Personalized Pricing and Quality Differentiation on the Internet

Transcription

1 Review of Marketing Science Working Papers Volume 2 Issue 1 Article Personalized Pricing and Quality Differentiation on te Internet Anindya Gose Carnegie Mellon University, agose@andrew.cmu.edu Vidyanand Coudary University of California, Irvine, veecee@uci.edu Tridas Mukopadyay Carnegie Mellon University, tridas@andrew.cmu.edu Uday Rajan Carnegie Mellon University, urajan@umic.edu Follow tis and additional works at: ttp://services.bepress.com/roms Recommended Citation Gose, Anindya; Coudary, Vidyanand; Mukopadyay, Tridas; and Rajan, Uday (2002) "Personalized Pricing and Quality Differentiation on te Internet," Review of Marketing Science Working Papers: Vol. 2: Iss. 1, Article 3. Available at: ttp://services.bepress.com/roms/vol2/iss1/paper3 Tis Working Paper is brougt to you for free and open access by Berkeley Electronic Press Services. It as been accepted for inclusion in Review of Marketing Science Working Papers by an autorized administrator of Berkeley Electronic Press Services.

2 Personalized Pricing and Quality Differentiation on te Internet Abstract No canges were made in te Abstract. Please use te previous Abstract tat was submitted Keywords Vertical Differentiation, Personalization, Price Discrimination, Electronic Commerce Tis working paper is available in Review of Marketing Science Working Papers: ttp://services.bepress.com/roms/vol2/iss1/paper3

3 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet Personalized Pricing and Quality Differentiation on te Internet Vidyanand Coudary Anindya Gose Tridas Mukopadyay Uday Rajan GSIA Carnegie Mellon University Pittsburg, PA t May 2002 We are grateful to seminar participants at WISE 2001 and Carnegie Mellon University, and to Kannan Srinivasan for elpful comments. All errors remain our own responsibility. Tel: (412) , Tel: (412) , Tel: (412) , Tel: (412) , Publised by Berkeley Electronic Press Services,

4 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 Vidyanand Coudary is an Assistant Professor of MIS at te Graduate Scool of Management, University of California at Irvine. He received is P.D. in Management from Purdue University. His researc interests are in te Economics of Information Systems, Impact of emerging tecnologies on firm s business strategies, analytical modelling of electronic marketplaces, product differentiation and price discrimination, Inter-temporal pricing of software products and upgrades. Anindya Gose is a Doctoral candidate in Information systems GSIA, Carnegie Mellon University. His primary area of interests is in te application of Game Teory to Industrial Organization in areas suc as Personalization in Online Business-to-Consumer commerce and modelling te impact of Internet Intermediaries on marketing cannel structures. Tridas Mukopadyay is Deloitte Consulting Professor of e-business at Carnegie Mellon University. He is also te Director of te Institute for ecommerce and MSEC (Master of Science in Electronic Commerce) program at CMU. He received is P.D. in Computer and Information systems from te University of Micigan in His researc interests include business-to-business commerce, Internet use at ome, business value of information tecnology, and software development productivity. In addition, Professor Mukopadyay as worked wit several organizations, suc as General Motors, Ford, IBM, Diamond Tecnology Partners, Crysler and Texas Instruments. He as been on te committee of several doctoral candidates in various disciplines, including marketing and information systems. He as publised in several journals, including Management Science and Information Systems Researc. Uday Rajan is an Associate Professor of Economics and Finance at GSIA, Carnegie Mellon University. He received is P.D. in Economics from Stanford University. He as been on te committee of several doctoral candidates in various disciplines, including economics, finance, marketing, and information systems. His main researc areas include Game Teory and applications of Game Teory to Finance and Industrial Organization. He as publised in several journals, including te American Economic Review, te Journal of Economic Teory, and te Journal of Financial Economics. 1 ttp://services.bepress.com/roms/vol2/iss1/paper3 2

5 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet Corresponding Autor : Anindya Gose, Pone: (412) Publised by Berkeley Electronic Press Services,

6 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 Abstract In uncertain environments, e-tailers learn about te most pro table prices troug price experimentation. Indeed, in tis electronic environment online retailers can easily experiment wit di erent prices to o er to di erent consumers. Retailers using te Internet as a medium for commerce can gater a remarkable wealt of information about teir existing and potential customers, and ence better estimate a consumer's reservation price. As Bakos (2001) reports, tecnology allows rms to identify and track individual consumers, bot witin an online store and across di erent websites. Tis leads to te creation and saring of consumer pro les, matcing of consumer identities wit relevant demograpic information and comparison wit te preferences of similar consumers troug various collaborative and content ltering tecniques. Based on suc information, te computing power of te Internet retailers' web server can be used to deploy complex pricebots and algoritms to determine prices to approac rst-degree price discrimination. Spurred partly by te low menu cost of canging prices on te Internet and partly as a response to consumer use of price-comparison sopbots, rms are exploring te idea of personalized prices for goods and services tat are currently sold at posted prices. Personalized pricing requires some knowledge of eac consumer's preferences, and an ability to carge di erent prices to di erent consumers. Te price o ered to a consumer wose valuation for a product is known may be iger or lower tan te posted uniform price carged by rms wo lack te sopistication to target individual consumers. In tis paper, we use te term personalized pricing, or PP, to refer to tecnologies tat facilitate suc rst-degree price discrimination. A retailer tat invests in PP can identify individual consumers, infer consumer valuations, and determine a consumer's willingness to pay for its product. Tis retailer can terefore o er a personalized price tat may provide te consumer greater surplus relative to te potential surplus from competitors' products. We develop an analytical game-teoretic framework to investigate te competitive implications of suc personalized pricing tecnologies (PP). Saked & Sutton (1982) and Gabszewicz and Tisse (1986), building on researc by Mussa and Rosen (1978), develop duopoly models of vertical di erentiation. Moorty (1988) extends te basic model by incorporating variable production costs and allowing consumers te opportunity to not buy a product. Our analysis extends Moorty's model by allowing tat one, or bot, rms can observe consumer valuations, and tereby engage in rst-degree price discrimination. We rst sow tat, even toug a monopolist makes a iger pro t wit PP, its optimal quality is te same wit or witout PP. However, te monopolist makes a iger pro t wit PP. Second, in a duopoly, unless a rm engages in product di erentiation, information about 1 ttp://services.bepress.com/roms/vol2/iss1/paper3 4

7 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet consumer preferences and valuations by itself does not provide any strategic advantage. Weter or not any of te rms ave PP, te outcome is still Bertrand competition, and rms do not earn any pro t. Hence, rms sould not invest in tis tecnology unless tey can di erentiate temselves from competitors. We ten consider a model of vertical product di erentiation, and sow ow personalized pricing on te Internet a ects rms' coices of quality di erentiation in a competitive scenario. First, if te rm wit PP as a low quality, its optimal price is non-monotonic in consumers' willingness to pay. Tat is, some ig valuation consumers are o ered lower prices tan some low valuation ones. Second, wen one rm adopts PP, te oter rm responds by lowering its price. Tis is a competitive response: a rm wit PP knows te valuation of eac consumer, and can terefore carge prices as low as its own marginal cost to a speci c consumer. It terefore encroaces into te market sare of te oter rm, wic responds to te increased competition by reducing its price. Tird, wen only one of te rms adopts PP, it is optimal for it to increase product di erentiation. Wile it is optimal for te rm adopting PP to increase product di erentiation, te non-pp rm seeks to reduce di erentiation by moving in closer in te quality space. Fourt, we nd tat, wen te PP rm as a ig quality bot rms raise teir qualities, relative to te uniform pricing case. Conversely, wen te PP rm as low quality, bot rms lower teir qualities. PP provides te low quality rm wit an opportunity to penetrate an untapped market segment furter to te left tan were it presently is. Hence it lowers its quality to extend its reac in te direction of decreasing consumer type. As a competitive response to di erentiate itself, te ig quality rm initially moves to te rigt as long as moving away is relatively inexpensive due to low convexity of its costs. But wen te costs start increasing at a muc faster rate, te potential loss per unit of market sare on te rigt is outweiged by te gains from moving to te left. Fift, depending on te convexity of te marginal cost function, we outline te incentives of rms to deploy suc tecnologies. Our model sows it is an optimal strategy for te low quality rm to adopt PP, if te oter rm does not. Regardless of weter te low quality rm as PP, te ig quality rm sould adopt PP only if te cost function is not too convex. Sixt, if bot rms acquire PP, ten bot rms earn lower pro ts tan in te case were neiter rm as PP. Essentially, tey are trapped in a prisoner's dilemma. Finally, consumer surplus falls (compared to te no PP case) if te PP rm as low quality, but rises if te PP rm as ig quality. In fact, consumer surplus is igest wen bot rms ave PP. Tis is due to te fact tat since bot rms can now price at marginal costs. 2 Publised by Berkeley Electronic Press Services,

8 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 Tus tis leads to te case of maximum market coverage and most intensi ed price competition. Tus, despite te treat of rst-degree price discrimination, personalized pricing wit competing rms can lead to an overall increase in consumer welfare. Tus our analysis o ers interesting strategic insigts for managers about ow to address te competitive problems associated wit personalized pricing and quality coices. Vertical Di erentiation, Personalization, Price Discrimination, Electronic Com- Keywords: merce ttp://services.bepress.com/roms/vol2/iss1/paper3 6

9 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet 1 Introduction In uncertain environments, e-tailers learn about te most pro table prices troug price experimentation. By its very nature, te Internet is well adapted to suc a learning process. Indeed, in tis electronic environment te menu costs of canging prices are negligible, and sellers can easily experiment wit di erent prices to o er to di erent consumers. In te near future, rms will ave te werewital to use te waves of personal pro le and consumer and supplier activity data to set personalized prices. Te state of te e-tailing industry now as put te consumer is in control. He is able to surf from site to site to compare prices, or even use automated agents tat ferret out te lowest prices, playing mercants against eac oter and forcing prices into te cellar. Suc a situation may render te prevailing \one price ts all" model obsolete. Interestingly, te Internet is a double-edged sword. Retailers using te Internet as a medium for commerce can also gater a remarkable wealt of information about teir existing and potential customers, and ence better estimate a consumer's reservation price. As Bakos (2001) reports, tecnology allows rms to identify and track individual consumers, bot witin an online store and across di erent websites. Tis leads to te creation and saring of consumer pro les, matcing of consumer identities wit relevant demograpic information and comparison wit te preferences of similar consumers troug various collaborative and content ltering tecniques. Based on suc information, te computing power of te Internet retailers' web server can be used to deploy complex pricebots and algoritms to determine prices to approac rst-degree price discrimination (Bailey, 1998). Spurred partly by te low menu cost of canging prices on te Internet and partly as a response to consumer use of price-comparison bots, rms are exploring te idea of personalized prices for goods and services tat are currently sold at posted prices. Personalized pricing requires some knowledge of eac consumer's preferences, and an ability to carge di erent prices to di erent consumers. Te price o ered to a consumer wose valuation for a product is known may be iger or lower tan te posted uniform price carged by rms wo lack te sopistication to target individual consumers. In tis paper, we use te term personalized pricing, or PP, to refer to suc rst-degree price discrimination. A retailer tat invests in PP can identify individual consumers, infer consumer valuations, and determine a consumer's willingness to pay for its product. Tis retailer can terefore o er a personalized price tat provides te consumer greater surplus relative to te potential surplus from competitors' products. If te retailer's Publised by Berkeley Electronic Press Services,

10 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 information indicates a particular consumer as a ig reservation price, te price discrimination algoritm will increase te price for tat consumer and vice versa. Tere are many recent examples of personalized pricing among online retailers. In , Books.com adopted a price discrimination strategy were di erent buyers were paying di erent prices for te same item based on teir sopping beavior. A well-known example, of course, is Amazon.com, wic varied prices to di erent consumers on its popular Diamond Rio MP3 player by up to $50 from te original $233 retail tag (Morneau, 2000). Later on, over a ve-day period, Amazon o ered discounts of twenty to forty percent o te list price on 68 of its 100 most popular DVD titles, wic again di ered by consumers. Tis promotion resulted in te same title being sold at a price ranging from $24 to $39. One way for a retailer to engage in price discrimination is troug intelligent agents dynamically inserting personalized discounts on pop-up windows on a consumer's screen. Software for tis is provided by, among oters, icoose, Das, and zbubbles (Jonson, 2000). Cen & Iyer (2001) report tat, in te Nort American long-distance telepone market, te major competitors (AT&T, MCI and Sprint) ave been able to improve te sopistication of consumer databases tat elps tem to provide specialized discounts to a majority of te population. Furter, Ford plans to move towards pricing its automobile nancing products dynamically, based on consumer pro les and coices, and expects to cut its $10 billion spending on non-targeted promotions signi cantly (Aron, et al., 2001). E-tailers are now using data-mining software and click-stream analysis products to track consumer beavior. 1 Of late quite a few software companies ave begun to o er personalized pricing witin e-commerce products. Calico's Dynamic Custom Price application enables sellers to o er personalized prices ( Zilliant software provides online businesses wit real-time feedback on consumer beavior and competitive pricing to support personalized pricing decisions. Many rms believe tat te concept of making te rigt o er to te rigt consumer will be te way of te future. In tis paper we intend to examine te following questions. How does competition between online retailers, in te presence of intelligent agents and price bots tat can extract buyer preferences and implement personalized pricing, a ect equilibrium outcomes in a 1 NetGenesis' NetAnalysis, for example, gleans beavioral data from Web server log les, a network sni er (software tat sits on te network and logs tra±c) and from Web server plug-ins. 2 ttp://services.bepress.com/roms/vol2/iss1/paper3 8

11 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet competitive scenario? Wat are te variables of strategic interest? Wen do rms competing on te quality of value added services bene t from personalized pricing and wat are te incentives for investing in suc tecnologies for competing rms? Does te improvement in rms' knowledge of individual consumers alleviate te pricing pressure on retailers or does it intensify price competition in te industry suc tat all competing rms become worse o? We consider tese questions in a duopoly framework in wic one or bot rms can perfectly identify valuations of eterogenous consumers. 2 Recent work on price discrimination and customization includes Ulp and Vulkan (2001), wo nd tat a rm tat rst-degree price discriminates is also better o if it mass-customizes. In a monopoly setting, Aron, et al., (2001) analyze te pricing, pro tability and welfare implications of agent-based tecnologies tat engage in pricing based upon product preference information revealed by consumers. In te context of consumer addressability, were rms can reac individual customers, Cen and Iyer (2001) nd tat wen product di erentiation and te cost of incremental addressability become small, rms strategically di erentiate in teir coice of addressability to mitigate destructive competition. Cen, et al., (2001), ave sown tat mistargeting can soften price competition in te market, and qualitatively cange te incentives for competing rms engaged in individual marketing. We derive a number of analytical results on rm pricing and quality di erentiation, and on consumer welfare, wen one or bot rms ave PP. First, te optimal quality for a monopolist is te same wit or witout PP. However, te monopolist makes a iger pro t wit PP. Second, in a duopoly, unless a rm engages in product di erentiation, information about consumer preferences and valuations by itself does not provide any strategic advantage. Weter or not any of te rms ave PP, te outcome is still Bertrand competition, and rms do not earn any pro t. Hence, rms sould not invest in tis tecnology unless tey can di erentiate temselves from competitors. Tird, if te rm wit PP as a low quality, its optimal price is non-monotonic in consumers' willingness to pay. Tat is, some ig valuation consumers are o ered lower prices tan some low valuation ones. Fourt, wen one rm adopts PP, te oter rm responds by lowering its price. Tis is a competitive response: a rm wit PP knows te valuation of eac consumer, and can terefore carge prices as low as its own marginal cost to a speci c consumer. It terefore 2 Tis assumption is made in order to provide bencmark results. Future potential notwitstanding, current tecnologies can only approximately determine consumer valuations. 3 Publised by Berkeley Electronic Press Services,

12 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 encroaces into te market sare of te oter rm, wic responds to te increased competition by reducing its price. Fift, wen only one of te rms adopts PP, it is optimal for it to increase product di erentiation. Tis can be interpreted as a move to reduce competition wit te oter rm. In addition to te above results, for a wide range of cost parameters, we demonstrate some properties of rm pro t and consumer surplus wit PP. First, witin tis range, it is a dominant strategy for te low quality rm to acquire PP. Tat is, regardless of weter te ig quality rm acquires PP or not, te low quality rm makes a iger pro t wit PP. Conversely, te ig quality rm sould acquire PP only if te costs of quality are not too steep. Next, if bot rms acquire PP, ten bot rms increase pro ts (if costs are not too convex). However, if marginal costs sarply increase in quality, ten bot rms earn lower pro ts compared to te case were neiter as PP. Essentially, tey are trapped in a prisoner's dilemma. 3 Finally, consumer surplus falls (compared to te no PP case) if te PP rm as low quality, but rises if te PP rm as ig quality. In fact, consumer surplus is igest wen bot rms ave PP. Te rest of te paper is organized as follows. Section 2 describes te model in detail and analyzes a monopolist's coices. Section 3 provides te intuition beind wy rms would sell eterogeneous products and tus lays te groundwork for furter analysis of quality based competition. Section 4 presents a preliminary result tat acts as a bencmark for comparative statics. Section 5 considers te cases of te PP rm coosing a low and a ig quality respectively. Tat is, we consider two equilibria, wit te PP rm being te lower quality rm in one equilibrium, and te iger quality rm in te oter. 4 We ten proceed to Section 6 to analyze te equilibrium wen bot rms ave PP. In Section 7 we provide some interesting observations using numerical analysis. We ten discuss some implications of our ndings, wit some concluding remarks in Section 8. All proofs are relegated to te Appendix in Section 9. 3 Sa er and Zang (1995) ad a similar result in teir model of coupon targeting. 4 We do not consider te question of wic equilibrium will emerge. In our model, neiter rm as te option of forcing te oter into a particular equilibrium. 4 ttp://services.bepress.com/roms/vol2/iss1/paper3 10

13 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet 2 Model We consider vertical di erentiation in a personalized pricing context. Saked & Sutton (1982) and Gabszewicz and Tisse (1986), building on researc by Mussa and Rosen (1978), develop duopoly models of vertical di erentiation. 5 Tese papers ave sown tat te strategic e ect of te desire to reduce price competition results in a product equilibrium were rms seek maximal product di erentiation. Moorty (1988) extends te basic model by incorporating variable production costs and allowing consumers te opportunity to not buy a product. Tis results in less tan maximal product di erentiation. Firms compete in bot te quality and price of te products tey o er. Formally, we model teir competition as a tree-stage game. At te rst stage, rms simultaneously coose te quality levels of teir products. At stage 2, te two rms simultaneously coose teir prices. Finally, at te last stage, consumers decide wic, if any, product to buy. Our analysis extends Moorty's model by allowing tat one, or bot, rms can perfectly observe consumer valuations, and tereby engage in rst-degree price discrimination. Consistent wit is model, weter rms ave PP or not, te pure strategy equilibria are caracterized by one rm coosing a ig quality (call tis rm ), and te oter one a low quality (call tis rm ). Consumers are modelled as utility maximizers. If a consumer purcases a product of quality q at price p, is utility is U(µ) =µq p, wereµ 2 [0; 1]. A consumer as positive utility for one unit only. Te type parameter µ indicates a consumer's marginal valuation for quality. For any given quality, a consumer wit a iger µ is willing to pay more for te product tan one wit a lower µ. If eiter of te two products o ers a positive net utility, a consumer buys te one tat maximizes is surplus. Oterwise, e cooses not to buy eiter product. As a bencmark, we consider te case of rms setting a single posted price (wic we call \uniform pricing") at stage 2. We ten examine outcomes under personalized pricing (PP), or rst-degree price discrimination. Consistent wit prior literature, we assume tat rms ave a marginal cost for production wic is invariant wit te quantity, but depends on te quality of te product. Tat is, bot rms ave te same cost function, but, depending on te quality levels tey coose, teir marginal costs may 5 Armstrong & Vickers (2001) provide an elegant framework tat incorporates muc of te earlier work on price competition in an environment wit multiple rms. In a model of orizontal di erentiation, Baskar & To (2002) nd tat, wit perfect price discrimination and free entry, tere is excessive entry. 5 Publised by Berkeley Electronic Press Services,

14 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 di er in equilibrium. Assumption 1 (i) Eac rm as a constant marginal cost for producing te good, denoted by c. (ii) c( ) is twice di erentiable, strictly increasing and strictly convex in q. Tat is, c 0 > 0 and c 00 > 0. Quality in tis model is a broad notion tat encompasses any features tat may a ect a consumer's willingness to pay for a good. Tese could include features intrinsic to te product itself (suc as durability and functionality) and tose related to te quality of te online sopping experience or te service level provided by te rm (suc as warranties, delivery times, and consumer service). Quality is observed perfectly by all consumers at no extra cost. Altoug cross-mercant product comparisons are a treat to mercant pro tability, tey are caracteristic of te retail marketplace and are ere to stay. Knowing tis, retailers add value to manufacturers' products to distinguis temselves from teir competitors. Tese value-added services include extended warranties, forgiving return policies on defective items, special gift services, superior customer service and support contracts, fast delivery times wit low costs, crossmanufacturer product con gurations, and so on. Depending on te product, tese value-added services can be critical to a consumer's buying decision regardless of te manner of sopping. Given te quality levels and prices o ered by te two rms, consumers make teir coices. Suppose, in te bencmark case of uniform pricing, rm 1 o ers (q 1 ;p 1 ), and rm 2 o ers (q 2 ;p 2 ). Tere will be a subset of consumers (possibly null) wo buy from eac of rms 1 and 2. Te pro t of rm j is its market coverage times (p j c(q j )). In te case of PP, we allow one or bot rms to be equipped wit a tecnology tat perfectly reveals te consumer's type before te price is disclosed to te consumer. Wile te rm o ers te same quality product to all consumers, it can coose a customized price, and ence engage in rst-degree price discrimination. In tis case, a rm's pro t from consumer µ is (p(µ) c(q j )). In practice, a personalized pricing tecnology of tis nature is likely to incur some xed costs. Most suc tecnologies involve developing software to employ intelligent agents to infer consumer valuations, as well as algoritms to provide personalized prices based on te estimated valuations. However, suc costs are independent of te quality of te product being o ered by te rm, and ence are xed costs wen considering te rm's coice of quality. For simplicity, in tis model, 6 ttp://services.bepress.com/roms/vol2/iss1/paper3 12

15 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet we treat tese costs as zero. Adding a xed cost does not cange te qualitative nature of our results. However, depending on te nature of te variable costs, we provide guidelines as to wen rms sould or sould not invest in PP. We consider pure strategy subgame-perfect equilibria of tis tree-stage game. Tat is, for any strategies te rms may coose at stages 1 and 2, consumers beave optimally at stage 3. Firms, in turn, not only anticipate tis beavior, but also coose optimal prices, given quality levels, at stage 2. Before considering te duopoly case, we rst consider te e ect of PP on a monopolist's coice of quality. 2.1 Monopoly Case Consider rst, a monopoly wit uniform pricing. Let q n m and p n m be te quality and price, respectively, o ered by te rm in tis case were te superscript n refers to te fact tat te rm does not ave PP and te subscript m denotes te fact tat it is a monopolist. De ne µ n m = pn m q n. Ten, m consumers wit types µ µ n m will buy te product (because tis leads to iger utility tan not consuming) and tose wit types µ<µ n m will not. Te monopolist's pro t function, terefore, is ¼ n m(p n m;q n m) = (1 µ n m)(p n m c(q n m)): Next, de ne q d m and p d m as te quality level and price, respectively, o ered by a monopolist wit PP were te superscript d denotes te fact tat te monopolist as PP tecnology. Since tis rm observes consumer types before coosing its price, p d m will be a function of consumer type, µ. Since marginal cost is constant in sales volume, a product sold to one consumer will ave no e ect on te price to any oter consumer. Hence te rm carges eac consumer is entire surplus from consuming te good. Tat is, p d m (µ) =µqd m. Tis price function is, trivially, increasing in µ: iger consumer types pay iger prices. Furter, te rm is willing to price as low as marginal cost, c(qm d ) to persuade a consumer to buy te product. At tis price, te lowest consumer type willing to buy is µ d m = c(qd m ). All types qm d iger tan µ d m buy te product, and pay te price p d m(µ) =µqm. d Hence, te pro t function of te PP monopolist is ¼ d m(q d m)= Z 1 µ d m (p d m(µ) c(q d m))dµ = Z 1 c(q d m ) q d m (µq d m c(q d m))dµ 7 Publised by Berkeley Electronic Press Services,

16 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 We rst sow tat, regardless of te availability of PP, a monopolist rm cooses te same quality. Tis result immediately implies tat a monopolist wit PP earns a iger pro t tan a monopolist witout PP. In fact, at te same quality, a monopolist wit PP will acieve a iger market sare tan one witout PP. Te ability to customize prices according to consumers' willingness to pay ensures tat te rm is now able to reac many more consumers tan it could before. Proofs for Proposition 1 and all oter Propositions, are provided in te Appendix. Proposition 1 In equilibrium, regardless of PP, a monopolist sets te same quality level: qm d = qm n.furter,¼d m =2¼n m : Increasing (decreasing) quality implies a trade o between increasing (decreasing) costs and decreased (increased) market penetration for te rm. Personalized Pricing gives it te ability to reac a previously untapped portion of te market, witout canging its product quality. By pricing at marginal cost for te tresold consumer, te rm ensures tat it is able to penetrate an additional market segment witout incurring additional costs. Tis case provides a bencmark to te one in wic one of two duopolists obtains a PP tecnology. As we sow in te next section, in te latter case, qualities of bot rms typically cange in response to te availability of PP. 3 Duopoly wit personalized pricing: No Quality Di erentiation We next turn to te duopoly case, wit two rms in te market. We rst sow tat te ability to price discriminate, by itself, is of no value unless rms also di erentiate in quality. Suppose tat one or bot rms ave access to PP. Suppose te two rms ave products of identical quality, so tat q 1 = q 2. Ten, regardless of access to personalized pricing, Bertrand competition is inevitable, and eac rm earns zero pro t. Proposition 2 Suppose bot rms o er te same quality, so tat q 1 = q 2. Ten, in equilibrium, regardless of te availability of PP, p 1 = p 2 = c(q 1 ),sotateac rmearnszeropro t. Tus, even wen one of te rms possesses a tecnology of extracting consumer valuations and pricing accordingly (PP), it does not ave any competitive advantage in te absence of some 8 ttp://services.bepress.com/roms/vol2/iss1/paper3 14

17 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet form of product di erentiation. Tis result implies tat online retailers will coose not to indulge in personalized pricing, unless tey can also provide value-added services to di erentiate teir product. Witout product di erentiation, retailers are reduced to competing at marginal cost, and are unable to earn a pro t. We terefore turn to te case in wic rms rst coose te quality of teir product, and ten te price. 4 Di erentiated Duopoly: Neiter Firm as PP As a bencmark case, we rst assume tat neiter rm as access to PP. We call tis case te no-pp case. As Moorty sows, in any pure strategy equilibrium, te rms coose di erent quality levels. Tis feature continues to prevail wen one or bot rms ave PP. As we ave sown, if rms coose te same quality, bot rms earn zero pro t. Hence, eac rms prefer quality di erentiation, regardless of weter it as iger or lower quality tan te oter. Wen tere is no access to PP, rm i, (i = ; ), cooses a quality qi n and price p n i,were te superscript n indicates tat neiter rm as PP. In equilibrium q n >q ǹ and p n >p ǹ. Hencefort te superscripts l ; and b will indicate te scenarios wen only one rm as PP and te PP rm cooses low quality or ig quality or wen bot rms ave PP. Te subgame-perfect equilibrium in tis case is determined by backward induction, starting wit stage 3. As sown by Moorty (1988, Proposition 1, part 3), in equilibrium at stage 3, te rms sare te market in te following manner. 6 Consumers wit valuations greater tan a cuto level µ n and less tan 1 purcase product, and tose wit valuations between a second cuto level µ n l and µ n purcase product. µn and, andµ n l is de ned by te consumer exactly indi erent between products by te consumer indi erent between product and not consuming at all. Tat is, µ n qn pn = µn qǹ p ǹ ; or, µ n = pn pǹ q n qǹ : TissituationisdepictedinFigure1below. µ n l qǹ p ǹ =0; or, µ n l = pǹ q ǹ : 6 Toug Moorty assumes quadratic costs, tis result depends only on consumer preferences, and not on costs. 9 Publised by Berkeley Electronic Press Services,

18 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 Buy neiter product ¾ - Buy product ¾ - Buy product ¾ - 0 µ n µ n 1 l Figure 1: Consumers' purcasing decision by consumer type (µ) 4.1 Price Competition at Stage 2 Terefore, we can write te pro t function of rm as ¼ ǹ =(µ n µn l )(pǹ c ǹ ),andtatof rm as ¼ n =(1 µn)(pn cn ). Now, consider stage 2 of te game, after rms ave cosen teir respective qualities, q n and qǹ.letc n = c(qn), and cǹ = c(q ǹ ). We solve for te prices cosen by te rms at stage 2. Lemma 1 In equilibrium, te prices of te two rms are p n = qn (2(qn qǹ )+c ǹ +2c n) 4q, n qǹ p ǹ = qn (qǹ +2c ǹ )+q ǹ (c n qǹ ) 4q. n qǹ Given tese prices, we now consider rms' coices of quality levels at stage Quality Competition at Stage 1 At tis stage, rms anticipate te prices tey will coose at stage 2 (as a function of te qualities cosen at stage 1), and teir resulting pro ts at stage 3. Pro ts for eac rm are ence written as a function of quality levels q n and qǹ alone. Denote tese pro t functions as ¼ n and ¼ǹ. In particular, suppose rm cooses a quality q n, and rm cooses q ǹ.ten, ¼ n = cn ( 2qn + qǹ )+q n (2qn 2qǹ + c ǹ ) 2 (q n qǹ )(4q n qǹ ) 2 Te rst-order condition for rm, ¼ ǹ = qn (qǹ (q n qǹ + c n )+(cǹ ( 2q n + qǹ ) 2 )) q ǹ (q n qǹ )(4q n qǹ ) 2 n = 0, de nes a reaction function for rm ; i.e., it determines te optimal quality level of rm as a function of q ǹ. Similarly, te rst-order condition 10 ttp://services.bepress.com/roms/vol2/iss1/paper3 16

19 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet ǹ = 0, denotes te reaction function of rm. Te equilibrium quality levels, q n and q ǹ, are determined by simultaneously solving tese two equations. In te next section, we consider te case in wic one rm as PP, and compare te resulting quality levels to tis bencmark case. 5 Duopoly wit personalized pricing: Only one Firm as PP We now consider te situation in wic one rm as access to PP i.e., it can infer consumer valuations and form a perfect estimate of eac consumer's willingness to pay for its product. As Proposition 2 suggests, tere is no pure strategy subgame perfect equilibrium in wic bot rms coose te same quality level, since tis results in zero pro ts for bot. Instead, eac rm prefers to ave a di erent quality (eiter iger or lower). Hence, tere are two equilibria in tis case; one in wic te PP rm cooses a lower quality tan te oter rm, and a second one in wic te PP rm cooses a iger quality. We consider eac of tese equilibria in turn. 5.1 PP Firm O ers Low Quality We denote te equilibrium qualities in tis case as q and q,witp and p (µ) denotingte equilibrium prices. In tis case, rm knows te type of eac consumer, and ence can o er prices tat depend on µ. In equilibrium, it must be willing to o er a price as low as its marginal cost, c = c(q), to eac consumer, if necessary. Furter, consistent wit price discrimination, it will carge as ig a price as it can from eac consumer it sells to. As before, we solve tis game by backward induction. At stage 3, rm (wic does not ave PP in tis case) will operate in a market segment [µ ; 1], and rm in a market segment [µ ;µ ]. Consider rst te location of te marginal consumer µ, wo is indi erent between buying from eiter rm. Tis consumer must obtain te same utility from eiter product. If p(µ ) >c, ten rm would lower its price for tis consumer, to ensure tat e strictly prefers to buy product. Hence, it must be tat p(µ )=c. Terefore, tis consumer is de ned by Similarly, µ µ q p = µ q c ; or µ p c = q : q is de ned by te consumer wo is indi erent between buying product and not consumingatall. Again,itmustbetatp(µ ) =c, else rm could increase its pro t by reducing 11 Publised by Berkeley Electronic Press Services,

20 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 its price for tis consumer. Hence, µ q c =0; or µ = c q We sow tat te equilibrium price function of rm is non-monotonic in consumer type; tat is, it carges some ig valuation consumers less tan it carges some low valuation consumers. De ne ^µ = p. q Proposition 3 In equilibrium, at stage 2, rm carges p = 1 2 +c). Forconsumers (q q +c in te range [µ ; ^µ], rm sets p =µq (µ), and for tose in te range (^µ; µ ],itsetsp (µ) = q). µ(q p TissituationisdepictedinFigure2. : 6 p Prices of ; ½@ p(µ) ½ s½ s 0 µ ^µ µ 1 ¾ - ¾ - Firm 0s market Firm 0 s market c Figure 2: Prices of rms and wen rm alone as PP Te intuition for te non-monotonicity of p (µ), is tat in te market segment [0; ^µ], rm faces no competition from rm. Tese consumers are not willing to buy product at te o ered quality and price. Hence, rm is able to extract teir entire consumer surplus, and consumers in tis range are left wit no surplus. However, consumers in te range [^µ; 1] obtain a positive utility from consuming product as well. Hence, rm faces competition in tis range, and must o er consumers at least as ig a surplus as rm, to induce tem to buy product. Tus,tese consumers ave a positive surplus tat is monotonically increasing in consumer type. 12 ttp://services.bepress.com/roms/vol2/iss1/paper3 18

21 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet Substituting in te optimal price of rm, te equilibrium price scedule for rm is 8 >< if µ 2 [µ µq ; ^µ] p (µ) = >: (1) 1 2 (q q + c + c ) µ(q q ) if µ 2 (^µ; µ ] Now, consider te coice of qualities at stage 1. Suppose rm cooses q, and rm cooses q. Furter, suppose rm cooses optimally (as given by Proposition 1), given te two qualities. p Ten, te pro t function of rm is ¼ (q ;q ) = Z ^µ µ (µq c Z µ )dµ + ^µ ( 1 2 (q q + c + c ) µ(q q ) c c)2 (p q q )dµ = : (2) 2(q q)q q q, Te rst-order condition for rm, tis yields = 0. Recalling tat p is also a function of (p q cq )(cq (q 2q)+q(p q (q q)(2(c)0 + (c)0 q))) q q 2(q q)2 (q)2 q = 0 (3) Let ;q) denote te left-and side of te above equation. Ã(q Since p >c,andq >q te solution to =) c q > c q (since c( ) is convex), te optimal quality q c q (q 2q )+q (p q (q q )(2(c )0 q + q (c )0 q is given by )) = 0: (4) Te solution to tis equation yields te reaction function of rm. Denotetisbyr(q ). Similarly, te pro t function of rm is ¼ (q ;q ) =(p c )(1 µ (p ;q ;c Te corresponding rst-order condition is d¼ dq =0,or + c)2 (q q c ;q )) = 2(q q) (q q c + c)(q q + c c 2(q q)(c )0 ) 4(q q)2 2 = 0 (5) q Let à ;q) denote te left-and side of tis equation. (q Since q >q, itcannotbetat(q q c + c ) = 0. Hence, te optimal quality of rm, is given by te solution to q q q + c c 2(q q )(c )0 = 0: (6) 13 Publised by Berkeley Electronic Press Services,

22 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 Let (q), te solution to tis equation, denote te reaction function for rm. r Denote (c )0 = c 0 (q )and(c)0 = c0 (q). First, we sow tat, eac of tese derivatives must be tat less tan 1 in equilibrium. Tis will be useful in sowing properties of te reaction and pro t functions in te next two results. Lemma 2 At te equilibrium qualities,(c )0 < 1, and(c)0 < 1. We can now demonstrate tat te reaction functions of bot rms are upward sloping. Tat is, if rm increases its quality, rm sould raise its quality, and vice versa. Proposition 4 Te reaction functions of bot rms are upward-sloping; tat is, dr dq > 0. dr dq > 0 and We sow tat, wen rm acquires PP, te competitive response of rm is to reduce its price. PP allows rm to price as low as marginal cost to a particular consumer, to induce im to buy product. Tis leads to an immediate increase in te market sare of rm, botamongst low valuation consumers, and tose wo were previously buying product. Inresponsetotis eigtened competition from rm, rm reduces its price. Tis response of rm, in turn, induces rm to lower its own quality, to reduce te competition wit rm. Proposition 5 Suppose bot rms o er te no-pp qualities, q n ;qǹ. If rm now acquires PP, compared to te no-pp case, (i) rm carges a lower price: p <pn, and (ii) if rm remains at its original quality, q n,ten rm lowers its quality. Of course, in equilibrium, bot rms cange teir qualities from te no-pp case. We expect te price of rm to be lower, and te quality of rm to be lower. Wat quality does rm coose? Observation 1 Given a cost function of te nature c(q) = q, if te cost function is not too convex (in particular, 1:2), rm cooses a iger quality in equilibrium. Conversely, if te cost function is igly convex ( >1:2), it cooses a lower quality. Tis is demonstrated in Figure 3 below. 14 ttp://services.bepress.com/roms/vol2/iss1/paper3 20

23 qualities Gose et al.: Personalized Pricing and Quality Differentiation on te Internet Hig quality firm Low quality firm Neiter firm as PP Low firm as PP α Figure 3: Qualities of rms (top) and (bottom) wit convexity of marginal cost function ( ) PP provides rm wit an opportunity to penetrate an untapped market segment furter to te left tan were it presently is. Hence it lowers its quality to extend its reac in te direction of decreasing consumer type. As a competitive response to di erentiate itself, rm initially moves to te rigt as long as moving away is relatively inexpensive due to low convexity of its costs. But wen te costs start increasing at a muc faster rate, te potential loss per unit of market sare on te rigt is outweiged by te gains from moving to te left. By moving towards te low quality rm, increases te uncontested portion of its market sare on te rigt were it faces no competition from. Tus, for a wide range of, bot rms reduce teir qualities wen te PP rm cooses a low quality. Furter, to give consumers a positive surplus and remain competitive, rm also reduces its price, after lowering its quality. We sow in Section 7 tat te non-monotonicity of 0s price also implies tat consumers are worse o tan in te no-pp case. 5.2 PP Firm O ers Hig Quality We denote te equilibrium qualities in tis case as q and q,wit p (µ) and p denoting te equilibrium prices. In tis case, rm knows te type of eac consumer, and is ence willing to 15 Publised by Berkeley Electronic Press Services,

24 Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art. 3 price as low as p (µ) =c if need be. At stage 3, rm (wic does not ave PP in tis case) will operate in a market segment [µ ;µ], and rm in a market segment [µ ; 1]. Consider rst te location of te marginal consumer µ, wo is indi erent between buying from eiter rm. Tis consumer must obtain te same utility from eiter product. If p (µ ),ten rm would lower its price for tis consumer, to ensure >c tat e strictly prefers to buy product. Hence, it must be tat p (µ. Terefore, tis )=c consumer is de ned by µ q c = µ q p ; or µ = c p q : q Similarly, µ is de ned by te consumer wo is indi erent between buying product and not consumingatall. Again,itmustbetatp,else rm could increase its pro t by reducing (µ )=c its price for tis consumer. Hence, c µ =0; or = : q c µ q Consider rm 0s pro tfunctionatstage2:¼ =(p c )(µ µ )=(p c )( c p q q Te rst-order condition for pro = 0, directly c ). q p = (c q + c q ) 2q (7) Substituting in te optimal price of rm, te equilibrium price scedule for rm is p (µ) = (c q + c q ) 2q + µ(q q ) Now, consider te coice of qualities at stage 1. Suppose rm cooses q, and rm q. Furter, suppose rm cooses p optimally, given te two qualities. Ten, te pro t function of rm is ¼ (q ;q )=R 1 µ (p (µ) c)dµ. Replacing te values of p (µ), ¼(q ;q )= (p +q q c )2 2(q q ). Te corresponding rst-order condition for rm, terefore, = 0, wic gives (p + q q c ) q q ( 1 (c )0 + q ((c)0 q c) 2(q + p + q q c )2 2(q q ) Let r ), te solution to tis equation, denote te reaction function for rm. (q 16 ) = 0 (8) ttp://services.bepress.com/roms/vol2/iss1/paper3 22

25 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet Similarly, te pro t equation for rm is given by (c q q )2 c 2q q (q ). Te corresponding rst-order q condition for rm, terefore, (c q c q )(c (q 2q )+q (c 2(c )0 (q )) q (2q (q = 0 (9) q ))2 Since c q > c,itcannotbetat(c q q given by te solution to c q ) = 0. Hence, te optimal quality of rm, q c (q 2q )+q (c 2(c )0 (q )) = 0: (10) q Let r (q ), te solution to tis equation, denote te reaction function for rm. is Proposition 6 Suppose bot rms are at te no-pp qualities, q n ;qǹ.if rm now acquires PP, compared to te no-pp case, (i) rm carges a lower price: p at its original quality, q ǹ,ten rm cooses a iger quality. <pǹ, and (ii) if rm remains Of course, in equilibrium, bot rms cange teir qualities from te no-pp case. We expect te price of rm to be lower, and te quality of rm to be lower. Wat quality does rm coose? Similar to te previous case, if te cost function is not too convex (in particular, 1:55), rm cooses a lower quality in equilibrium. Conversely, if te cost function is igly convex ( >1:55), it cooses a iger quality. Tus, for a wide range of, bot rms increase teir qualities wen te PP rm cooses a iger quality. Furter, te price of rm falls. We sow in Section 7 tat tis implies tat consumers are better o tan in te no-pp case. Te rm wit PP as a strategic advantage, since it knows consumer valuations and can price at marginal cost for te tresold consumer. To maximize tis strategic advantage, it seeks to di erentiate itself furter from te oter rm and avoid ead-to-ead competition. As long as costs are increasing at a moderate rate, te non-pp rm seeks to increase product di erentiation by moving away. However wen cost function becomes steep, te non-pp rm seeks to reduce quality di erentiation and come closer to te PP rm in te quality space. Tat is, if te PP rm as a low quality, in equilibrium, bot rms end up wit lower qualities tan previously. Te converse outcome occurs if te PP rm cooses ig quality; tat is, in equilibrium bot rms end up wit iger qualities. 17 Publised by Berkeley Electronic Press Services,

26 qualities Review of Marketing Science Working Papers, Vol. 2, Iss. 1 [2002], Art Hig quality firm Low quality firm Neiter firm as PP Hig firm as PP α Figure 4: Qualities of rms (top) and (bottom) wit convexity of marginal cost function ( ) We furter note tat, wen only one rm as PP, regardless of weter it cooses a ig or low quality, te oter rm o ers a lower price tan te corresponding price in te case in wic neiter rm as PP. Since it knows tat PP immediately equips te oter rm wit an ability to lower prices werever necessary, te initial strategic response by te non-pp rm, is to lower its own price in order to remain competitive. 6 Bot Firms ave PP Suppose, as before, tat rm cooses q b and rm cooses qb. Ten, µb = cb cb cb, µ =,and q b b qb q b ^µ = cb q b.recalltat rmsellstoconsumers in te region [µ b ; 1] and rm 2 in te region [µb;µb]. As before, ^µ represents te point beyond wic rms compete for consumers, so tat te price o ered by te low rm is declining in consumer type. Consider stage 2 of tis game, were te rms coose teir price scedule, given qualities q b ;qb. Te pro t function of rm H, is given by ¼ b = R 1 µ b (p b (µ) cb )dµ. Te maximal price rm can carge any consumer µ is te price at wic e is exactly indi erent between buying te low quality 18 ttp://services.bepress.com/roms/vol2/iss1/paper3 24

27 Gose et al.: Personalized Pricing and Quality Differentiation on te Internet product at c b (te lowest price rm is willing to carge) and te ig quality product at pb (µ). Terefore, or p b (µ) =cb + µ(qb qb). Tus, µq b pb (µ) = cb; µqb ¼ b = Z 1 µ b (c b + µ(qb qb) cb )dµ = (qb qb cb + cb)2 2(q b qb) : Notice tat tis is exactly te same as te pro t function of rm wen only rm as PP, equation (5). Hence, it follows tat te reaction function of rm is identical to tat expressed by equation (5). Next, consider te pro t function of rm. Weave¼ b = R µb (p b (µ) cb)dµ. Now, as before, in µ b te region [µ b; ^µ], rm faces no e ective competition from rm (since tese consumers will not buy good even at a price c b ). Hence, in tis region, it carges pb(µ) =µqb. In te region [^µ; µ b ], rm is willing to price as low as c b. Hence, rm must price so tat µqb pb(µ) µqb cb, or p b(µ) cb µ(qb qb). Te optimal price in tis region is, terefore, pb(µ) =cb µ(qb qb). Hence, its pro t function is ¼ b = Z ^µ µ b Z µ b (µq b cb)dµ + (c b µ(qb qb) cb)dµ = (cb qb qbcb)2 2q b qb (qb qb) ^µ Notice tat tis pro t function is exactly te same as te pro t function of rm wen only rm as PP. Hence, it follows tat its reaction function is identical to equation (9). To compare te qualities in tis case wit te cases in wic only one rm as PP, we parameterize te cost function as c(q) =Aq.For >1, tis function is convex. We assume tat A> 1. Tis function satis es assumption 1. We sow tat bot rms o er a iger quality tan in te case in wic only rm as PP, but o er a lower quality tan in te case in wic only rm as PP. Interestingly, compared to tecasewenneiter rmadpp,weobservetatteigquality rmlowersitsqualityandte low quality rm raises its quality. Tis implies tat bot rms actually come closer to eac oter. Te intensi ed competition leaves bot rms worse o. Proposition 7 Suppose c(q) =Aq,were >1 and A> 1. Ten, te equilibrium qualities, qb and q b, satisfy q <q b <q and q <q b <q 19. Publised by Berkeley Electronic Press Services,