Targeted Pricing, Consumer Myopia and Investment in Customer-Tracking Technologie

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1 No 3 Targeted Pricing, Consumer Myoia and Investment in Customer-Tracking Tecnologie Irina aye, Geza Sai February 204

2 IMPRINT DICE DISCUSSION PPER Publised by düsseldorf university ress (du) on bealf of Heinric Heine Universität Düsseldorf, Faculty of Economics, Düsseldorf Institute for Cometition Economics (DICE), Universitätsstraße, Düsseldorf, Germany Editor: Prof. Dr. Hans Teo Normann Düsseldorf Institute for Cometition Economics (DICE) Pone: +49(0) , e mail: DICE DISCUSSION PPER ll rigts reserved. Düsseldorf, Germany, 204 ISSN (online) ISN Te working aers ublised in te Series constitute work in rogress circulated to stimulate discussion and critical comments. Views exressed reresent exclusively te autors own oinions and do not necessarily reflect tose of te editor.

3 Targeted Pricing, Consumer Myoia and Investment in Customer-Tracking Tecnology Irina aye Geza Sai y February 204 bstract We analyze ow consumer myoia in uences investment incentives into a tecnology tat enables rms to track consumers urcases and make targeted o ers based on teir references. In a two-eriod Hotelling setu rms may invest in customer-tracking tecnology. If a rm acquires te tecnology, it can ractice rst-degree rice discrimination among consumers tat bougt from it in te rst eriod. We distinguis between te cases of all consumers being myoic and wen tey are soisticated. In equilibrium rms collect customer data only wen consumers are myoic. In tat case two asymmetric equilibria emerge, wit eiter one rm investing in customer-tracking tecnology. We derive several surrising results for consumer olicy: First, contrary to conventional wisdom, rms are better-o wen consumers are soisticated. Second, consumers may be better-o being myoic tan soisticated, rovided tey are su ciently atient (te discount factor is ig enoug). Tird, in te latter case tere is a tension between consumer and social welfare, and corresondingly between consumer and oter olicies: Wit myoic consumers, banning customer-tracking would increase social welfare, but may reduce consumer surlus. JEL-Classi cation: D43; L3; L5; O30. Keywords: Price Discrimination, Customer Data, Consumer Myoia. Corresonding utor: Düsseldorf Institute for Cometition Economics (DICE), Heinric Heine University of Düsseldorf. y Euroean Commission DG COMP - Cief Economist Team and Düsseldorf Institute for Cometition Economics (DICE), Heinric Heine University of Düsseldorf. Te views exressed in tis article are solely tose of te autors and may not, under any circumstances, be regarded as reresenting an o cial osition of te Euroean Commission.

4 Introduction Te raidly imroving ability of rms to collect, store and analyze customer data created large oortunities for ersonalized ricing and oter ersonalized marketing activities. One of te imortant sources of customer data are loyalty rograms, wic are articularly widesread in te retail and airline industries (see, for examle, Coi, 203). Te CEO of Safeway Inc., te second-largest suermarket cain in te U.S., Steve urd, said tat Tere s going to come a oint were our self ricing is retty irrelevant because we can be so ersonalized in wat we o er eole (Ross, 203). irlines ave also develoed soisticated tecniques to utilize customer insigts tey obtain from frequent- yer rograms (see, for examle, Kola, 203). Consumer online urcases and oter tyes of online activities rovide furter imortant sources of customer information.,2,3 Te increased use of customer data for targeted marketing activities as triggered strong reactions from consumer olicy advocates. Te debate as been furter eated by several incidents were rms collected beavioral data and used it or sold it for marketing uroses witout te awareness of consumers. 4 Consumer olicy tyically regards informing consumers about te consequences of teir coices as igest riority and strikes down on fraudulent business ractices were rms misguide consumers about tese consequences. Limited consumer foresigt, eiter a trait or a result of deliberate marketing strategy, is considered as a main source One anonymous comuter scientist working for online retailers noted tat...it s common for big retail web sites to direct di erent users to di erent deals, o ers, or items based on teir urcase istories or cookies... nd comanies frequently o er secial deals for customers wit a few items in teir soing bags-from discounts on additional items, to free siing, to couons for future urcases. Ingenuity, rater tan rice-tamering, is now te name of te game (Klosowski, 203). 2 In 202 Home Deot, an merican retailer of ome imrovement and construction roducts and services, acquired lacklocus, a start-u tat develos tecnologies for data-based ricing for retailers using among oters customers online store data (see Taylor, 202). 3 Siller (203) uses microdata on a large anel of comuter users to estimate te ro tability of rst-degree rice discrimination based on di erent tyes of user data. He nds tat te inclusion of data on te individual web browsing beavior for rst-degree rice discrimination increases ro ts muc above te level, wic is attained wen only demograic data is used for tailored ricing. 4 Te Federal Trade Commission, te main consumer olicy watcdog, recently investigated fraudulent business ractices by a igly oular smartone alication develoer. rigtest Flasligt, an a tat allows a one to be used as a asligt, deceived consumers about ow teir geolocation information would be sared wit advertisers and oter tird arties (FTC, 203). In a similar vein, electronics roducer LG was recently accused of its smart TVs secretly recording data on consumer viewing abits tat was used to dislay targeted advertisements, even after consumers oted out from tis feature (dams, 203). 2

5 of consumer arm. 5,6 Te argument backing tis view is intuitive: If consumers are unable to or wrongly foresee te consequences of teir actions, tey solve te wrong otimization roblem, wic er se cannot maximize teir true welfare. In tis article we argue tat tis intuition may not always old: Under very natural circumstances, wen rms invest in customer-tracking tecnology anticiating te reaction (or te absence tereof) of consumers, te latter may be better o being myoic tan soisticated. In tis article we analyze te incentives of cometing rms to invest in customer-tracking tecnology deending on consumer awareness. We consider a two-eriod model. In te rst eriod eac rm decides weter to invest in a tecnology, wic allows a rm to collect information on te references of its rst-eriod customers. In te second eriod rms comete and make use of te collected data for targeted ricing. We consider myoic and soisticated consumers: Te former do not know tat te collected data will be used for rice discrimination and care only about te current rices. In contrast, soisticated consumers are informed about te ability of rms to track teir beavior and anticiate receiving targeted o ers in te future. Our article contributes to te literature on cometitive rice discrimination wit demandside asymmetries, were consumers can be classi ed into di erent grous deending on teir references for te rms. Tisse and Vives (988) were te rst to sow te famous risoners dilemma result stating tat eac rm as a unilateral incentive to rice-discriminate, wic eventually makes bot rms worse-o, because rms end u o ering low rices to te loyal consumers of te rival. 7 Most articles in tis strand assume tat customer data is available exogenously. In our analysis we endogenize rms ability to collect customer data and sow tat it is collected in equilibrium only if consumers are myoic. In tat case two asymmetric 5 DG SNCO of te Euroean Commission, Euroe s rimary consumer olicy institution, lists limited foresigt and consumer myoia among te major cannels of beavioral biases tat give rise to consumer detriment. See tt://ec.euroa.eu/consumers/strategy/docs/study_consumer_detriment.df,.97. Retrieved January 6, In 202 te Euroean Commission roosed a major reform of te Euroean Union s data rotection rules, wic will, among oters, reinforce consumer rivacy in online services. See tt://ec.euroa.eu/justice/datarotection/. Retrieved February 6, similar contribution is made in Sa er and Zang (995) and ester and Petrakis (996). Oter aers sow tat rms ability to discriminate based on consumer brand references does not necessarily lead to a risoners dilemma. For examle, in Sa er and Zang (2000) rms may bene t from te ability to discriminate among te two consumer grous loyal to eac of te rms if tese grous are su ciently eterogeneous in te strengt of teir loyalty. Cen, Narasiman and Zang (200) sow tat wen te targeting ability of one or bot rms imroves, but remains imerfect, rms ro ts may increase. In Sa er and Zang (2002) a rm wit a stronger brand loyalty may bene t from rms ability to discriminate among individual consumers based on te strengt of brand loyalty. 3

6 equilibria emerge, were only one of te rms invests in customer-tracking tecnology. Wile tis investment is individually ro table, in te sirit of Tisse and Vives rms joint ro ts over two eriods are lower comared to te no-investment case. However, wen consumers are soisticated, individual incentives to invest vanis, and rms avoid te reduction in joint ro ts. Our article is also related to te literature on beavior-based rice discrimination, were rice discrimination emerges as equilibrium beavior (see, for instance, Fudenberg and Villas-oas, 2005). We argue tat investment incentives into a tecnology tat enables targeted ricing deend crucially on consumer awareness: Wit soisticated consumers rms coose not to invest, and rice discrimination does not take lace in equilibrium. Soisticated consumers correctly anticiate tat a rm olding customer-tracking tecnology will use te collected data for targeted ricing and reduce teir rst-eriod demand resectively. y avoiding investment rms commit not to rice discriminate, wic restores consumer demand. Cen and Iyer (2002) and Liu and Serfes (2004) directly address rms incentives to invest in customer data (tecnology). Cen and Iyer consider a Hotelling model were rms can invest in a database tecnology, wic allows to reac individual consumers wit customized rices. Te autors sow tat full addressability never emerges in equilibrium even wen te marginal cost of te database tecnology is zero, because it leads to a very intense rice cometition. Similarly, in our model rms never collect data about all consumers in te market. Even wen consumers are myoic, only one of te rms invests in equilibrium, because if bot rms old customertracking tecnology, cometition would intensify in bot eriods. Liu and Serfes (2004) also consider a Hotelling model and analyze rms incentives to acquire data on consumer brand references of an exogenously given quality, wic can be used for targeted ricing. Te autors sow tat wen data quality is low, rms do not acquire customer data in equilibrium. We also nd te equilibrium, were rms do not invest in customer-tracking tecnology and, ence, do not gain customer data, rovided consumers are soisticated. Finally, our article contributes to te beavioral industrial organization literature, esecially to te strand focusing on myoic consumers. Gabaix and Laibson (2006) discuss ow consumer myoia can exlain te existence of srouded attributes for some consumer goods. Myoic consumers buying certain goods (e.g., rinters) may not take into account te rice of comlementary roducts (e.g., rinter cartridges). Gabaix and Laibson sow tat if te sare of myoic 4

7 consumers is large enoug, te srouded rices equilibrium exists, were rms carge ig addon rices and ide tis information from consumers in te rimary market. In tis equilibrium myoic consumers are worse o comared to soisticated consumers, because tey ay ig add-on rices, wile te former bene t from te low base-good rices and substitute away from te exensive add-ons. In our analysis myoic consumers can be better o tan soisticated consumers, if te discount factor is large enoug. Wit myoic consumers a rm nds it individually ro table to invest in customer-tracking tecnology, wic, owever, decreases rms joint ro ts and bene ts consumers. Wen consumers are soisticated, individual incentives to invest vanis. Hence, we nd tat rms are always better-o wen consumers are soisticated. 8 Our article is organized as follows. In te next section we introduce te model. In Section 3 we rovide te equilibrium analysis of te second eriod of te game. In Section 4 we derive te equilibrium of te rst eriod of te game for te case of myoic consumers. In Section 5 we rovide te equilibrium analysis of te rst eriod of te game for te case of soisticated consumers. In Section 6 we comare te equilibrium results for te cases of myoic and soisticated consumers and analyze rms incentives to educate consumers. Finally, Section 7 concludes. 2 Te Model We consider a standard Hotelling model were two rms, and, sell two versions of te same roduct. Firms are located at te end oints of an interval of unit lengt wit x = 0 and x = denoting teir locations. Tere is a mass of consumers normalized to unity. Every consumer is caracterized by an address x 2 [0; ] denoting er reference for te ideal roduct. If a consumer does not buy er ideal roduct, se as to incur linear transortation costs roortional to te distance to te rm. Te utility of a consumer wit address x from buying te roduct of rm i = ; in eriod t = ; 2 at te rice t i is U t i ( t i; x) = v t jx x i j t i, 8 Tere are oter studies, wic sow tat rms are not necessarily worse o wen consumers become more soisticated. For examle, Eliaz and Siegler (20) introduce a model were marketing activities of te rms can in uence te set of alternatives, wic te boundly rational consumers erceive as relevant for teir urcasing decisions. Tey sow tat rms ro ts may increase wen consumers become more rational. 5

8 were v > 0 is te basic utility, wic is assumed to be large enoug suc tat te market is always covered in equilibrium. consumer buys from te rm delivering a iger utility. 9 We consider a two-eriod game. Initially, rms old no customer data, but can invest in customer-tracking tecnology, wic allows to collect data on te brand references of consumers wo buy from tem in te rst eriod. 0 In te second eriod te rm(s) wit customer data can engage in rst-degree rice discrimination among consumers wose data it (tey) ave. Precisely, te timing is as follows. Period : Stage (Investment). Firms decide indeendently and simultaneously weter to invest in customer-tracking tecnology. Stage 2 (Cometition wit uniform rices). First, rms ublis indeendently and simultaneously teir uniform rices. Consumers ten observe tese rices and make teir urcasing decisions. Period 2: Stage (Cometition wit uniform rices and discounts). Firms indeendently and simultaneously coose teir uniform rices. Subsequently, te rm(s) wit customer data issues (issue) discounts to consumers. Finally, consumers make teir urcasing decisions. Te timing of te cometition stage in Period 2 is consistent wit a large body of literature on cometitive rice discrimination were rms make teir targeted o ers after setting regular rices (e.g., Tisse and Vives, 988; Sa er and Zang, 995, 2002; Liu and Serfes, 2004, 2005; Coudary et al., 2005). It re ects te observation tat discounts issued to ner consumer 9 We follow Liu and Serfes (2006) and use two tie-breaking rules. ssume tat bot rms o er equal utilities. In tis case a consumer cooses te closer rm if bot rms old (or bot rms do not old) customer-tracking tecnology (if x = =2, ten te consumer visits rm ). Second, a consumer cooses te rm olding customertracking tecnology, if te oter rm does not ave it. 0 In te literature on beavior-based rice discrimination one usually assumes tat in te second eriod a rm can only distinguis among consumers wo boug from it and te rival in te rst eriod (see, for instance, Fudenberg and Villas-oas, 2005). We follow Liu and Serfes (2006) and assume tat in te rst eriod rms collect data on te references of teir customers. Tis assumtion relies on te observation tat modern information tecnologies allow rms to learn more about te own customers tan just distinguising tem from tose of te rival. For examle, cookies tat collect data on consumers web browsing beavior or consumer ro les in social networking websites can serve as sources of additional data on consumers references. Note tat tis timing is equivalent to te following: i) in te subgame were bot rms old customertracking tecnology, rms coose all te rices simultaneously, and ii) in te subgames were only one rm olds customer-tracking tecnology, te rm witout data cooses its rices rst, and te oter rm follows. 6

9 grous can be canged easier tan rices targeted at broader consumer grous. Moreover, if rms decide simultaneously on regular rices and discounts, no Nas equilibrium in ure strategies may exist. We assume tat rms maximize te discounted sum of ro ts over two eriods using common discount factor 0. We distinguis between two cases, wit myoic and soisticated consumers. Te former take into account only rices in te rst eriod wile making urcases in tat eriod, because tey do not realize tat te rm(s) olding customer-tracking tecnology will use customer data collected in te rst eriod for rice discrimination in te second eriod. In contrast, soisticated consumers maximize te discounted sum of utility over bot eriods. s is common in te literature, we assume tat soisticated consumers use te same discount factor as te rms (see, for instance, Fudenberg and Tirole, 2000). We will also use tis discount factor to comute te discounted consumer surlus over two eriods wen consumers are myoic. We seek for a subgame-erfect Nas equilibrium and start te analysis from te second eriod. 2 3 Equilibrium nalysis of te Second Period Deending on rms coices weter to invest in customer-tracking tecnology in te investment stage of te rst eriod, tree tyes of subgames can emerge: i) subgame, were only one of te rms invested, ii) subgame, were bot rms invested, iii) subgame, were none of te rms invested. In te latter case our game reduces to two indeendent static Hotelling models, were in equilibrium rms carge rices t = t = =2 (t = f; 2g), and eac rm serves alf of te market. To te subgames i) and ii) we will refer as asymmetric and symmetric subgames and will denote tem wit te subscrits s and S, resectively. We will assume tat it is rm, wic olds customer-tracking tecnology in te asymmetric subgame. Let ( ; ) denote te market sare of rm in te rst eriod, to wic we will sometimes refer wit to simlify te notation. We will assume tat consumers wit brand 2 Unlike in Fudenberg and Tirole (2000) wo ave a game wit incomlete information and, ence, solve for a erfect ayesian equilibrium, our game is a game wit comlete information. In Fudenberg and Tirole (2000) a rm knows only weter a given consumer boug from it or from te rival in te rst eriod. Hence, rms sould form beliefs about te references of consumers in tose two grous. We assume, in contrast, tat customertracking tecnology allows rms to observe te references of consumers it served in te rst eriod. Since te market is always covered in equilibrium, all oter consumers boug from te rival, suc tat a rm olding customer-tracking tecnology also knows wic consumers were served by te rival. 7

10 references x (x > ) bougt from rm () in te rst eriod. 3 To te former (te latter) we will refer as te turf of rm (). Similarly, we will denote te market sare of rm in te second eriod as 2 ( 2 ; 2 ). Furtermore, consumers wit x =2 (x > =2) we will call te loyal consumers of rm (). symmetric subgame. In te second eriod rm can discriminate among consumers on its turf and as to carge a uniform rice to consumers on te turf of rm. Firm, in contrast, as to o er a uniform rice to all consumers. Te following roosition caracterizes te equilibrium of te second eriod for any. Lemma. (Second eriod. symmetric subgame.) ssume tat only rm invested in customer-tracking tecnology in te rst eriod. Te equilibrium of te second eriod deends on te size of rm turf as follows. i) If it is relatively small, (3 tose wit x > (5 + 2 )=8. 2)=2, rm loses consumers on its turf and serves Firm carges te rice 2;s ( ) = t(3 2 )=2. Te discriminatory rice of rm is 2;s x; = t 3 2 =2 + t( 2x), on te turf of rm it carges te rice 2;s x; = t 5 6 =4. Firms realize ro ts 2;s ( ) = t 28 i =32 and 2;s ( ) = t(3 2 ) 2 =6. ii) If it is relatively large, > (3 2)=2, rm loses consumers on its turf and serves tose wit x 3=4. Firm carges te rice 2;s ( ) = t=2. Te discriminatory rice of rm to consumers wit x 3=4 is 2;s (x; ) = t=2 + t( 2x), to all oter consumers rm carges te rice 2;s Proof. See endix. (x; ) = 0. Firms realize ro ts 2;s ( ) = 9t=6 and 2;s ( ) = t=8. In te asymmetric subgame rm as a cometitive advantage as it olds customer data and can better target consumers. Wen increases, rm gets more data and can also on average better estimate te references of consumers on te turf of rm. Tis allows rm to gain consumers on te turf of rm, owever, only if is not large. In equilibrium, te uniform rice of rm as to strike an otimal balance between gaining new market sares and extracting rents from its most loyal consumers. Wen is low ( (3 2)=2), rm olds data on consumers wic are relatively loyal to it and cometing for wom is costly for rm, suc tat te latter follows te rent-extraction strategy, carges a relatively ig uniform rice 3 We will rove below tat tis olds in any subgame, symmetric and asymmetric. 8

11 and loses consumers on its turf. Wen is large ( > (3 2)=2), te ability of rm to comete for te loyal consumers of te rival increases, suc tat rm is forced to rotect its market sares by carging a relatively low uniform rice, and its market sares increase. In tat case rms second-eriod market sares do not deend on, because te non-discriminatory rice of rm is zero, and te rice of rm does not deend on directly, only troug te equilibrium rice of rm on s turf, because rm targets te most loyal consumers on its turf. We now consider ow rms ro ts, 2;s () and 2;s (), cange wit. On te interval (3 2)=2, were te second-eriod market sare of rm increases in, te ro t of rm rst increases and ten starts to decrease. Te latter aens because te uniform rice of rm, wic decreases in, uts a downward ressure on rm s discriminatory rices. Wen rm switces to a market-rotection strategy (at = (3 2)=2), te ro t of rm decreases abrutly and does not cange wit a furter increase in, because bot its rices and market sares do not cange in. On te interval (3 2)=2 bot te uniform rice and te market sare of rm decrease in, so does its ro t. On te interval > (3 2)=2, were rm adots a market-rotection strategy bot its uniform rice and te market sare remain constant, so tat te ro t of rm does not cange in eiter. Symmetric subgame. In te second eriod eac rm can discriminate among consumers on its turf. Te following lemma states te equilibrium of te second eriod deending on. Lemma 2. (Second eriod. Symmetric subgame.) ssume tat bot rms invested in customertracking tecnology in te rst eriod. Te equilibrium of te second eriod deends on te size of rm s turf as follows. i) If =2, ten on te turf of rm rms carge rices 2;S x; = t ( 2x) and 2;S x; = 0, were rm serves all consumers. On te turf of rm rms carge rices 2;S x; = t 2 =2 and 2;S x; = t 2 =2 + t (2x ), were rm serves consumers wit x < 2 + =4. Firms realize ro ts 2;S = t 4 i =8 and 2;S = t 4 i =6. ii) If > =2, ten on te turf of rm rms carge rices 2;S x; = t ( 2x) + t 2 =2 and 2;S x; = t 2 =2, were rm serves consumers wit x 2 + =4. On te turf of rm rms carge rices 2;S x; = 0 and 2;S x; = t 2 =2, were rm serves all consumers. 2;S = t 4 i =6 and 9

12 2;S = t i =8 are rms ro ts over two eriods. Proof. See endix. In equilibrium in te symmetric subgame a rm never loses consumers on its turf if it only served te own loyal consumers, because it as data on teir recise brand references and can undercut any uniform rice of te rival. Te latter cannot ten do better tan carging te rice of zero on a rm s turf. In contrast, a rm always loses consumers on its turf if it served some of te rival s loyal consumers in te rst eriod. In equilibrium te rival targets its loyal consumers on a rm s turf and always makes some of tem switc. We now turn to te cange in rms ro ts deending on. s rms are symmetric, we only consider rm. If =2, te ro ts of rm increase in for two reasons. First, rm is able to extract more rents on its turf, because it gains more data on its loyal consumers, and te negative cometition e ect is absent as rm always carges te rice of zero tere. lso, rm increases its market sares on rm s turf. If > =2, te ro ts of rm increase in, altoug it loses market sares. Tis is due to iger rents rm gets on its turf, because it faces a ositive cometition e ect as rm targets wit te non-discriminatory rice its most loyal consumers tere wit an address close to. s a result, te ro ts of rm increase for any. Neverteless, rm s ro ts in a symmetric subgame reac te ro t level in te subgame were none of te rms invested in customer-tracking tecnology only if it olds data on more tan 90 ercent of consumers in te market (recisely, if > 2 =2). Te reason is tat in te symmetric subgame every rm can distinguis between its own loyal consumers and tose of te rival, and rices aggressively te latter grou. Precisely, for any =2 rm carges te rice of zero to te loyal consumers of rm on te latter s turf. Tisse and Vives (988) rst identi ed tis negative cometition e ect driven by te availability of data on consumers brand references. Our results are di erent from Fudenberg and Tirole (2000), were in te second eriod rms can only distinguis between consumers on te two turfs. In teir model a rm may lose consumers on its turf even if it contains only its loyal consumers, because a rm does not ave data on teir recise brand references and as to carge a uniform rice. Ten if its turf is relatively large, a rm refers to extract rents from its more loyal consumers, wile te less loyal consumers switc to te rival. lso, di erent from our result on a ositive monotone relationsi between te size of a rm s turf and its second-eriod ro ts, in te case of a uniform consumer 0

13 distribution in Fudenberg and Tirole tis relationsi is U-saed. Pro ts are lowest wen rms turfs are of equal sizes, in wic case every rm can erfectly discriminate among its own loyal consumers and tose of te rival, and cometition is most intense. Pro ts are igest if one of te rms served all consumers in te rst eriod, because tis outcome is least informative leading to te weakest cometition. In contrast, if a rm did not serve any consumers in te rst eriod, in our model te rival olds te largest data leading to te most intense cometition. 4 Equilibrium nalysis of te First Period wit Myoic Consumers Myoic consumers do not foresee tat te rm, wic invested in customer-tracking tecnology, will use te data collected in te rst eriod for rice discrimination in te second eriod. Hence, te address of te indi erent consumer in rst eriod, ( ; ), is given by a standard exression: ( ; ) = =2 = (2t). Te following lemma summarizes our results on te equilibrium in te asymmetric subgame wit myoic consumers. Lemma 3. (First eriod. symmetric subgame. Myoic consumers.) ssume tat only rm invested in customer-tracking tecnology and consumers are myoic. In equilibrium in te rst eriod rices are ;s () = t = (5 + 24) and ;s () = t = (5 + 24), were rm serves consumers wit x ;s () and ;s () = (24 )=(0 + 48). Pro ts in te rst eriod are ;s () = t (24 ) = [(5 + 24) (0 + 48)] and ;s () = t ( + 24) = [(5 + 24) (0 + 48)]. Te discounted sum of rms ro ts in bot eriods is +2;s () = t = 4 (5 + 24) 2i and +2;s () = t = Proof. See endix. 2 (5 + 24) 2i. Since rms maximize te discounted sum of teir ro ts, tey distort rst-eriod rices for iger second-eriod ro ts. Te ro ts of rm in te second eriod decrease in te size of rm s turf (rovided is not very large, wic is te case in equilibrium). Ten in te rst eriod rm carges a relatively low rice to revent te rival from gaining muc customer data. In contrast, rm carges a relatively ig rice in te rst eriod, altoug it means obtaining less customer data, because tis secures iger second-eriod ro ts by making rm rice less aggressively ten. s a result, in te rst eriod rm serves less consumers tan

14 te rival and gains data only on its most loyal consumers. s rms distort teir rst-eriod rices to increase ro ts in te second eriod, eac reas lower ro ts in te rst eriod tan in te subgame were neiter rm invests in customertracking tecnology. However, in te second eriod rm gains iger ro ts due to its informational advantage, and its discounted ro ts over two eriods are iger, wile te ro ts of rm over two eriods are lower comared to te subgame were rms do not invest. We next consider te symmetric subgame wit myoic consumers. Te following lemma summarizes our results. Lemma 4. (First eriod. Symmetric subgame. Myoic consumers.) ssume tat bot rms invested in customer-tracking tecnology and consumers are myoic. Two asymmetric equilibria exist were in te rst eriod rms carge rices ;S i () = t 2 2 = (2 + ) and ;S j () = t = (2 + ), and ;S i () > ;S j (), i; j = f; g and i 6= j. Firm i serves consumers wit x (2 ) = [2 (2 + )]. In te rst eriod rms realize rofits ;S i () = t (2 ) 2 2 = 2 ( + 2) 2i and ;S j () = 3t ( + 4) = 2 ( + 2) 2i. Firms ro ts over two eriods togeter are +2;S i () = t = 4 ( + 2) 2i and +2;S j () = t = 2 ( + 2) 2i. Proof. See endix. s sown in Lemma 2, eac rm s ro ts in te second eriod increase monotonically in te size of its turf, suc tat eac rm as an incentive to carge a relatively low rice in te rst eriod to gain more customer data. Interestingly, we get two asymmetric equilibria in te rst eriod, were rms carge di erent rices. Tis result is driven by te fact tat te second-eriod ro t of a rm is given by two di erent functions deending on weter a rm ad a larger or a smaller market sare in te rst eriod. Te rm wit a smaller turf as a low incentive to decrease its rst-eriod rice, because its second-eriod ro ts would increase slowly. On te oter and, te rm wit a larger turf as a low incentive to increase its rst-eriod rice, because its second-eriod ro ts would decrease substantially ten. Firms are worse-o in bot eriods comared to te subgame were tey do not old customer-tracking tecnology and realize te ro t of t=2. Second-eriod ro ts are low due to te negative cometition e ect driven by rice discrimination described above. First-eriod ro ts are low, because rms comete intensively for market sares to collect more customer data. Tere is a similar result in two-eriod models were consumers ave switcing costs. 2

15 Tere rms comete in te rst eriod to lock-in more consumers and gain lower ro ts tan in te static game (see, for instance, Klemerer, 995). However, di erent from tose models in our case ro ts are also lower in te second eriod comared to te static ro ts. In te next roosition we summarize rms incentives to invest in customer-tracking tecnology in te rst eriod. Wit te subscrit m we will refer to te equilibrium values wen consumers are myoic. Proosition. ( Myoic consumers. Investment incentives and welfare.) If consumers are myoic, two asymmetric equilibria exist, were one of te rms invests in customer-tracking tecnology. +2 ;m () = t = 4 (5 + 24) 2i is te ro t over two eriods of te investing rm and +2 ;m () = t = 2 (5 + 24) 2i is te ro t over two eriods of te rm wic does not invest. Te discounted social welfare and consumer surlus over two eriods are given by SWm +2 () = v( + ) t = 4 (5 + 24) 2i and CSm +2 () = v( + ) t = 4 (5 + 24) 2i, resectively. Proof. See endix. If te rival does not invest in customer-tracking tecnology, a rm as a unilateral incentive to do tat. s we sowed in Lemma 3, in tat case a rm realizes lower ro ts in te rst eriod, wic are outweiged by iger second-eriod ro ts driven by its informational advantage. However, a rm does not ave an incentive to invest in customer-tracking tecnology if te rival does te same, because cometition would ten intensify in bot eriods. s a result, in equilibrium only one of te rms invests. 4 Tis result is similar to Cen and Iyer (2002) were ex-ante symmetric rms make asymmetric investments in customer data to mitigate cometition. Wile over two eriods te rm olding customer-tracking tecnology realizes iger ro ts, rms joint ro ts are lower comared to te case were rms do not invest in customer-tracking tecnology. In equilibrium social welfare is also smaller comared to te case witout investment. Tis is because te asymmetric investment decisions boil down into asymmetric market sares in bot eriods suc tat some consumers do not buy from teir most referred rms imlying allocative ine ciency. Consumer surlus can be iger tan in te case were rms do not 4 In reality we often observe tat rms di er in teir abilities to collect and analyze customer data for targeted ricing. Te most rominent examle is te UK s retail industry, were Tesco, te world s tird largest suermarket grou, became te leading suermarket cain in te UK after te successful introduction of a loyalty card (see Winterman, 203). Using is loyalty card Tesco collects data on consumers references and based on tat data designs individual discounts and rewards to consumers. 3

16 invest in customer-tracking tecnology, if > = 0:9. In tat case consumers bene t more from lower ayments to te rms tan tey lose from iger transortation costs. 5 Equilibrium nalysis of te First Period wit Soisticated Consumers Soisticated consumers correctly anticiate tat a rm olding customer-tracking tecnology will use te data collected in te rst eriod for targeted ricing in te second eriod and adat resectively te demand in te rst eriod. We will consider again in turn eac subgame (asymmetric and symmetric) and will start wit te derivation of consumer demand in te rst eriod. symmetric subgame. Te following lemma states consumer demand in te rst eriod in te asymmetric subgame. Lemma 5. (First eriod. symmetric subgame. Soisticated consumers. Demand.) ssume tat only rm invested in customer-tracking tecnology and consumers are soisticated. Ten te demand of rm in te rst eriod is given by: 8 >< ;s ( ; ) = >: if < t 2 + 2t if t < t(2 t(4 5)+4( ) 2t(4 3) if t(2 0 if > 2) 2) t(3 2 4) 4 t(4 5) + 4 t(4 5) + 4. () Proof. See endix. If = 0, demand () yields a standard exression for te market sare of rm in te rst eriod: ( ; ) = =2 + = (2t). Oterwise, it is di erent from te latter in two ways: First, it is discontinuous and second, it is given by a corresondence suc tat if rm carges a moderate rice, t(2 2) t(3 2 4)=4 < t(2 2), it can gain eiter relatively few or many consumers. ot roerties are related to te discontinuity of te otimal strategy of rm in te second eriod at te oint = 3 2 =2, were rm switces from a rent-extraction ( 2;s ( ) = t(3 2 )=2) to a market-rotection strategy ( 2;s ( ) = t=2). If 3 2 =2, in te second eriod rm exands its market sares and carges ositive rices to all consumers wose references it learns. In tat case tere is a 4

17 disadvantage of buying at rm in te rst eriod related to reference revealing, suc tat te indi erent consumer sould ave a relatively strong reference for rm imlying a relatively large market sare of rm. If > 3 2 =2, in te second eriod rm exands its market sares, and rm carges te rice of zero to te indi erent consumer. In tat case tere is no disadvantage of buying at rm in te rst eriod related to reference revealing, and te indi erent consumer can ave a relatively weak reference for rm imlying a relatively small market sare of rm. Hence, under a moderate rst-eriod rice te market sare of rm can be eiter relatively large or small. In te latter case consumers correctly anticiate tat tey will receive targeted o ers in te second eriod based on te revealed references in case of buying at rm and reduce te rst-eriod demand resectively. If 3 2 =2, rm faces in te rst eriod a more elastic demand tan if > 3 2 =2. In te former case uon buying at rm () in te rst eriod, in te second eriod te indi erent consumer buys at rm at a discriminatory (non-discriminatory) rice. ot rices decrease in te address of te indi erent consumer (te market sare of rm in te rst eriod). However, te discriminatory rice decreases more because it is targeted directly at tat consumer. Hence, wen te rst-eriod market sare of rm gets larger, te di erence between te discriminatory rice of rm and non-discriminatory rice of rm in te second eriod decreases as well as te disadvantage related to reference revealing to rm. s a result, for a given rice reduction by rm more consumers want to buy from it in te rst eriod tan in te case > 3 2 =2, were tere is no disadvantage related to reference revealing to rm. In te next lemma we caracterize te equilibrium of te rst eriod. Lemma 6. (First eriod. symmetric subgame. Soisticated consumers.) ssume tat only rm invested in customer-tracking tecnology and consumers are soisticated. Te equilibrium of te rst eriod deends on te discount factor as follows. i) If ( )=2, ten in te rst eriod rms carge rices ;s () = t( )=(96 52) and ;s () = t( )=(96 52), te market sare of rm is ;s () = (24 23)=(48 26). +2;s () = t = 8 (3 24) 2i and +2;s () = t = 8 (3 24) 2i are rms ro ts over two eriods. ii) If ( )=2 < < 6=7, ten in te rst eriod rms carge rices ;s () = 0 and 5

18 ;s () = t( )=(32 28), te market sare of rm is ;s () = (7 6)=(7 8). Over two eriods rms realize ro ts +2;s = t = 32 (7 8) 2i and +2;s = t = [6 (8 7)]. iii) If 6=7, ten in te rst eriod rms carge rices ;s () = 0 and ;s () = t(5 4)=4, te market sare of rm is ;s () = 0. Firms ro ts over two eriods are +2;s () = 25t=32 and +2;s () = (29 6) t=6. Proof. See endix. Firm carges a ositive rice and serves some consumers in te rst eriod only if te discount factor is su ciently small ( ( )=2). Under a iger discount factor (( )=2 < < 6=7) rm as to reduce its rst-eriod rice to zero to attract some consumers. Finally, if te discount factor is large ( 6=7), rm does not serve any consumers in te rst eriod altoug it carges te rice of zero wile te rival s rice is ositive. Soisticated consumers correctly anticiate tat if tey buy at rm in te rst eriod, it will discriminate in te second eriod based on teir references, and reduce te demand for rm. s a result, under any discount factor over two eriods rm realizes lower ro ts tan in te subgame were neiter rm olds customer-tracking tecnology. Tis is di erent in te asymmetric subgame wit myoic consumers, were lower rst-eriod ro ts of rm are comensated by iger ro ts in te second eriod. Wit myoic consumers rst-eriod ro ts of rm are low for two reasons. First, rm rices aggressively to revent rm from gaining muc customer data. Second, rm carges a relatively ig rice to serve less consumers in te rst eriod to make rm rice softer in te second eriod. On te to of tat, wit soisticated consumers rm su ers from a decrease in te rst-eriod demand, suc tat te resulting losses cannot be anymore comensated by iger ro ts in te second eriod. Symmetric subgame. Te following lemma states consumer demand in te rst eriod in te symmetric subgame. Lemma 7. (First eriod. Symmetric subgame. Soisticated consumers. Demand.) ssume tat bot rms invested in customer-tracking tecnology and consumers are soisticated. Ten 6

19 te demand of rm in te rst eriod is given by: 8 >< ;S ; = >: 2 0 if t(2 ) if if > t(2 ) 2 t(2 ) 2 t(2 ) 2 t(2 ) < 2. (2) Proof. See endix. Similar to te rst-eriod demand in te asymmetric subgame, in te symmetric subgame, demand wen consumers are soisticated is more elastic tan wen consumers are myoic. If =2, uon buying at rm in te rst eriod, te indi erent consumer buys at rm in te second eriod at a discriminatory rice 2;S = t 2. If instead se urcases at rm in te rst eriod, rm does not learn er references, and in te second eriod te indi erent consumer buys at rm at te non-discriminatory rice 2;S = t 2 =2. ot rices decrease in, but te discriminatory rice decreases more because it is targeted at te indi erent consumer directly. Hence, te di erence between te two rices becomes smaller, and more consumers switc to rm in case of a rice reduction comared to te case of myoic consumers wo do not take into account rices in te second eriod wile making teir rsteriod urcases. 5 In te following lemma we state te equilibrium in te symmetric subgame wen consumers are soisticated. Lemma 8. (First eriod. Symmetric subgame. Soisticated consumers.) ssume tat bot rms invested in customer-tracking tecnology and consumers are soisticated. Two asymmetric equilibria exist. ;S i () = t = (24 0) and ;S j () = t = (24 0) are rices in te rst eriod, were te market sare of rm i is ;S = (2 7) = (24 0), wit i; j = f; g and i 6= j. Over two eriods rms realize ro ts +2;S i () = t = 2 (5 2) 2i and +2;S j () = t = 5 Tis result is di erent from Fudenberg and Tirole (2000), were wit a uniform consumer distribution and soisticated consumers rst-eriod consumer demand is less elastic if rice discrimination in te second eriod is banned (in te latter case rst-eriod consumer demand is same as in te case wit myoic consumers in our analysis). In Fudenberg and Tirole te indi erent consumer of te rst eriod switces from te rm it bougt in te rst eriod. ssume tat te address of te indi erent consumer gets larger. Ten uon buying at rm in te rst eriod, te indi erent consumer will buy at rm in te second eriod at a iger rice, because rst-eriod consumers of rm become on average more loyal to rm. In contrast, in tat case in our model uon buying at rm in te rst eriod, te indi erent consumer will buy (again) at rm in te second eriod at a lower rice, because se becomes less loyal to rm. Tis di erence makes rst-eriod demand in Fudenberg and Tirole (2000) less resonsive to rice canges tan in te symmetric subgame wit soisticated consumers in our model. 7

20 4 (5 2) 2i. Proof. See endix. s we know from Lemma 2, eac rm s second-eriod ro t increases in te size of its turf and te amount of data collected about consumers. Similar to te symmetric subgame wit myoic consumers, every rm as ten an incentive to reduce its rst-eriod rice to get more customer data. However, wit soisticated consumers rms face a more elastic demand in te rst eriod leading to a more intense cometition. s a result, rms carge lower rices in te rst eriod and get lower ro ts over two eriods comared to te case of myoic consumers. Finally, in te following roosition we caracterize rms equilibrium incentives to invest in customer-tracking tecnology wen consumers are soisticated. Wit te subscrit s we will refer to te equilibrium values wen consumers are soisticated. Proosition 2. (Soisticated consumers. Investment incentives and welfare.) If consumers are soisticated, tere exists te unique equilibrium (in dominant strategies), were neiter rm invests in customer-tracking tecnology. Over two eriods eac rm realizes te ro t +2 i;s () = t ( + ) =2. Social welfare and consumers surlus over two eriods are given by SW +2 s () = (v t=4) ( + ) and CS +2 s () = (v 5t=4) ( + ). Proof. See endix. Di erent from te case of myoic consumers were one of te rms invests in equilibrium, wit soisticated consumers no investment is made in customer-tracking tecnology. In te latter case a rm does not ave a unilateral incentive to invest, because it cannot make advantage of its ability to collect data as consumers anticiate tat tis data will be used for rice discrimination in te second eriod and reduce teir rst-eriod demand resectively. Similarly, a rm does not ave an incentive to invest if te rival invests. Wit soisticated consumers investment incentives in tat case are even weaker tan wit myoic consumers, because in te symmetric subgame wit soisticated consumers rms face a more elastic demand, wic intensi es cometition in te rst eriod. Te intuition beind our results is similar to te one, wic exlains te cange in monoolist s ro ts over two eriods wen it can recognize consumers in te second eriod comared to te case wen recognition is not ossible (see, for instance, Fudenberg and Villas-oas, 2005). Te ro ts increase wen consumers are myoic and decrease wit soisticated consumers. In te latter case te monoolist faces a lower demand in te rst eriod as some consumers ostone teir urcases to a second eriod to buy 8

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