Dynamic targeted pricing with strategic consumers

International Journal of Industrial 27 (2009) 43–50 Int. J. Ind. Organ. 27Organization (2009) 43–50

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International Journal of Industrial Organization j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / i j i o

Dynamic targeted pricing with strategic consumers☆ Yuxin Chen a, Z. John Zhang b,⁎ a b

The Leonard N. Stern School of Business, New York University, 44 West Fourth Street, New York, NY 10012, United States The Wharton School, University of Pennsylvania, 700 Jon M. Huntsman Hall, 3730 Walnut Street, Philadelphia, PA 19104-6340, United States

a r t i c l e

i n f o

Article history: Received 30 January 2007 Received in revised form 23 March 2008 Accepted 24 March 2008 Available online 1 April 2008 JEL classification: L11 L40 M31 Keywords: Dynamic pricing Price discrimination Targeted promotions

a b s t r a c t We investigate in this paper whether dynamic targeted pricing based on consumer purchase history could benefit a practicing firm even when consumers are “strategic” in that they actively seek to avail themselves of a low price in the future. Such strategic behavior on the part of consumers has been shown in the literature to render such dynamic targeted pricing unprofitable, even for a monopoly firm. We show that dynamic targeted pricing can benefit competing firms, when they actively pursue customer recognition based on consumer purchase history. This is because in order to pursue customer recognition, competing firms need to price high to “screen out” price-sensitive consumers and hence price competition is moderated. As a result, all competing firms can become better off with targeted pricing than without even when consumers behave strategically. Interestingly, because of this competition moderation effect, the paradoxical outcome occurs where dynamic targeted pricing may not benefit a monopolist, but it may benefit competing firms. We also show that dynamic targeted pricing can expand the market such that social welfare unambiguously improves. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Dynamic targeted pricing based on consumer purchase history is a wide-spread practice. For instance, a telecom company may charge a higher price to its current customers than to its prospective customers, including those who are currently with a rival carrier, by offering a new subscriber discount. Similarly, a magazine or newspaper may charge a higher rate for renewals than for new subscriptions, as the renewal customers have revealed themselves to like the magazine or newspaper and hence are less price sensitive. This practice is also commonly observed in club membership, credit cards, and ISP businesses as well as in catalog retailing.1 Such targeted discounts could benefit a firm at a given point in time, as the firm no longer has to offer the same discount to those who have a strong preference for its product in order to induce the patronage of those who do not. However, as dynamic targeted pricing based on consumer purchase history gains popularity, its benefit becomes increasingly

☆ Yuxin Chen is an associate professor at the Stern School of Business of the New York University. Z. John Zhang is a professor of marketing and Murrel J. Ades Professor at the Wharton School, University of Pennsylvania. We thank the seminar participants at University of California at Berkeley, University of California at Los Angeles, University of Texas at Dallas, and University of Maryland for their helpful comments. We are also grateful to J. Miguel Villas-Boas for his detailed comments and to Kinshuk Jerath for proofreading the manuscript. However, we are responsible for the content of this paper. ⁎ Corresponding author. E-mail addresses: [email protected] (Y. Chen), [email protected] (Z.J. Zhang). 1 See Feinberg et al. (2002) for more extensive examples. 0167-7187/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ijindorg.2008.03.002

doubtful. This is because “some consumers get savvy and change their buying behavior to accommodate the new realities of dynamic pricing,” or to “outsmart” targeted pricing mechanisms, all through forgoing or delaying current consumption in a bid for a lower price (Kambil et al., 2002; Maw, 2002). In the case of telephone service, for instance, a consumer who prefers AT&T can still get its discount meant for attracting new customers if she simply terminates (or even threatens to terminate) AT&T service temporarily. A customer looking to renew her subscription to a magazine can trigger a substantial discount if she simply waits and let the first renewal notice to pass.2 Such strategic behavior is especially worrisome in an online environment where firms use real-time price cuts to induce “hesitant” customers to purchase (Hamilton, 2001). In that context, consumers frequently learn to become hesitant in their online purchases in order to trigger a price cut, even though they may fully intend to purchase the product at the full price and they share online their tricks to foil a firm's attempt to recognize individual consumers and charge them different prices.3 In this paper, we investigate the implications of the dynamic interactions between strategic consumers and firms, and 2 Apparently, for magazines such as Reader's Digest and National Geographic, the price for renewal is substantially lower if you show some reluctance to renew your subscription through delaying. Such a pricing practice is also used by many membership clubs. Many customers, including the authors for this paper, for instance, pay a lower membership fee by taking advantage of AAA's and Ameniti's offers of a substantial membership discount once they let their membership renewal notices expire at the time of renewal. 3 See, for instance, http://yro.slashdot.org/comments.pl?sid=73101&cid=6580585, a public interest website.

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shed some light on the viability and profitability of dynamic targeted pricing. Past theoretical and empirical studies have shown that targeted pricing can benefit competing firms (Rossi, McCulloch, and Allenby, 1996; Shaffer and Zhang, 2000, 2002; Chen et al., 2001).4 However, that conclusion is drawn under the premise that consumers with varying brand preferences are all passive recipients of a targeted price and they do not react when a firm takes away their surplus. This premise is harder to defend when consumers become aware of firms' practice of targeted pricing (Feinberg et al., 2002). Could targeted pricing still benefit a practicing firm in the presence of strategic consumers? The answer no longer seems affirmative. A study by Villas-Boas (2004) shows how strategic consumers could make a firm worse off in the context of dynamic targeted pricing. Once a consumer starts to anticipate future prices, she may choose to forgo a purchase today to avoid being recognized as an “old” customer and hence to avail herself of a low price targeted at new buyers. Such strategic waiting on the part of consumers can hurt a firm both through reducing the benefit of price discrimination and through forgone sales. A more recent study by Acquisti and Varian (2005) has come to a similar conclusion, showing that it is never profitable for a monopolist to condition its pricing on purchase history, unless a sufficient number of consumers are not sophisticated enough to see through the seller's targeting strategy or the monopolist can provide enhanced services to boost consumer valuation subsequent to a purchase. However, in a competitive context, a firm cannot benefit from dynamic targeted pricing at all if targeting is based on consumer purchase history. Therefore, the future of dynamic targeted pricing seems rather dim. We shall revisit this profitability issue here. Our analysis shows that the pursuit of customer recognition by competing firms based on consumer purchase history can moderate price competition in a market. As a firm strives to glean more accurate, actionable customer information for subsequent targeted pricing, it must seek “exclusivity” in its pricing. Exclusivity can come only with a high price, relative to the rival's price, such that not all consumers purchase from the firm. As a result, the firm has a strategic incentive to raise its price in its pursuit of customer recognition and price discrimination to the benefit of all competing firms. Our study of dynamic targeted pricing complements that of Fudenberg and Tirole (2000). We identify a different motivation for competing firms to raise their prices in a two-period game. Their study shows that in the second period a firm always has the incentive to offer discounts to the rival firm's customers who have revealed, through their prior purchase, their preference for the rival firm's product. Such discounts tend to reduce consumer price sensitivity for a firm's product in the first period, as consumers rationally anticipate them, and hence prices rise in the first period thanks to anticipated customer poaching. However, it will become clear as our analysis progresses that this demand-driven effect is quite different from our firm-driven competition moderation effect. In addition, they assume away strategic waiting on the part of consumers to focus on consumer brand switching, while we do not. These two key differences in modeling explain why, in our model only, competing firms can benefit from dynamic targeted pricing, even if first-period prices do not rise. Our study of firms' quest for customer recognition also complements the research on how a customer's learning about firms' products and firms' learning about a customer's preference may affect competitive pricing over time (Bergemann and Välimäki, 1996, 2006). Our study differs from that line of inquiry in that our consumers are not homogeneous so that the recognition of customer types plays an important role in a firm's pricing decisions over time. More closely related to our study is the literature on price experimentation 4 Other studies, such as Shaffer and Zhang (1995), Chen (1997), Villas-Boas (1999), and Taylor (2003) have concluded, in the context of equally-matched firms (symmetry) and/or in a dynamic game, that firms are worse off due to competitive targeted pricing.

(Kihlstrom et al., 1984; Mirman et al., 1993). This literature has shown that a firm may optimally “experiment” with its pricing decision at the cost of its current profit in order to enhance the informativeness of the observed market demand. The information thus gleaned from the experimentation can help the firm to increase its future profit. As Mirman et al. (1994) have subsequently shown, such information always helps a monopolist, but may be deleterious to competing firms. In our model, firms also “experiment” with their prices. However, they do so not to gauge an uncertain market demand more accurately, but to recognize the individual segments of a certain market demand for the purpose of implementing targeted pricing. For that reason, our analysis uncovers an intriguing phenomenon: the quest for customer recognition may not benefit a monopolist but competing firms can all become better off when they all actively pursue customer recognition. This paradoxical outcome is due to the fact that with competition the rise in one firm's price will in turn encourage its rival firm to raise its price. We show that this strategic effect can qualitatively alter the outcome of dynamic targeted pricing in favor of competitive firms, even in the presence of strategic consumers. Finally, our study also complements two recent studies by van Ryzin and Liu (2005) and Su (2006). The former study investigates a monopolist's quantity decisions in a two-period capacity rationing model where consumers behave strategically to obtain a low price by accelerating or postponing their purchases. The latter study develops a continuous-time model where a monopolist adjusts its price dynamically to sell a fixed inventory to strategic consumers with heterogeneous waiting costs in a finite time horizon. Our study differs from both mainly in that we examine competitive pricing behavior in the context of targeted pricing. The interactions between sellers and buyers we model are not how frequent sales in a market train consumers to only buy on sale, but how firms may compete on price when strategic consumers try to foil their attempts to identify their willingness-to-pay. In what follows, we first set up our basic model. Then, we proceed to discuss the implications of customer recognition for dynamic targeted pricing. Finally, we extend our model to discuss the welfare implications of dynamic targeted pricing and conclude with suggestions for future research. 2. Basic model Consider a market where two firms, denoted respectively as Firm A and Firm B, each produce a differentiated product at a constant marginal cost, which we set to zero for simplicity. There are three segments of consumers in this market. The first two segments consist of those consumers who are loyal to, respectively, Firm A and Firm B, and these two loyal segments have the equal size of γ. These are the price-insensitive consumers who always purchase from a particular firm as long as the firm's price is below their reservation price and who cannot be induced to purchase from the rival firm with a feasible price incentive. The third segment of consumers consists of switchers with the size of α N 0. These are the price-sensitive consumers who always purchase from the lowest-priced firm as long as the lowest price is below their reservation price. We normalize the total market size to 1 so that we have 2γ + α = 1. We assume in our basic model that all consumers in this market have a common reservation price, which we normalize to 1 without any further loss of generality. In Section 4, we will extend our analysis to the case where switchers and loyal customers have different reservation prices. Firms in this market compete only for switchers. This set up is commonly used in the literature (Narasimhan, 1988; McGahan and Ghemawat, 1994; Chen et al., 2001), and is analogous to Varian (1980) where firms compete only for “informed” consumers. To model the dynamics of competition in this market where a firm can potentially recognize consumers who have purchased from the

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firm before, we assume that the competing firms play a two-period game. On the supply side, the size of each consumer segment is common knowledge to all firms. However, a firm can recognize a consumer's type only after it has sold to a single segment of consumers. This means that neither firm can recognize a consumer's type in the first period and hence a firm can only charge a uniform price in that period. This also means that a firm will not be able to distinguish between its own loyal customers and switchers if the firm has sold to them both in the first period. In that case, the firm has no choice but to charge a uniform price in the second period, too. However, if a firm sells to only one segment in the first period, we assume that the firm has the ability to recognize these “old” customers in the second period. Consequently, the firm can charge two prices in the second period: one for the identified segment and the other for the rest of the market which is not identified. We assume that the discount rate for both firms is δF ∈ (0, 1). In both periods, firms set their prices simultaneously. On the demand side, each consumer can buy at most one unit of the products from one of the two firms in each of the two periods. All consumers can rationally anticipate future prices and make their purchase decisions to maximize their total surplus. This means that a consumer can be strategic in that she may decide to forgo a purchase in the first period, in order to avail herself of a low price in the second period. We assume that the discount rate for consumers is δC ∈ (0, 1). All consumers and firms are risk neutral in our model. Before proceeding to analyze this model, we first establish the benchmark case where firms can automatically recognize consumers in the second period regardless of their purchase histories, while maintaining all other assumptions for our basic model. This benchmark case will help us to isolate the competitive effect of firms' actively pursuing customer recognition. As the payoffs for each firm in the second period are not history-dependent, we only need to examine each period separately to derive the equilibrium pricing strategy and payoffs for each firm in this benchmark game. Starting with the second-period game, we note that both firms can charge two segment-specific prices that are targeted, respectively, at their own loyal customers and switchers. In equilibrium, each firm will simply charge its own loyal customers a price equal to their maximum willingness-to-pay and switchers a price equal to its marginal cost. Therefore, the payoffs for each firm in the second period are γ. In the first period, consumers are anonymous such that each firm can only set one price. Following the same logic as that in Varian (1980), we can show that there is no pure-strategy equilibrium in this first-period game. However, a unique mixed-strategy equilibrium exists where both firms' equilibrium price supports are identical. This identical support is the set P = {p ∈ (p b, 1)}, where the lower bound of the price support p b is to be determined in equilibrium. In addition, we can also show that a firm's equilibrium price distribution has no mass point. To solve for the equilibrium distributions, let 0 ≤ Hit(p) ≤ 1 denote the probability that firm i's price in period t is greater than or equal to p, i.e. Hit(p) = 1 − Pr(pit b p), and πi denote firm i's profit in the first period.5 We refer to the rival firm as firm j. In any mixed-strategy equilibrium, if firm i charges p ∈ P, it sells to all of its loyal customers at that price and to all switchers, too, whenever the rival firm charges a higher price. Firm i's expected profit is then given by πi(p) = γp + αHj1(p)p. However, firm i can always guarantee itself a profit of γ by setting p = 1 such that all switchers in the market purchase from the rival firm with probability 1. As in any mixed-strategy equilibrium, a firm is necessarily indifferent among all prices in its price support, we must have gp + aHj1 ðpÞp = g;

ð2:1Þ

5 We define Hit(p) in this slightly unconventional way to be more convenient in expressing the mass point at the top of the price support which occurs in the second period equilibrium for the basic model.

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for all p ∈ P. We can solve for Hj1 from Eq. (2.1) and use the regularity conditions 0 ≤ Hj1(p) ≤ 1 to get Hj1 ðpÞ = p˜ b =


 g g  for all pa p˜ b ; 1 and j = A; B; ap a

g ; p = g: g+a j

ð2:2Þ ð2:3Þ

Thus, in this benchmark case, both firms use a “Hi-Lo” pricing strategy in the first period and implement targeted pricing in the second period. Despite the difference in pricing strategies across the two periods, a firm's payoffs from each period are identically γ, yielding a total profit of γ + δFγ from the two periods. Interestingly, this total profit is also the profit that a firm makes in this market if customer recognition is not feasible and neither can implement targeted pricing. This suggests that competitive targeted pricing enabled by automatic customer recognition yields no benefit to a practicing firm in this market. 3. Strategic implications of customer recognition In practice, customer recognition, the prerequisite for a firm to implement targeted pricing, comes about as a result of a firm actively pursuing it. In this section, we investigate the implications of the pursuit of consumer recognition by competing firms on the basis of consumer purchase history. Specifically, if a firm gains the patronage of only one segment of consumers in the first period, the firm can recognize them in the second period. If the firm sells to two segments instead, the firm cannot distinguish between price-sensitive and price-insensitive consumers in the second period. This means that the two periods in our game are no longer independent. We solve this game backward to derive the subgame-perfect equilibrium, assuming that any individual consumer is sufficiently insignificant so that her buying behavior alone will have no impact on either firm's pricing decision. 3.1. Benefit of dynamic targeted pricing 3.1.1. Equilibrium in the second period In the second period, a firm's pricing strategy depends on the history of price competition. Define pit as firm i's price in period t, where i = A, B and t = 1, 2. We have either pA1 N pB1 or pA1 b pB1, where both prices are less than or equal to 1—the maximum willingness-topay by all consumers. The probability of a tie in prices is zero in any first-period equilibrium. Otherwise, either firm could have lowered its price ever so slightly to secure the patronage of all switchers.6 Without any loss of generality, we consider the history where pA1 N pB1. In this case, a switcher must have purchased from Firm B in the first period. This is because if she were to purchase from Firm A at a higher price to pretend as a Firm A's loyal customer, she would have paid higher prices in both periods. If she were to forgo a purchase in the first period, the price charged to her in the second period by both firms would not have changed but she would have forgone a positive surplus, given pB1 b1. Similarly, Firm B's loyal customer must have purchased from Firm B in the first period, as forgoing a purchase would only forgo a positive surplus in the first period without affecting her treatment by both firms in the second period. All these imply that Firm B must have sold to both its own loyal customers and all switchers so that it can charge only a uniform price pB2 for all consumers, but Firm A can charge two prices in the second period, one targeted at its own loyal customers (pA2l ) and the other at switchers (pA2s ).

6 When a tie occurs, we assume that switchers are equally likely to purchase from either firm. This means that none of the firms can distinguish between its own loyal customers and switchers.

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However, Firm A's customer recognition need not be perfect, as some of Firm A's loyal customers may have decided to forgo a purchase in the first period in anticipation of a higher targeted price in the second period. To account for that possibility, denote 0 ≤ ψ ≤ 1 as the proportion of Firm A's loyal customers who have forgone a purchase. The size of ψ will, of course, depend on the anticipated difference between pA2l and pA2s and will be determined in equilibrium in the first period. As Firm A does not compete with Firm B for its own recognized loyal customers, it has no incentive to charge them anything other than pA2l = 1, their maximum willingness-to-pay, and makes a profit of πlA = (1 − ψ)γ from them. However, when setting pA2s , Firm A must compete with Firm B for the set of consumers that includes all switchers, all Firm B's loyal customers, and some of Firm A's loyal customers who have forgone a purchase. The price setting game for this sub-market is the same as that modeled in Narasimhan (1988). Using the same logic, we can show that a unique mixed-strategy equilibrium exists, which is characterized by two distribution functions HA2s (pA2s ) and HB2(pB2). The identical price support for both distribution functions is given by (pb, 1] with only Firm B having a mass point at 1. We will determine pb below in equilibrium. To derive the equilibrium, note that for any pA2s ∈ (pb, 1), Firm A's loyal customers who have pretended to be a switcher by forgoing a purchase in the previous period will always buy from the firm at that price and contribute to the firm's profitability in the amount of pA2sψγ. In addition, the firm also sells to switchers whenever the rival firm charges a higher price, which happens with probability HB2(pA2s ), and hence the firm's expected profit from switchers, πsA, is given by HB2 (pA2s )αpA2s . Then, in equilibrium, we should always have     psA = wg + HB2 psA2 a psA2 ; for all psA2 aðpb ; 1Þ:

ð3:1Þ

From Firm B's perspective, whenever it charges pB2 = 1, it will sell only to its own loyal customers and guarantee itself the profit of γ from the loyal segment. Thus, Firm B shall expect to make the same profit if it charges any other price from the price support in a mixedstrategy equilibrium, or πB2 = γ for all pB2 ∈ (pb, 1]. When charging a pB2 ∈ (pb, 1], Firm B's loyal customers will purchase at that price and switchers will also purchase at that price whenever Firm B's price happens to be lower, which happens with probability HA2s (pB2). In equilibrium we must have   s pB2 = g = g + HA2 ðpB2 Þa pB2 ; for all pB2 aðpb ; 1:

ð3:2Þ

Eqs. (3.1)–(3.2) are all the equations we need to solve for the equilibrium.7 We have in equilibrium g g  for all paðpb 1Þ; ap a 8 gðwg + aÞ wg > HB2 ð pÞ = >  for all paðpb 1 ; < aðg + aÞp a > > :0 if pN1:

s ðpÞ = HA2

psA =

  g ða + gÞ gðwg + aÞ g ; pB2 = g; pb = ; E psA2 = ln ; g+a g+a a g

ð3:3Þ

ð3:4Þ

where E (pA2s ) is the expected price charged to Firm A's unrecognized customers. As we show below, this expected price will affect the purchasing decision of Firm A's loyal customers in the first period.

7 From Eq. (3.2), we can solve for pb using the regularity condition HA2s (pb) = 1 and further for HA2s (p). Then, using the regularity condition HB2(pb) = 1 and the expression for pb, we can solve for HB2(p) and πsA from Eq. (3.1).

Then, Firm A's total profit in the second period is πA2 = πsA + πlA = γ + B, Þga where B = ð1w g + a . Note that, in this equilibrium, the firm that can institute targeted pricing always makes a higher profit than the firm that cannot, i.e. πA2 N πB2, if ψ b 1. As these two firms are otherwise symmetric, the difference between their profits, i.e. B, must measure the benefit of price discrimination to a firm. This benefit is what motivates a firm to pursue customer recognition in devising its pricing strategy in the first period. 3.1.2. Equilibrium in the first period In the first period, a firm makes its pricing decision, rationally anticipating how such a decision may affect the firm's payoff in the second period. Once again, the same reasoning as in Varian (1980) and Narasimhan (1988) shows that there exists no pure-strategy equilibrium, but a unique mixed-strategy equilibrium exists. The equilibrium distribution function Hi1(p), where i = A, B, is continuous with no mass point over the price support (p b, pt). Both 0 b p b and pt ≤ 1 are to be determined in equilibrium. Let πi be Firm i's equilibrium profit from both periods. We now derive this equilibrium. Note that if pA1 N pB1, a Firm A's loyal customer should rationally anticipate that the firm will implement targeted pricing in the second period. If the consumer proceeds to purchase in the first period, she will be identified as a loyal customer and be charged a price of pA2l in the second period. Her total surplus from the two periods is 1 − pA1 + δC(1 − pA2l ). However, if she were to forgo a purchase, she will be charged a switcher's price pA2s subsequently, which has an expected value of E(pA2s ) given in Eq. (3.5). In that case, her total expected surplus is δC[1 − E(pA2s )]. Thus, a Firm A's loyal customer will not forgo a purchase if
    1  pA1 + dC 1  plA2 zdC 1  E psA2 or   s  P pA1 V1  dC 1  E pA2 = p:

ð3:5Þ

The p ¯¯ in Eq. (3.6) is, in fact, the highest price that Firm A will ever charge in any first-period equilibrium and hence it is the pt in the price support. To see this, note that E(pA2s ) does not depend on ψ. This ¯¯, none of a firm's loyal customers means that if pt is ever larger than p will make any purchase from the firm in the first period when the firm charges pt, and nor will any switcher. Then, the firm makes zero profit in the first period. In the second period, none of the firms can recognize consumers and they each make their guaranteed profit of γ. ¯¯ cannot be an equilibrium because it is dominated by Therefore pt N p ¯¯. When pt = p ¯¯, a firm makes a positive profit in the first setting pt = p period and at least the guaranteed profit γ in the second period (by ¯¯ is also dominated by simply fixing its price at 1). In addition, pt b p ¯¯ because by increasing pt to p ¯¯ a firm will gain additional margin pt = p without losing any demand (the demand from loyal customers is still ¯¯ γ at p ¯¯ and the demand from switchers is 0 at pt). Thus, we have pt = p in any equilibrium and we must have pA1 ≤ p¯¯. Because of this, we necessarily have ψ = 0 in any first-period equilibrium. In other words, none of a firm's loyal customers will be given an incentive to fake switchers in the first period. To determine Hi1(p), we note that if Firm i sets a price pi1 ∈ (pˆb, pt), its profit from its loyal customers in the first period is γpi1. The firm also sells to switchers at that price in the first period whenever the rival's price is higher, generating an expected profit of Hj1(pi1)αpi1 from these customers. This price will also affect the firm's payoff in the second period. With a probability of Hj1(pi1), the rival firm's price is higher than Firm i's in the first period. In that case, only the rival firm can recognize consumers and Firm i's expected profit in the second period is γ, as we have discussed before. However, with a probability of (1 − Hj1(pi1)), Firm i's price in the first period is higher and it becomes the sole firm that can recognize consumers. In that case, the firm's expected profit in the second period is given by πA2. Since in a

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mixed-strategy equilibrium, any price from a firm's price support should generate the same expected profit for the firm, we must have   pi = g + Hj1 ðpi1 Þa pi1

    ga + dF Hj1 ðpi1 Þg + 1  Hj1 ðpi1 Þ g + ; for p b bpi1 bpt : g+a

ð3:6Þ

Solving Eq. (3.7) and using regularity conditions Hj1(pˆb) = 1 and Hj1 (pt) = 0, we have the equilibrium results as follows:  gpt + dF gga g ðg + aÞ ˆ +a ; ; pb = pt = 1  dC 1  ln g+a  a g ga pi = gpt + dF g + ; g+a

 g pt  dF g g+ a g   for all pa pˆ b ; pt and j = A; B: Hj1 ð pÞ =
a a p  dF g g+ a

ð3:7Þ

ð3:8Þ

By comparing this equilibrium with that of the benchmark case, we can isolate the profit impact of firms pursuing customer recognition. Let ¯¯ F b 1.8 We have the following proposition. dF = ð1  pt Þ g a+ a, where 0 ≤δ Proposition 1. Dynamic targeted pricing based on consumer purchase history can benefit all competing firms, even when consumers behave strategically, if δF N δ¯¯F. Firms are better off because their pursuit of customer recognition has the strategic effect of moderating price competition. The first part of Proposition 1 can be deduced from the fact that πi in Eq. (3.8) is always larger than γ +δFγ, the total profit that a firm makes when customer recognition is either infeasible or automatic, if δF N δ¯¯F. An immediate implication from the comparison is that the competing firms are better off not because of their ability to implement targeted pricing, but critically because of their active pursuit for customer recognition. Why is the competing firms' quest for customer recognition so critical? 3.2. Customer recognition and price competition To address that question, we need to derive a firm's equilibrium payoff in the first period. We do so by first deriving πi2, a firm's expected payoff in the second period. Note that in the second period, a firm's payoff is either γ when customer purchase history does not allow the firm to implement targeted pricing or g + B when it does, where B = gga + a as ψ = 0. However, whether or not a firm achieves customer recognition depends on whether the firm's price in the first period is higher or lower than the rival's. With the equilibrium price distribution functions being symmetrical, a firm ends up having an equal chance of charging a higher or lower price. This means that the expected payoff for a firm in the second period is given by Epi2 = dF

  1 1 1 g + ðg + BÞ = dF g + B : 2 2 2

ð3:9Þ

Then, the first period expected profit can be easily derived from πi in Eq. (3.8). We have 1 ð3:10Þ Epi1 = pi  Epi2 = gpt + dF B: 2 With customer recognition, a firm's expected payoff in the second period is unambiguously higher in comparison with that in the benchmark case, as Eπi2 N δFγ. The gain is entirely due to price

47

discrimination enabled by customer recognition. This benefit has been previously studied in the context of different models (Shaffer and Zhang 2002; Chen et al., 2001). The comparison for the firm's firstperiod profits is rather ambiguous. The first term in Eq. (3.10), γpt, is the firm's guaranteed payoff from loyal customers, which is no higher than γ, the first-period profit in the benchmark case, given pt ≤ 1. The lower payoff captures the downward pressure on price exerted by consumer forward-looking behavior. This downward pressure is captured in Villas-Boas (2004) and it increases with δC. Surprisingly, however, the benefit of targeted pricing B also enters the firm's expected payoff in the first period, even though targeted pricing is not possible in that period. Whence comes this additional term for the firm's payoff in the first period? To answer that question, we need to delineate the strategic incentives facing the competing firms and those facing forward-looking consumers. We can easily do so by setting δC = 0–all consumers are myopic–such that only the strategic incentives facing the competing firms are present. In that case, we have pt = 1 and Epi1 = g + dF 12 B. By comparing Eπi1 here with that in the benchmark case, we can readily recognize that the firms' active pursuit for customer recognition in the first period raises their payoffs in the amount of dF 12 B, which explains the second term in Eq. (3.10)). Intuitively, to achieve customer recognition, a firm's price must be “exclusive” enough so that it does not sell to all consumers in the market. However, exclusivity can be achieved only through a high price relative to the price that the rival firm charges. In other words, the benefit of price discrimination in the second period motivates a firm to price high in the first period to achieve necessary exclusivity or selectiveness in order to glean more precise, actionable customer information, which in turn induces the rival firm to price less aggressively. Indeed, as a firm becomes more patient, it has more an incentive to capture the benefit of targeted pricing in the second period and hence faces more an incentive to price higher than the competition to achieve customer recognition. By analyzing δ¯¯ F in Proposition 1, we can also see that the cutoff point increases with δC and decreases with γ (or increases with α). These comparative statics suggest that in the industries where consumers tend to be less patient, either due to a low price (Loewenstein and Prelec,1992) or due to a long consumer purchase cycle, or where there are more priceinsensitive consumers, firms are more likely to benefit from dynamic targeted pricing. Therefore, those are the kinds of industries where firms should have more an incentive to implement dynamic targeted pricing and where one is more likely to observe this pricing mechanism. It is important to note that the strategic effect of customer recognition here is quite distinct from what Fudenberg and Tirole (2000) have identified. In their model, customer poaching in the second period reduces marginal consumers' price sensitivity for their firstperiod purchases, which in turn provides a firm with incentives to raise its first-period price. This demand-driven effect hinges critically on consumer foresight, and it disappears when consumers are myopic. Said differently, when consumers are myopic, the first-period prices in Fudenberg and Tirole (2000) are the same regardless of whether or not customer poaching is allowed. Indeed, a firm's consideration of the second-period payoffs, when making the first-period pricing decision, is always negligible in the neighborhood of the symmetrical equilibrium they analyze. Therefore, a forward-looking firm will not distort its firstperiod pricing decision if it were not for the fact that customer poaching reduces the price sensitivity of forward-looking consumers in the first period. In contrast, the strategic effect in our model captures the supplyside incentive that a forward-looking firm faces when dynamic targeted pricing is feasible. The existence of this incentive hinges only on a firm's foresight, not at all on consumer foresight. 4. Extension

8

To show 0 ≤ δ¯¯ F b 1, we note, first of all, δ¯¯ F = 0 when δ C = 0. Further, it is straightforward to show that δ¯¯F is monotonically increasing with δC. However, we have δ¯¯F b 1 when δC = 1.

In our basic model, we have assumed that both switchers and loyal customers have an identical reservation price. However, we can

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Y. Chen, Z.J. Zhang / Int. J. Ind. Organ. 27 (2009) 43–50

extend our analysis with little difficulty to allow the more realistic possibility that the reservation price for switchers is smaller than that for loyal customers. As we show in Appendix (1), when switchers have a lower reservation price s, where s b 1, the solutions are more complex. The additional complexity comes from the fact that switchers may not purchase when the prices in the market are too high relative to what they are willing to pay. However, as we also show in Appendix (1), Proposition 1 is not qualitatively altered. Aside from showing the robustness of our conclusions, this extension also allows us to gain two additional insights. The first one is about the welfare implications of dynamic targeted pricing and the second the interaction effect between competition and targeted pricing. In our basic model, social welfare is unchanged relative to the benchmark case such that whenever firms are better off, consumers are worse off, if δF =δC. As we show in Appendix (2), this conclusion need not always be true when s b 1. Proposition 2. Customer recognition and targeted pricing in the presence of strategic consumers can improve social welfare as long as δF ≥ δC. Such improvement may result from both higher profits and higher consumer surplus or from higher profits but lower consumer surplus. Relative to the benchmark case, social welfare improves here because targeted pricing allows a firm to separate loyal customers from switchers and, along with firms' efforts to discourage waiting, allows many more switchers to purchase in both periods. This market expansion effect is noticeably absent in the previous literature on competitive targeted pricing based on consumer purchase history. Without this market expansion effect, the previous research, e.g. Chen (1997) and Fudenberg and Tirole (2000), has come to the opposite conclusion that dynamic targeted pricing is welfare reducing, as its net effect is only to induce consumers to purchase less preferred products. The second insight uncovers the interaction effect between competition and targeted pricing. The strategic effect we have identified in the context of dynamic targeted pricing is quite different from the effect that has been examined by a number of seminal studies, such as Kihlstrom et al. (1984) and Mirman et al. (1993), where a firm may experiment with its initial prices or quantities (away from their myopically optimal level) to ascertain its future aggregate demand. Such experimentation reduces a firm's current profits, but enhances the informativeness of observed market outcomes and hence increases its future profits. As Mirman et al. (1994) have subsequently shown, such information-seeking experimentation, when carried out, always benefits a monopolist but, in the context of duopoly, players may all become worse off because of it. In contrast, a firm in our model distorts its initial price to identify specific segments of the market demand and to bid for the benefit of targeted pricing. It turns out that this kind of price “experimentation” generates a paradoxical outcome special only to behavior-based targeted pricing. The following proposition makes this clear. Proposition 3. Competition amplifies the strategic effect of price moderation. As a result, dynamic targeted pricing based on consumer purchase history may benefit practicing duopolists but make a monopolist worse off. Proposition 3 can be shown by conducting a thought experiment: what would happen if competition were to disappear in the extended model and only a monopoly firm were to sell to its loyal customers of size γ and to the switchers of size α? To carry out this thought experiment, we continue to use the same notations and terminology as in the competitive case and let Firm A be the monopolist. As in the competition case, we assume that each consumer buys at most one unit of the product in each of the two periods and that the monopolist sells to both segments of consumers if targeted pricing is not feasible as we have by assumption sN g g+ a. Thus, if targeted pricing is not

feasible, the firm will set pA1 = pA2 = s in both periods and obtain a total profit of πN = s(γ + α) + δFs(γ + α). In the benchmark case with automatic customer recognition, i.e., when targeting is exogenous and none of the consumers in the market can behave strategically to avoid being targeted in the second period, the monopolist will set pA1 = s in the first period, and pA2l = 1 to the loyal segment and pA2s = s to the switcher segment in the second period. Its total profit in this case is πM = s(γ + α) + δF(γ + sα). We can easily see that we have πN b πM. This means that targeted pricing makes the monopolist better off if customer recognition is automatic. In practice, customer recognition is not automatic, of course. When the monopolist actively pursues customer recognition through pricing and consumers behave strategically, some loyal customers may decide to forego a purchase in the first period in order to get a low price in the second period. Let ϕ denote the fraction of loyal customers who forgo a purchase in period 1. In the second period, given sN g g+ a, the monopolist optimally charges s to all customers who are not recognized as loyal customers for any given ϕ and charges 1 to the recognized loyal customers. Therefore, the surplus for the loyal customers who forgo a purchase in period 1 is δC(1 − s) and the surplus for the loyal customers who purchase in period 1 is 1 − pA1. Then, a loyal customer will purchase in the first period only if the inequality 1 − pA1 ≥ δC(1 − s) is satisfied, or pA1 V pt ; where pt = 1  dC ð1  sÞ:

ð4:1Þ

As pt in Eq. (4.1) is not a function of ϕ, we must have ϕ = 1 if pA1 Npt and ϕ = 0 if otherwise. In addition, we should also have pt N s as δC ∈ (0, 1). The monopolist has two alternative strategies in this game: (1) use targeted pricing by setting p1 =pt in the first period, pA2l = 1 to the loyal segment and pA2s =s to the switcher segment in the second period; or (2) do not use targeted pricing by setting pA1 =pA2 =s in both periods. The total profit from the first alternative is πT =ptγ +δF(γ +sα) = [1 −δC(1 −s)] profit from the second is πN =s(γ +α) +δFs(γ+α). γ +δF(γ +sα) and the total s g+ a , which is always satisfied if δC ≥δF, we must have Then, if dC NdF  g ðg1s Þ g +a πT bπN. This means that the monopolist prefers not to use targeted pricing. As we also have πN b πM, it is clear that targeted pricing per se does not make the monopolist worse off, but the existence of strategic consumers does. In other words, the monopolist can become worse off if it were to pursue customer recognition for the purpose of implementing targeted pricing, while a firm facing competition may benefit from such a pursuit. Proposition 3 is consistent with the conclusion of Villas-Boas (2004) and Acquisti and Varian (2005). This paradoxical outcome is quite intuitive in hindsight. The feasibility of dynamic targeted pricing gives a monopolist only the option to tradeoff the loss of current profit against the benefit of targeted pricing. However, competing firms can gain the additional strategic benefit of moderated price competition. This role of competition in amplifying the strategic effect thus suggests that firms in a more competitive industry tend to be better positioned to benefit from dynamic targeted pricing. 5. Conclusion Customer recognition based on consumer purchase history is perhaps the most common way to implement targeted pricing in practice. However, little research has been done to assess the viability and profitability of this practice in the long run. Specifically, it is not clear whether this form of targeted pricing can benefit practicing firms with the emergence of strategic consumers. We address that issue here in a competitive context. Our main conclusion is that, even if consumers in a market behave strategically, dynamic targeted pricing based on consumer purchase history can still benefit a firm. Surprisingly, however, competing firms are better positioned than a monopolist to reap the benefit. This is because competitive pursuit of customer recognition with the

Y. Chen, Z.J. Zhang / Int. J. Ind. Organ. 27 (2009) 43–50

presence of strategic consumers can significantly reduce price competition, in addition to the benefit of price discrimination. This conclusion has two significant implications. First, from a theoretical perspective, it identifies an economic mechanism through which firms may benefit from dynamic targeted pricing and hence advances our understanding of a burgeoning pricing practice. Second, from the perspective of practice, it suggests a profitable future for this form of targeted pricing, especially in a competitive industry. Indeed, this form of targeted pricing can also be a blessing for consumers and the society as a whole. Our analysis shows that consumer welfare and social welfare may all increase because of competitive targeted pricing based on consumer purchase history. Future research can investigate the robustness of our conclusions by incorporating inventory constraints and other marketing variables besides price, and through empirical studies. It will also be interesting for future research to analyze multi-period contracts in the context of dynamic pricing with customer recognition. Appendix A (1). Model extension To solve the extended model where s b 1, we assume that sN g g+ a so that both firms always have incentives to sell to switchers. To proceed, we first prove a general lemma. Lemma 1. Let the size of firm i's loyal customers be βi, that of firm j's loyal customers βj, and the size of switchers be α. If each firm can only set b one price, βi ≤ βj, sN bi b+i a and sN bj +j a, then, (1) if βi = βj, we must have h i bi bi bi  bai , and Eðpi Þ = bai ln sðbib+ aÞ + as πi = βi, Hi ð1Þ = as  a ; (2) if
βi b βj, we i sðbj + aÞ bj b b ðbj bi Þa + asj  aj s. must have pi = bi + b + a , πj = βj, and Eðpi Þ = a ln b j

j

Proof. Following the same logic of Varian (1980) and Narasimhan (1988), there is no pure-strategy equilibrium in this game, but there is a unique mixed-strategy equilibrium. If βi = βj, firms' equilibrium price support is {1} ∪ (pb, s), where pb is to be determined in the equilibrium. If βi b βj, the equilibrium price supports for firm i and firm j are (pb, s] and {1} ∪ (pb, s) respectively. If βi = βj, We have that, in the equilibrium, pi = b  i ðif pi = 1Þ  pi = bi + Hj ðpi Þa pi ðif pb bpi bsÞ: Solving the above equations with the regularity condition Hi(pb) = 1, bi  bai and we have the equilibrium results as follows: πi = βi, Hi ð1Þ = as bi Hi ðpÞ = ap  bai ðpb bpi bsÞ, pb = h i sðbi + aÞ bi bi  bai . + as a ln b

bi bi + a,

i ð pÞ and Eðpi Þ = ∫psb p ∂H dp + Hi ð1Þ = ∂p

i

Similarly, if βi b βj, we have that in the equilibrium,   pi = bi + Hj ðpi Þa pi ðif pb bpi VsÞ pj = bj if pj = 1       pj = bj + Hi pj a pj if pb bpj bs : Solving the above equations with the regularity condition Hi(pb) = 1, ðb b Þa we have the equilibrium results as follows: pi = bi + bj j + ia , πj =βj, b

b

Hi ðpÞ = apj  aj ðif pb bpi VsÞÞ, pb =
 sðbj + aÞ bj b b + asj  aj s. □ a ln bj

bj bj + a,

i ð pÞ and Eðpi Þ = ∫psb p ∂H dp + sHi ðsÞ = ∂p

No Targeting Case: For the case where firms do not have the ability to target, the two periods are identical and independent. Denote πik to be firm i's profit in period k. From Lemma 1, we have πik = γ and the total profit, πN, for each firm is γ + δFγ. The probability mass, q , at pi = 1 g  ga. is qˆ = Hi ð1Þ = as Automatic Targeting Case: In the case with automatic targeting in the second period, each firm will charge loyal consumers pi2l = 1 and

49

switchers pi2s = 0 in the second period. The first period is the same as the no targeting case. Therefore the profit from the second period is πi2 = γ and the total profit is πM = γ + δFγ. In the first period, the g  ga. probability mass, qˆ, at pi = 1 is qˆ = Hi ð1Þ = as Dynamic Targeted Pricing: Suppose that 1 ≥ pA1 N pB1 and pB1 ≤ s in the first period. A switcher will buy from Firm B. This is because if she bought from Firm A to pretend as Firm A's loyal customer, she would pay higher prices in both periods. If she did not purchase at all in the first period, she would pay the same price as other switchers in the second period but would forgo a positive surplus in the first period since pB1 ≤ s. Similarly, a loyal consumer to Firm B will also buy from Firm B in this case. However, in this case a loyal consumer of Firm A may have incentive to forgo purchase in the first period. We denote ψ as the proportion of Firm A's loyal consumers who forgo purchases in the first period when 1 ≥ pA1 N pB1 and pB1 ≤ s. We first look at the second-period game under this case. Lemma 1, we have psA = Obviously, pA2l = 1 and πlA = (1 − ψ)γ. From  s  g hsðg + aÞi  g g ðgwgÞa g + as  a s. Therefore wg + g + a , π B2 = γ,pb = g + a,E pA2 = a ln g

Þa pA2 = plA + psA = g + ðgwg g+a . If a loyal consumer of Firm A purchases at pA1, her expected surplus in two periods is 1 −pA1 +δC(1−pA2l ) = 1 −pA1. On the other hand, if this loyal consumer forgoes the purchase in the first period, her expected surplus in two periods is δC(1 −E(pA2s )). Therefore, the condition for a loyal consumer to purchase from Firm A when 1 ≥pA1 N pB1 and pB1 ≤s is

      1  pA1 z dC 1  E psA2 Z pA1 V 1  dC 1  E psA2

  g sðg + aÞ
g g +  s = pt : = 1  dC 1  ln a g as a The above condition is invariant with ψ since E(pA2s ) is not dependent on ψ. We focus on the case when pt ≤ s which leads to a unique symmetric equilibrium and is sufficient to show that the main conclusions of Proposition 1 can still hold for s b 1. When pt ≤ s, (pˆb, pt) is the firms' first-period equilibrium price support where pb is to be determined in the equilibrium. The reasons are as follows. First, when pt ≤ s, the equilibrium distribution on (pˆb, pt) is continuous with no mass point because each firm can undercut the other's price by an arbitrarily small amount and obtain the demand of all the switchers. This is similar to Varian (1980). Second, given firm i's price support (pˆb, pt), it is not optimal for firm j to have pj1 N pt as this leads to zero demand for firm j in the first period. Third, it is not optimal to have the upper bound of the price support below pt as a firm can increase this upper bound to pt with demand unchanged. Finally, it is not optimal for firm j to have pj1 b pb given the other firm's price support as (pˆb, pt) because this leads to the same demand as pj1 = pb but with lower margin. Because pt is the upper bound of equilibrium price support, we have ψ = 0 in this equilibrium. We are now ready to solve for the first-period game. If pt ≤s, we have   pi = g + Hj1 ðpi1 Þa pi1



     ga + dF Hj1 ðpi1 Þg + 1  Hj1 ðpi1 Þ g + if pˆ b b pi1 b pt : g+a Solving the above equation with the regularity conditions Hi1(pˆb) = 1 results as follows: and H j1 (pˆ
b ) = 1, we  have theg pequilibrium ð t dF g g+ aÞ g , H  ð p Þ = ð pi = gpt + dF g + gga p ˆ i1 b bpbpt ; i = A; BÞ a n d +a a aðpdF g g+ aÞ gpt + dF g ga p b = g + a + a. Similar to the basic model, we can also
calculate  the firms' expected profits in each period. We have Epi2 = dF g + 12 gga + a and Epi1 = gpt + dF 12 gga + a. n The h condition  g for  iπoi N π M = π N implies that: if pt = 1  dC 1  ga ln sðg g+ aÞ + as  ga s Vs, pi NpM = pN Z dF NdF = ð1  pt Þ g a+ a. I n particular, π i N π M = π N always holds when δ F = δ C = 1. If δ F = δ C =1,

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h  g g i π M = π N = 2 γ, and we have pt = ga ln sðg g+ aÞ + as  a s bs because   ∂ðpt sÞ g 1 g g j =  1  1b0 as sN and p j  s = 0. Therefore, t sY sb1 a s g+a ∂s n n  g g o gga+ a sðg + aÞ g we have pi  2g = g a ln g + as  a s + g + a  g = g ga ln sðg g+ aÞ +  g g  g g   sðg + aÞ g g + as  a s = E psi2 Npb = g g+ a. as  a s  g + agN0 because a In g Hence, from the results derived here, we can see that the main conclusions of Proposition 1 can still hold for s b 1 case. (2). Analysis of social welfare As we assume away costs of production, total social welfare (SW) in this market is given by the sum of total consumer surplus and firms' profits in the two periods. We have CS1 = 2g + as  2Epi1 = 2g + as  2gpt  dF

ga g+a

ðA:1Þ



2Epi2 ga = dC 2g + as  2g  CS2 = dC ð2g + asÞ  dF g+a

ðA:2Þ

SW = CS1 + 2Epi1 + CS2 + 2Epi2

ðA:3Þ



ga = 2g + as + dC ð2g + asÞ + ðdF  dC Þ 2g + g+a

ðA:4Þ

where CS1 and CS2 are consumer surplus in each period, Eπi1 and Eπi2 are firms' expected profits in each period derived in Appendix (1). The term 2γ in above expressions is the social welfare resulting from consumption by the two firms' loyal customers as the size of those loyal consumers is 2γ and their reservation price is 1. The term αs in above expressions is the social welfare resulting from consumption by switchers as they have a segment size of α and a reservation price of s. The corresponding welfare expressions for the benchmark case with automatic targeting in the second period are given by h
 i 2 CSM1 = 2g + a 1  qˆ s  2g

ðA:5Þ

CSM2 = dC ð2g + as  2gÞ

ðA:6Þ

SWM = CSM1 + 2g + CSM2 + dF ð2gÞ

ðA:7Þ 2

= 2g + as + dC ð2g + asÞ + ðdF  dC Þð2gÞ  a qˆ s:

ðA:8Þ

The term α(1 − qˆ2)s in the above expressions is the social welfare resulting from consumption by switchers in the first period. Switchers have a segment size of α and a reservation price of s, and they purchase with 1 − qˆ2 probability (i.e., the probability that at least one firm sets a price equal to or below s) in the first period. Similarly, the welfare expressions for the no targeted pricing case are given by h
 i 2 CSN1 = 2g + a 1  qˆ s  2g CSN2 = dC

nh


 i o 2 2g + a 1  qˆ s  2g

SWN = CSN1 + 2g + CSN2 + dF 2g 2 2 = 2g + as + dC ð2g + asÞ + ðdF  dC Þð2gÞ  a qˆ s  dC a qˆ s:

ðA:9Þ ðA:10Þ ðA:11Þ ðA:12Þ

Obviously, SWN SWM N SWN when δF ≥δC and s b 1 (so that qˆ N 0). The remaining claims in Proposition 2 on firms' profits and consumer welfare can be numerically verified. For example, when g = a = 13 ; δC =δF =1 and s =0.8 we have pt =0.67, SW= 1.87N SWM =1.85N SWN =1.83, pi = 0:72NpM = pN = 23, CS=0.42b CSN =0.50 b CSB =0.52. When g = a = 13 ; δ C = δ F = 1 and s = 0.6, we have p t = 0.58, SW = 1.73 N SW M = 1.64 N SWN = 1.56, pi = 0:69NpB = pN = 23, CS = 0.35 N CSB = 0.31 N CSN = 0.22. In the latter case, the improvement in social welfare results from both higher profits and higher consumer surplus; and in the former case, it results from higher profits but lower consumer surplus. □ References Acquisti, Alessandro, Varian, Hal R., 2005. Conditioning prices on purchase history. Marketing Science 24 (3), 367–381. Bergemann, Dirk, Välimäki, Juuso, 1996. Learning and strategic pricing. Econometrica 64 (5), 1125–1149. Bergemann, Dirk, Välimäki, Juuso, 2006,. Dynamic price competition. Journal of Economic Theory 127 (1), 232–263. Chen, Yongmin, 1997. Paying customers to switch. Journal of Economics and Management Strategy 6, 877–897. Chen, Yuxin, Narasimhan, Chakravarthi, Zhang, Z. John, 2001. Individual marketing with imperfect targetability. Marketing Science 20 (1), 23–41. Feinberg, Fred, Krishna, Aradhna, Zhang, Z. John, 2002. Do we care what others get? A behaviorist approach to targeted promotions. Journal of Marketing Research 39, 277–291 (August, 2002). Fudenberg, D., Tirole, J., 2000. Customer poaching and brand switching. RAND Journal of Economics 31, 634–657. Hamilton, P. David, “The Price Isn't Right: Internet pricing has turned out to be a lot trickier than retailers expected,” The Wall Street Journal, 02/12/2001. Kambil, Ajit, Wilson III, H. James, Agrawal, Vipul, 2002. Are you leaving money on the table. Journal of Business Strategy 23, 40–44. Kihlstrom, Richard, Mirman, Leonard J., Postlewaite, A., 1984. Experimental consumption and the ‘Rothschild effect. In: Boyer, M., Kihlstrom, R.E. (Eds.), Bayesian Models of Economic Theory. Elsevier, Amsterdam. Loewenstein, George, Prelec, Drazen, 1992. Anomalies in intertemporal choice: evidence and an interpretation. Quarterly Journal of Economics 107 (2), 573–597 May. McGahan, A.M., Ghemawat, Pankaj, 1994. Competition to retain customers. Marketing Science 13 (2), 165–176 Spring. Maw, Adah, 2002. Dynamic pricing. Center for Marketing Newsletter, London Business School 1, 2–4. Mirman, Leonard J., Samuelson, Larry, Urbano, Amparo, 1993. Monopoly experimentation. International Economic Review 34, 549–563. Mirman, Leonard J., Samuelson, Larry, Schlee, Edward E., 1994. Strategic information manipulation in duopolies. Journal of Economic Theory 62, 363–384. Narasimhan, Chakravarthi, 1988. Competitive promotional strategies. Journal of Business 61 (4), 427–449. Rossi, P.E., McCulloch, R.E., Allenby, G.M., 1996. The value of purchase history data in target marketing. Marketing Science 15, 321–340. Su, Xuanming, 2006. Inter-temporal Pricing with Strategic Customer Behavior. manuscript. Shaffer, Greg, Zhang, Z. John, 1995. Competitive coupon targeting. Marketing Science 14 (4), 395–416. Shaffer, Greg, Zhang, Z. John, 2000. Pay to switch or pay to stay: preference-based price discrimination in markets with switching costs. Journal of Economics and Management Strategy 9, 397–424 (Fall, 2000). Shaffer, Greg, Zhang, Z. John, 2002. Competitive one-to-one promotions. Management Science 48 (9), 1143–1160. Taylor, C., 2003. Supplier surfing: competition and consumer behavior in subscription markets. RAND Journal of Economics 34 (2), 223–246 Summer 2003. van Ryzin, G., Liu, Q., 2005. Strategic Capacity Rationing to Induce Early Purchases. manuscript. Varian, R. Hal, 1980. A model of sales. American Economic Review 70 (4), 651–659. Villas-Boas, J. Miguel, 1999. Dynamics competition with customer recognition. RAND Journal of Economics 30, 604–631. Villas-Boas, J. Miguel, 2004. Price cycles in markets with customer recognition. Rand Journal of Economics 35 (3), 486–501.