b < a ≤ 0. First, this case does not admit the Hotelling
equilibrium, nor the equilibrium with one-way poaching by firm A. Second, the equilibrium with one-way poaching by firm B exists only if a < −1/4. In this case, firm A
has no incentives to deviate. Firm B’s deviation involves exercising PPD on [−1/2, b],d = π P P D (b). Thus firm B does not deviate either if π = 1/16 ≥ π P P D (b)leading to πB
B
B
B√
or b ≤ 2 − 6. This implies that the equilibrium with one-way poaching by firm B exists√
if b < a < −1/4 and b ≤ 2 − 6. Third, for the PPD equilibrium without full market
coverage, we also need to consider the case where firm B’s optimal deviation involves√
d = 1/4, which is possible if 1/16 ≥ (2+3a−2a2 )/4 or a ≤ (3− 23)/4. In this case, firmqB√
P P D (b) ≥ 1/6 or b ≥ 2 − 6. Summarizing, the PPD
B does not deviate from PPD if πB√√equilibrium without full market coverage can also exist if (3 − 23)/4 ≥ a > b ≥ 2 − 6.
The other case 0 ≤ b < a is analogous to the case b < a ≤ 0. First, neither
the Hotelling equilibrium nor the equilibrium with one-way poaching by firm B exists.
Second, the equilibrium with one-way poaching by firm A exists if 1/4 < b < a and√a ≥ −1 + 6. Third, the PPD equilibrium without full market coverage can also exist√√
if (−3 + 23)/4 ≤ b < a ≤ −2 + 6.
Proof of Proposition 8. We start with the fully targeted market. First, consider thecase a < 0 < b. Then with passive consumers, the equilibrium is with two-way poaching
and total industry profit is equal to 1/4. With active consumers, we have the PPD
equilibrium with partial Thisse-Vives outcome where total industry profit is bounded
below by 1/4 and is equal to 1/4 if and only if −a = b = 1/2, as can be verified from36

(7). Consider next the case 0 ≤ a < b or a < b ≤ 0. With passive consumers, theequilibrium is with one-way poaching where total industry profit is bounded above by
11/32. With active consumers, we have either the equilibrium with partial Thisse-Vives
outcome or the equilibrium with one-way poaching. In the former case, total industry
profit is bounded below by 9/16 since one firm exercises PPD for all its loyal consumers,∫0∫ 1/2
hence its profit is not smaller than −1/2 (1 − y/2)dy = 0 (1 + x/2)dx = 9/16. In thelatter case, total industry profit is 11/32 as shown in (8).
We now turn to the partially targeted market. First, consider the case b < 0 < a.
With passive consumers, the equilibrium is with partial Hotelling outcome and total industry profit is bounded above by 1/2. With active consumers, there are three possibilities. First, in the PPD equilibrium, it can be verified that the conditions in Proposition√
4 imply that the range of (a, b) admitting this equilibrium is such that a < ( 17−4)/2 <√P P D (1/16)+π P P D (−1/16) > 1/2.
1/16 and b > (− 17+4)/2 > −1/16. It is easy to see πA
BSecond, in the equilibrium with PPD and a uniform price, πA + πB ≥ 3/4, as can beverified by (9). Third, in the Hotelling equilibrium, total industry profit is 1/2. Next
consider the case b < a ≤ 0. With passive consumers, the equilibrium is either with
one-way poaching or with partial Hotelling outcome. Total industry profit is at most
11/32 in the former and 1/2 in the latter. With active consumers, we have the PPD
equilibrium without full market coverage or the equilibrium with PPD and a uniform
price, or the equilibrium with one-way poaching. In the first two cases, total industry
profit is always greater than 1/2. In the third case, total industry profit is 11/32 and the√range of (a, b) supporting this equilibrium is b ≤ 2 − 6 and b < a < −1/4. It is easy
to see that this range of (a, b) admits only the equilibrium with one-way poaching when
consumers are passive. The same argument applies to the remaining case 0 ≤ b < a.

37

Appendix B: Evidence on active consumers
In this appendix, we oﬀer some evidence in support of our assumption that someconsumers are active in the way described in this paper. We note first that, firms invarious service industries oﬀer new customer-only special deals at considerable discountcompared to what existing customers pay. Examples of these industries include retailbanking, information and communications, and cable TV services. Table 1 shows thesavings received by new customers relative to existing customers.
— Table 1 goes about here. —The information on whether existing customers haggle and also receive these newcustomer-only oﬀers - active consumers in our terminology - is not publicly available.
But one can search inside various Internet forums specifically designed to share experiences that consumers have in dealing with their service providers. For example, oursearch captures instances where posters indicate they are existing customers, where theymentioned the new customer oﬀer, and where they reported to have made savings. Although our evidence is based on unverifiable cheap talk and is plagued by issues such as
selection bias, it nonetheless tells us that a large number of consumers proactively react
to firms’ strategies to price-discriminate. The method we used to gain some insight fromsuch data is as follows:(1) We start with the search engine Google within the Internet forum to identify messages that contain a set of keywords that are likely to indicate that the messages
are related to existing customers negotiating with their service providers.
(2) With the number of hits from (1) as a base, we further add keywords to the searchthat indicate some level of success in the negotiation.
(3) If reported, we record the dollar value of savings from the negotiation, although
this relied on individual scraping of a subset of these results.
Table 2 shows the sources of our search, the sample size, and the keywords used forthe search. As for the keywords that indicate a post from an existing customer, we used
identifiers such as ‘loyal’, ‘existing’ or ‘current’. We chose identifiers such as ‘saved’,‘reduced’ or ‘discounted’ as the keywords indicating successful negotiation. We started
our search with Reddit (https://www.reddit.com/), one of the largest websites for social
news aggregation, web content rating, and discussions. Our search covered over 205
million posts and returned hits in services such as cable TV, credit cards, broadband
Internet, and cell phone plans. Next, we extended our search to all Internet forums
including any indexed page from Google that is categorized as a ‘forum’. The searchcovered over 20 billion posts.
— Table 2 goes about here. —38

Table 3 shows the results from each search as well as average savings from a successful negotiation. For example, the results from Reddit forum indicate that around0.22 million customers reportedly negotiated with their Internet service providers with
70% being successful for average savings of $138. The search over all forums obviously
returned more hits but with varying degrees of success across diﬀerent types of services.
It is interesting that success rates are lower in this case than those reported in Reddit
forum, especially for Internet and cell phone plans. Nonetheless, a significant number ofconsumers report to have haggled with their current service providers and succeeded insecuring a discount. Unfortunately we cannot tell whether these savings are equivalent towhat the existing customers could have secured from new customer-only deals. Judging
from the information given in Table 1, the savings could be a fraction of new customer
savings. But the presence of such active consumers and the savings they secure throughnegotiation undoubtedly undermine the eﬀectiveness of discriminatory pricing, which inturn softens price competition.
— Table 3 goes about here. —References
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41

𝑝𝑝𝐵𝐵 (𝑦𝑦) = −𝑦𝑦

𝑝𝑝𝐴𝐴 (𝑥𝑥) = 𝑥𝑥 − 𝑏𝑏/2

A→A

A→B

B→B

𝑞𝑞𝐴𝐴 = 0−1/2

𝑞𝑞𝐵𝐵 = −𝑏𝑏/2
𝑏𝑏

𝑏𝑏/2

0

Figure 1: Equilibrium with one-way poaching by firm B

1/2

𝑝𝑝𝐵𝐵 (𝑦𝑦) = −𝑦𝑦

𝑝𝑝𝐴𝐴 (𝑥𝑥) = 𝑥𝑥

𝑞𝑞𝐴𝐴 = 0
−1/2

A→A

B→A

A→B

B→B

𝑞𝑞𝐵𝐵 = 0𝑎𝑎0𝑏𝑏

Figure 2: Equilibrium with two-way poaching

1/2

𝑝𝑝𝐵𝐵 (𝑦𝑦) = −𝑦𝑦 + 𝑞𝑞𝐴𝐴

𝑝𝑝𝐴𝐴 (𝑥𝑥) = 𝑥𝑥 + 𝑞𝑞𝐵𝐵

B

A

𝑞𝑞𝐴𝐴 = (2𝑎𝑎 − 𝑏𝑏)/3
−1/2

𝑏𝑏

𝑞𝑞𝐵𝐵 = (𝑎𝑎 − 2𝑏𝑏)/30𝑧𝑧 =𝑎𝑎 + 𝑏𝑏
3

𝑎𝑎

Figure 3: Equilibrium with partial Hotelling outcome

1/2

5/4

5/4

𝑝𝑝𝐵𝐵 (𝑦𝑦) = 1 − 𝑦𝑦/2

-1/2

𝑝𝑝𝐴𝐴 (𝑥𝑥) = 1 + 𝑥𝑥/20𝑎𝑎 = 𝑏𝑏

Figure 4: PPD equilibrium

1/2

5/4

5/4

𝑝𝑝𝐵𝐵 (𝑦𝑦) = 1 − 𝑦𝑦/2

𝑝𝑝𝐴𝐴 (𝑥𝑥) = 1 + 𝑥𝑥/2

𝑝𝑝𝐵𝐵 (𝑦𝑦) = −𝑦𝑦

-1/2

𝑎𝑎

𝑝𝑝𝐴𝐴 (𝑥𝑥) = 𝑥𝑥

0

𝑏𝑏

1/2

Figure 5: PPD Equilibrium with partial Thisse-Vives outcome

𝑝𝑝𝐵𝐵 (𝑦𝑦) = −𝑦𝑦 + 1/4

𝑞𝑞𝐴𝐴 = 1/4
−1/2

0

1/4

𝑏𝑏

𝑎𝑎

Figure 6: Equilibrium with one-way poaching by firm A

1/2

5/4

-1/2

𝑝𝑝𝐵𝐵 (𝑦𝑦) = 1 − 𝑦𝑦/2

𝑏𝑏0

𝑝𝑝𝐴𝐴 (𝑥𝑥) = 1 + 𝑥𝑥/2

5/4

𝑎𝑎

1/2

Figure 7: PPD equilibrium without full market coverage

𝑝𝑝𝐵𝐵 (𝑦𝑦) = 1 − 𝑦𝑦/2

𝑞𝑞𝐴𝐴 = 1 + 𝑏𝑏/2
−1/2

𝑏𝑏

0

𝑎𝑎

Figure 8: Equilibrium with PPD and a uniform price

1/2

Table 1: Savings for New Customers
Category
Cell phone
Bank or credit card fees
TV/Broadband/HomephoneAll

New Customer Savings (annualised, USD)
$360
$230
$410
$375

Source: Offers collected from Whistleout.com, choice.com, whirlpool.net.au, comparethemarket.com
during May – June, 2017. HTML pages and aggregate data were cleaned by web scraping methods using
grep.

Table 2: Sample Source and Sentiment Operators in Google Search
SampleRedditAll Forums
Sentiment
Successfully saved money
Mentioned existing

Google search operator
Unqualified sample size
https://www.reddit.com
205,000,000
Inurl:forum
20,900,000,000
Words and operators(Saved OR reduced OR discounted OR gave me OR discounted
OR rebate) AND (quantity OR percent OR free)(time OR duration) OR loyal OR long-time OR long+time OR
existing+customer OR loyal+customer OR current+customer OR
existing+user OR loyal+user OR current+user

Table 3: Evidence of Active Consumers from Internet Forums

Category# of results# of results withsuccessful
savings

Cable

143,094

102,056$187.50

Credit card
Internet
Cell phone

74,723223,01753,88762,376
176,085
51,114$119.00$138.00$262.33

RedditRedditRedditRedditCable
Credit card
Internet
Cell phone

1,210,084
915,047
1,420,083
899,054705,002632,067
476,021361,043$231.21$85.35$202.25$147.50

All forums
All forums
All forums
All forums

Averagesaved (USD)

Source