Behavior-Based Price Discrimination and Switching Costs
Yuncheol Jeong, Keio University
Masayoshi Maruyama, Kobe University
Abstract
This paper examines the equilibrium incentive for firms to use behavior-based price
discrimination in a duopoly market with exogenous switching costs. We find that if there is a
large difference in the existing market shares between two firms, then discriminatory pricing
is a unique Nash equilibrium. Otherwise, there are three Nash equilibria: both firms engage in
discriminatory pricing, or engage in uniform pricing, or engage in mixed strategies. The
respective firms are worse off in the discriminatory equilibrium compared with the others.
Introduction
In recent years, many transactions are computer mediated, and sellers have compiled vast
databases of individual customer data and use them to study purchase behavior. Along with
this, pricing conditioned on previous purchase behavior is becoming widely practiced as
shown by Acquisti & Varian (2005). In the case of customers who frequently purchase goods
and services from supermarkets and airlines, they are presented with coupons and point cards
as part of customer loyalty programs. Fudenberg and Tirole (2000) use the term "behaviorbased" price discrimination to describe such conditioning prices on purchase history. It is a
form of dynamic price discrimination, but it can be distinguished from the different prices for
the same products during different periods, i.e. inter-temporal price discrimination.
The behavior-based price discrimination is related to the marketing literature of consumer
addressability, that is, the capabilities about identification of specific customers. Consumer
addressability is applied to situations where customers can be identified by a characteristic
such as a telephone number or a mailing address etc., which is viewed as a prominent feature
of interactive marketing (Blattberg and Deighton, 1991; McCulloch et al., 1996). McCulloch
et al. (1996) evaluate empirically the value of information on household-specific purchase
history. A consequence of this phenomenon is that it gives firms the ability to reach individual
customers and to customize price and promotional efforts. Chen et al. (2001) and Chen and
Iyer (2002) focus on the use of targeting technology to facilitate price discrimination. Chen
and Iyer (2002) show that consumer addressability helps a firm to extract consumer's surplus,
however, the competitive investment in addressability drives destructive price competition.
Chen et al. (2001) focus on a similar aspect, targetability, "the ability to predict purchase
behaviors of individual consumers". And they show that improvement of targetability can
lead to win–win competition; however, too high a level of targetability intensifies price
competition. As shown later, these results share common implications with ours.
When the seller can provide a personalized service that is valuable to consumers, it creates
"exogenous" switching costs for the consumers because they would then have to rebuild the
relationship with the seller like mobile phone market. In addition, reward program such as
frequent-flier programs offered by airlines, frequent-guest programs offered by hotels, and
frequent-shopper programs offered by supermarkets creates "endogenous" switching costs.
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The behavior-base price discrimination has received much attention also in the economic
literature recently, and a number of papers have based their studies on the issue of uniform
versus discriminatory pricing in a duopolistic market with switching costs. The literature can
be divided into two variant models of markets with and without exogenous switching costs.
The first strand of models assumes that there are no real costs from switching, even if
artificial costs may exist. Caminal & Matutes (1990) and Fudenberg & Tirole (2000) study a
two-period, differentiated-product duopoly model of markets without exogenous switching
costs. Caminal & Matutes (1990) analyses a model in which firms can pre-commit to a
second-period discount for their loyal customers, i.e., “paying customers to stay”, that
generates switching costs endogenously. Fudenberg & Tirole (2000) study a model where
firms try to “poach” the customers of their competitors by offering them inducements to
switch. Villas-Boas (1999) extends their model to the case of two infinitely lived firms facing
overlapping generations of consumers. The second strand deals with competitive
discrimination with exogenous switching costs. Bester & Petrakis (1996) and Shaffer &
Zhang (2000) analyse the price discrimination in a one-period duopoly model based on a
static setting. Chen (1997) studies the practice of offering discounts to new customers, i.e.
“paying customers to switch” in a two-period duopoly model of “homogeneous” goods.
Taylor (2003) extends this to a multi-period oligopoly.
However, in all of the previous analyses of behavior-based price discrimination mentioned
above, the firms’ pricing policies are assumed, and there is no discussion on whether the
respective firms do in fact select a strategy of carrying out price discrimination.The purpose
of this paper is to examine the equilibrium incentive for firms to use behavior based-price
discrimination in a duopolistic market with switching costs. Comparing to the current state of
the literature on strategic pricing policies, our results get more precise results, that is, both of
price discrimination and uniform pricing might be the firm's choices. And we also derive the
probability of each choice. For example, in a static duopoly model on spatial pricing policies,
Thisse and Vives (1988) show that price discrimination is the dominant strategy for both
firms.
The Basic Model
We describe the competition of firms in a market with exogenous switching costs. Suppose
that there are two firms, A and B, who produce products A and B, respectively, with constant
marginal cost c . Each consumer can consume either a unit of product A or a unit of product
B, but not both. Total number of consumers is normalized to one. We assume that the
consumer’s reservation price is so high that in the equilibrium, all consumers will use one of
the products. We consider competition in the period after all consumers have purchased some
products. Let ! denote the market share of firm A in the previous period, and 1 " ! that of
firm B. During the current period, the two firms sell new products with the same features and
quality, and all consumers buy the new products that are now provided. At this time, in cases
where given consumers switch to the other firm, the switching cost s must be borne by these
consumers. We assume that the switching cost s is uniformly distributed across the consumer
population on the interval [0, ! ] with density 1 ! . To ensure the equilibria (specifically, to
satisfy the second-order conditions), it is assumed that 0 < ! < 9 2 . We set ! = 1 without loss
of generality. Then there is a cut-off s AB such that among the consumers who have bought
from firm A in the previous period, all consumers with s > s AB continue to buy from firm A,
and all consumers with s < s AB switch to buy from firm B. This cut-off is determined by the
prices proposed by the firms.
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The structure of the game is as follows. We consider a two-stage game, with simultaneous
moves in each stage. In stage one, the firms decide on their pricing policy. That is, they can
exercise price discrimination or uniform pricing. In stage two, knowing each other’s pricing
policy, the firms choose the price and consumers make their purchase decisions. If a firm
chooses a price discrimination policy in stage one, then in stage two it can set different prices
of p0i for its own previous (original) customers and pNi for new customers who switch away
from its rival. Otherwise, a firm chooses a uniform price of p i for all customers ( i = A, B).
The Equilibrium
As a result of the selections of pricing policy by the two firms in stage one, four cases are
possible: (DP, DP), (UP, UP), (DP, UP), (UP, DP). Here, “DP” indicates discriminatory
pricing and “UP” indicates uniform pricing. Thus, for example, “(DP, UP)” indicates that firm
A is using discriminatory pricing and firm B is using uniform pricing. Below, we examine
equilibrium prices in stage two for each of these respective cases.
For the cases of (DP, DP) and (UP, UP) there were similar analyses by Chen (1997), and we
expand them to the asymmetric cases. The whole results are as follows.
When both firms use discriminatory pricing; (DP, DP),
p0A * = p0B * = c + 2 3 , p NA * = p NB * = c + 1 3 , " A * = (1 + 3! ) 9 , " B * = ( 4 # 3! ) 9 .
When both firms use uniform pricing; (UP, UP),
p A * = c + (1 + ! ) / 3! , p B * = c + (2 " ! ) / 3! , " A * = (1 + ! ) 2 / 9! , " B * = (2 # ! ) 2 / 9! if p A ! p B ,
p A * = c + (1 + ! ) / 3(1 " ! ), p B * = c + (2 " ! ) / 3(1 " ! ), " A * = (1 + ! ) 2 / 9(1 # ! ), " B * = (2 # ! ) 2 / 9(1 # ! ) if p A < p B .
When firm A practices discriminatory pricing and firm B uses uniform pricing; (DP, UP),
A
2
B
2
p 0A * = c + (5 " ! ) / 6, p NA * = c + (2 " ! ) / 6, p B * = c + (2 " ! ) / 3, " * = (4 + 17! # 5! ) / 36, " * = (2 # ! ) / 9
When firm A practices uniform pricing and firm B uses discriminatory pricing; (UP, DP),
A
2
B
2
p A * = c + (1 + ! ) / 3, p 0B * = c + (4 + ! ) / 6, p NB * = c + (1 + ! ) / 6, " * = (1 + ! ) / 9, " * = (16 # 7! # 5! ) / 36.
We suppose that the two firms select pricing strategies in stage one to maximize their own
profits. Then we derive the following proposition.
Proposition 1
If there is a large difference in market shares, or formally either 0 ! " < 1 5 or 4 5 < " ! 1 is
satisfied, then (DP, DP) is a unique Nash equilibrium regardless of the value of c . Otherwise,
there are two pure-strategy equilibria (DP, DP), (UP, UP), and one mixed-strategy
equilibrium p* = (4 " 5! )(4 + ! ) /(16 " 16! " ! 2 ) and q* = (2 " ! )(2 + 5! ) /(4 + 8! " ! 2 ) ,
where p * and q * (! [0,1]) are the probabilities of firms A and B exercising price
discrimination, respectively.
Explanation and Implications
The intuition behind this proposition is as follows. If one firm engages in DP and tries to
poach customers from its competitor by offering them special discounts, then the other firm
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should respond to retain its customers. In this case, it is more profitable for the other firm to
also engage in DP than it is to respond by lowering its price uniformly for all customers under
UP. Assuming each firm has existing customers, DP is the best-response strategy for each
firm against other firm’s DP. Thus, (DP, DP) is one of the equilibria. On the other hand,
suppose that one firm engages in UP. If the other firm also employs UP, then it allows firms
to relax their price competition, thereby raising prices and earning higher profits on their
partially locked-in customers. Usually this is profitable for each firm, and so (UP, UP) is
another equilibrium. However, when there is an extremely large difference in the existing
market shares, i.e., 0 ! " < 1 5 or 4 5 < " ! 1 , the equilibrium outcome is different. Then, a
smaller firm has a greater incentive to employ DP and tries to poach customers from its
competitor, regardless of the rival firm’s pricing policy. That is, DP is a dominant strategy for
a smaller firm. In this case, (DP, DP) is a unique equilibrium.
Proposition 2
Regardless of the values of c and ! , both firms’ equilibrium profits are lower under (DP, DP)
than under (UP, UP).
Proof: Comparing the profits, it is easy to prove this proposition.
Unlike the monopoly case, competitive price discrimination intensifies competition, and the
profits of each firm will be lower than if none of the firms practice price discrimination. This
result is similar to results found in the analysis involving coupon-based price discrimination
carried out by Bester and Petrakis (1996), the poaching analysis carried out by Chen (1997),
and the analysis of loyalty-rewarding pricing schemes by Caminal and Claici (2007).
The result comes from the fact that firms differ in their view of which markets are strong and
which are weak, i.e., the “best-response asymmetry” termed by Corts (1998). In our model of
customers’ switching costs, each firm has a “strong market” of its own partially locked-in
customers, preferring to set a higher price in this market than in the “weak market” of rival’s
customers. Thus, the two firms have different strong markets. When price discrimination is
permitted and some firm offers a lower price to its competitor’s customers, we would expect a
rival firm to react by offering a lower price to these customers, with the result that prices for
every group may be lower than the uniform price. This escalation of competition may make
firms worse off.
The analysis in this paper has been applied to several areas. To the extent that the firms have
information about consumers’ purchase histories, it may be possible for firms to engage in
behavior-based price discrimination. We think our results are most applicable to the mobile
telephone market. For this reason, we have briefly listed below the major special
characteristics of the mobile telephone market.
The first major characteristic is that mobile telephones are system goods, consisting of
integrated hardware (terminals) and services (telecommunication-related services). In
addition, at present, mobile terminals and telecommunication services are being provided,
which are not compatible between the different firms. For this reason, consumers buying their
first system goods from one firm must buy other system goods again when they switch to
another firm.
The second major characteristic is that, if the consumer switches to another firm, in addition
to having to buy another new mobile telephone, they must also pay all costs related to the
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initial subscription fees. It is also necessary to change to a new telephone number and a new
email address, making it necessary to pay for re-entering all the numbers stored in memory.
The large cost of switching is a major characteristic of the mobile telephone market.
The third major characteristic is that, in the case of the mobile telecommunications market,
the pace of development related to both mobile telephones and the telecommunication
services is very rapid. In addition, other firms duplicate new mobile telephone functions, and
the new telecommunications services and similar products are rapidly launched into the
market. In other words, the various mobile telephone firms continue to compete in the area of
technological innovation to find ways to differentiate their products and services from their
competitors, and they quickly copy the new features of other firms in order to compete. For
example, in the Japanese mobile telephone market, NTT DoCoMo was the first company to
provide the “i-mode” service, but quickly thereafter, similar types of services began to be
provided by au (ezweb), and Vodafone also began to provide a similar service on the Web.
The same occurred in the case of Vodafone’s picture–mail service, au’s call arrival song
service and Tsu-Ka’s simple-to-use calls-only telephones for the elderly. Thus, as time has
passed, all firms have come to have similar products and services.
All of the above major special characteristics meet the specification of our basic model. Thus,
our analysis has implications for mobile phone market. From the beginning, when NTT
DoCoMo dominated the market, this market has been characterized by such practices as
selling mobile telephones to new customers for one yen (approximately, one cent) and other
examples of price discrimination. These efforts have caused extremely severe price
competition and they make firms worse off. However, when there is not so large difference of
market shares in recent years, such a discriminatory pricing becomes rare. These facts
coincide with our propositions.
Conclusion and Discussion
We have considered the behavior-based price discrimination in a duopoly market with
switching costs. From a marketing perspective, price discrimination in our model can be
interpreted as a marketing strategy. That is, UP (uniform pricing) corresponds to "mass
marketing" and DP (discriminatory pricing) to "segmented or individual marketing".
To simplify the model, we set some assumptions. However, some of them can be further
generalized, for example, a change in the range of distribution of switching costs, from the
assumption of [0, 1] to [0, ! ] . Furthermore, the total number of consumers is normalized to
one, however this assumption can also be generalized. Instead of the market share of firm A
in the previous period equaling ! and that of firm B equaling 1 " ! , letting ! be the number
of consumers who are previous buyers from firm A and currently have a reservation price
high enough to buy from either firm, and ! be the number of consumers from firm B, makes
no change to our results and propositions. We are not sure if the assumption that all
consumers will buy only one of the products can be generalized or not, however this
assumption clearly shows the pure effect of exogenous switching costs.
For further research, the empirical evidence of mobile phone markets that are close to
duopoly competition, such as the market in England, Japan and Korea (where two or three
firms exist), can be made. This will provide implications for marketing, including firms'
promotion strategies such as handset subsidies and rebate programs.
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