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

Transcription

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: [email protected] 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. [email protected]. y Euroean Commission DG COMP - Cief Economist Team and Düsseldorf Institute for Cometition Economics (DICE), Heinric Heine University of Düsseldorf. [email protected]. 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

21 at a lower rice. Ten if te monoolist could coose weter to recognize consumers, it would refer to recognize (not to recognize) wen consumers are myoic (soisticated). Parallel to tat result, in our model in equilibrium a rm invests (does not invest) in customer-tracking tecnology if consumers are myoic (soisticated). 6 Comarison of Equilibria wit Myoic and Soisticated Consumers In tis section we comare te equilibrium results in te two versions of our model and ten conclude on rms incentives to educate consumers. Precisely, we assume tat rms could communicate to consumers tat customer data collected using customer-tracking tecnology allows rms to discriminate among tem. Te following roosition summarizes our results on te equilibrium comarison. Proosition 3. (Comarison: Myoic consumers vs. soisticated consumers.) Comared to te case of soisticated consumers, wen consumers are myoic: i) rms realize lower discounted joint ro ts over two eriods, ii) discounted social welfare over two eriods is smaller, iii) consumers enjoy a larger discounted surlus over two eriods if > = 0:9 and a (weakly) smaller oterwise. Proof. See endix. In te literature on cometitive rice discrimination wit demand-side asymmetries tere is a famous risoners dilemma result, wic states tat eac rm as an individual incentive to discriminate wile bot rms jointly are worse-o comared to te no-discrimination case (see, for instance, Tisse and Vives, 988). In our model rms do not end u in te risoners dilemma: In equilibrium at most only one rm invests in te ability to discriminate (wen consumers are myoic). voiding investment in te asymmetric subgame rm foregoes te oortunity to learn te references of consumers on its turf but bene ts from softer cometition 9

22 in bot eriods. 6,7 Firm, in contrast, cooses to invest in customer-tracking tecnology, if consumers are myoic. Wile it is individually better-o, in te sirit of Tisse and Vives rms joint ro ts over two eriods decrease comared to te no-investment case. However, wit soisticated consumers te unilateral incentives to invest vanis too. In case of investment te ro ts of rm in te rst eriod are too low, because consumers resond wit demand reduction in tis eriod. s a result, surrisingly, rms jointly are better-o wen consumers are soisticated. In eac eriod, social welfare is smaller wen consumers are myoic. In tat case te asymmetric distribution of consumers between te rms driven by te asymmetric investment decisions, gives rise to te allocative ine ciency. Precisely, in te rst eriod some loyal consumers of rm buy at rm, because teir referred rm carges a relatively ig rice to kee its market sare small in order to soften cometition in te second eriod. In te second eriod, some of te loyal consumers of rm buy at rm, because te latter is able to o er tem better rices as it olds some customer data. Over two eriods myoic consumers ay less to te rms tan soisticated consumers, but at te same time ave to bear iger transortation costs. Te rst e ect dominates if te discount factor is su ciently large ( > =), in wic case consumers enjoy a iger surlus wen tey are myoic. To understand tis result, consider te equilibrium (asymmetric) wen consumers are myoic. s sown in Table, rms joint ro ts in te rst eriod decrease wen te discount factor becomes larger, because in tat case rms value a lot second-eriod ro ts and distort more rst-eriod rices. ltoug tis leads to a lower rst-eriod market sare of rm and, ence, to iger transortation costs, consumer surlus in tat eriod gets larger because teir ayments to te rms decrease. Given a smaller turf of rm, in te second eriod rm rices softer, wic results in iger ro ts for eac rm. 6 Wen consumers are myoic, in te rst eriod in equilibrium te uniform rice of rm in te asymmetric subgame is iger tan any rice in te two asymmetric equilibria in te symmetric subgame (comare Lemmas 3 and 4). lso, in te second eriod te uniform rice of rm on te turf of rm is iger in te asymmetric subgame comared to te second-eriod rice in any asymmetric equilibrium in te symmetric subgame. (Indeed, comare 2;s (x; (24 ) = (0 + 48)) = t (2 + 7) = (5 + 24) wit 2;S (x; (2 ) = (24 + 2)) = t= ( + 2) and 2;S (x; 3 ( + 4) = (24 + 2)) = 0.) 7 Liu and Serfes (2004) also introduce te investment stage were rms decide weter to acquire customer data of an exogenously given quality. Tey nd tat if customer data is erfect (te case most similar to ours), rms end u in te risoners dilemma. Comared to Liu and Serfes, in our model (wit myoic consumers) a rm as weaker incentives to invest in customer-tracking tecnology given tat te rival invests, because in case of investment cometition intensi es in bot eriods (were rms collect and comete using te collected customer data), wile in Liu and Serfes cometition intensi es only in one eriod. 20

23 In contrast, consumer transortation costs decrease, because rm gains little customer data and attracts only a few loyal consumers of te rival in te second eriod. s a result, wit an increase in, consumer surlus in tat eriod becomes smaller because consumers ayments to te rms increase. Wen is large enoug, te gains in consumer surlus in te rst eriod outweig te losses in te second eriod, and over two eriods myoic consumers enjoy a iger surlus tan soisticated consumers. Our results imly tat if te discount factor is large enoug ( > =), tere is a con ict between te maximization of consumer surlus and social welfare. Wile social welfare is always larger wen consumers are soisticated (and no investment in customer-tracking tecnology takes lace), in tat case consumers are better-o wen tey are myoic (and one of te rms invests). Ten governmental intervention aiming at te maximization of social welfare sould eiter educate consumers or roibit customer-tracking. However, bot tose olicies would decrease consumer surlus. Table : Comarison of te Equilibria in te Cases of Myoic and Soisticated Consumers Myoic Comarison consumers t = t = 2 t = t = t =@ + t ;m t ;s t =@ + t ;m t t + P t =@ + t P i;m t i;s t =@ + +2 ;m t =@ + +2 t () =2 + i P i i ;s + ;m +2 ;s +2 P i;m +2 2 t () =@ + CSm t CSs t + CSm +2 CSs +2 + if > if < SW t m i SW t s SWm +2 SWs +2 Note: + stays for a ositive sign and for a negative sign. Subscrit m ( s ) denotes te equilibrium value wen consumers are myoic (soisticated). We next analyze rms incentives to educate consumers troug making it known to tem tat customer-tracking tecnology allows rms to collect customer data, wic can be used for rice discrimination. We will sow tat rms coose to educate consumers, wic is otimal from te social welfare ersective and increases rms joint ro ts, but may arm consumers (if > =). We assume tat initially consumers are myoic and introduce Period 0, 2

24 were rms decide simultaneously and indeendently weter to educate consumers. Consumers become soisticated if at least one of te rms educates tem. We relax te assumtion tat rm is te rm, wic invests in te asymmetric equilibrium wen consumers are myoic and assume instead tat it is rm wit robability 2 [0; ] and wit robability it is rm. Table 2 resents te discounted sum of rms ro ts over two eriods deending on teir decisions to educate consumers. We searc for a subgame-erfect Nas equilibrium. Te following roosition summarizes our results on rms incentives to educate myoic consumers. Table 2: Firms Pro ts over Two Periods Deending on Teir Decisions to Educate Consumers Firm Educate Not Educate Firm t(+) 2 ; t(+) 2 t(+) 2 ; t(+) t(+) 2 ; t(+) 2 Educate Not Educate 2 f(); g() ()+ ( ) +2 ;m () and g() := ( ) +2 ;m () + +2 ;m (), () and +2 () are stated in Proosition. Note: f() := +2 ;m were +2 ;m ;m Proosition 4. (Firms incentives to educate myoic consumers.) are initially myoic. ssume tat consumers For any 2 [0; ] tere exists te equilibrium, were bot rms educate consumers. If < () ( > ()), tere exists te oter equilibrium, were only i i rm ( ) educates consumers ( () := t ( + ) =2 +2 ;m () = +2 ;m () +2 ;m () and i () := +2 ;m () t ( + ) =2 = +2 ;m () +2 ;m i). () If () (), ten two oter equilibria exist, were one of te rms educates consumers. Proof. See endix. In Gabaix and Laibson (2006) te srouded rices equilibrium were rms ide ig addon rices is sustained because rms do not ave an incentive to educate myoic consumers. Educating myoic consumers a rm teaces tem ow to exloit te existing rices at te market, wo refer in te end te srouding rival because of its low base-good rice. We sow, in contrast, tat if rms can educate consumers, ten in any equilibrium at least one of te rms does tat to revent te individually ro table investment in te customer-tracking tecnology, wic increases rms joint ro ts. Wile rms coices are e cient from te social welfare ersective, consumers are worse-o if te discount factor is su ciently large ( > =). 22

25 7 Conclusions In tis article we considered an industry were rms can invest in customer-tracking tecnology, wic allows a rm to collect data on te brand references of its customers. Our article makes four main contributions. First, we sow tat at most one of te rms invests in customer-tracking tecnology in equilibrium, suc tat rms never ave data on all consumers in te market. Investment by bot rms would intensify cometition in bot eriods: In te rst eriod rms would comete for larger market sares and more customer data, and in te second eriod eac rm would comete aggressively for te loyal consumers of te rival. Second, in equilibrium investment in customer-tracking tecnology takes lace only if consumers are myoic, wic makes bot rms worse-o comared to te case wen consumers are soisticated, were rms do not invest. Soisticated consumers correctly anticiate tat te rm olding customertracking tecnology will use te data collected in te rst eriod to rice discriminate in te second eriod and decrease te rst-eriod demand for tat rm resectively. Tird, myoic consumers can be better o tan soisticated consumers. Precisely, if te discount factor is su ciently large, myoic consumers bene t from lower ayments to te rms driven by teir investment decisions. s social welfare is always larger wen consumers are soisticated, in tat case tere is a tension between te maximization of consumer surlus and social welfare. Fourt, if rms can educate consumers, tey always ave an incentive to do tat in order to make te investment in customer-tracking tecnology individually unro table for any rm and tus secure iger joint ro ts. Wile rms decisions are e cient, consumers are better o remaining myoic if te discount factor is su ciently large. 8 endix In tis endix we rovide te roofs omitted in te text. Proof of Lemma. We start wit te otimal strategy of rm on its turf, wic is to make any consumer indi erent wenever ossible wit a non-negative rice: 2;s (x; 2 ) = max 0; 2 t(2x ). If 2 t 2, rm serves consumers wit x =2 + 2 = (2t) on its turf. If 2 > t 2, rm gains all consumers tere. We now turn to te turf of rm. If rms rices are not too di erent, tere is an indi erent consumer x I ( 2 ; 2 ) = =2+( 2 2 )=2t. Ten on rm s turf rm maximizes te ro t 2 x I ( 2 ; 2 ). Te 23

26 otimal strategy of rm on turf is 2;s (2 ; 2 t(2 )) = 0, 2;s (2 ; t(2 ) < 2 < t(3 2 )) = 2 + t 2 =2 and 2;s (2 ; 2 t(3 2 )) = 2 t. Using te otimal strategies of rm on te two turfs we get te demand of rm as D 2 2 ; 2 t(2 ) = =2 2 = (2t), D2 2 ; t(2 ) < 2 < t 3 2 = 3 2 =4 2 = (4t) and D2 2 ; 2 t(3 2 ) = 0. It is straigtforward ten tat we sould distinguis between te cases =2 and > =2 to derive te otimal rice of rm. Case : =2. Te otimal rice of rm is 2;s ( ) = t(3 2 )=2, and it serves consumers wit x > (5 + 2 )=8 and realizes te ro t 2;s = t(3 2 ) 2 =6, wile 2;s = t R 0 (5 2 4x)=2 dx + t(5 6 ) 2 =32 = t 28 i =32. Case 2: > =2. In equilibrium it can eiter be 2 t(2 ) or t(2 ) 2 < t(3 2 ), wile 2 t(3 2 ) is not ossible, because 2;s (2 ; ) = 0 ten. s 2;s (2 ; ) is given by di erent functions on te two intervals, we rst derive te maximal ro t on eac interval and ten comare tem to conclude about te otimal rice. We start wit 2 t(2 ). FOC yields 2 = t=2. Comaring t=2 and t(2 ) we conclude tat te ro t-maximizing rice of rm is 2 3=4 = t(2 ) and 2 > 3=4 = t=2. We get 2;s (t(2 ); ) = t( )(2 ) and 2;s 2 t(2 2;s t=2; = t=8. Hence, on te interval ) te maximal ro t of rm is 2;s 3=4 = t( )(2 ) and > 3=4 = t=8. We consider now te interval t(2 ) 2 < t(3 2 ). FOC yields 2 = t(3 2 )=2. Comaring t(3 2 )=2 and t(2 ) we conclude tat if 5=6, te ro t-maximizing rice of rm is 2 ( ) = t(3 2 )=2 and 2;s (t(3 2 )=2; ) = t(3 2 ) 2 =6. If > 5=6, te ro t-maximizing rice of rm is 2 = t(2 ) and 2;s (t(2 ); ) = t( )(2 ). Finally, we ave to determine te otimal rice of rm. 2;s t(3 2 )=2; > 2;s t(2 ); and 2;s = t(3 2 )=2 if 3=4. ssume 3=4 < 5=6. If (3 2)=2, we ave 2;s (t(3 2 )=2; ) 2;s t=2; and 2;s = t(3 2 )=2. If > (3 2)=2, te oosite inequality olds and 2;s = t=2. ssume > 5=6, in wic case 2;s t=2; > 2;s (t(2 ); ) and 2;s = t=2. Combining te cases =2 and > =2 we conclude tat te otimal rice of rm is 2;s ( (3 2)=2) = t 3 2 =2, 2;s ( > (3 2)=2) = t=2. In te former case 24

27 2;s = t R x =2 dx + t =32 = t 28 i =32 and 2;s ( ) = t(3 2 ) 2 =6. In te latter case 2;s = t R 3=4 0 (3=2 2x) dx = 9t=6 and 2;s ( ) = t=8. Q.E.D. Proof of Lemma 2. Consider rst te turf of rm, were its otimal strategy is to make any consumer indi erent wenever ossible wit a non-negative rice: 2;S (x; 2 ) = max 0; 2 t(2x ). Firm serves consumers wit x min =2 + 2 = (2t) ;. Maximizing te ro t min =2 + 2 = (2t) ; wit resect to yields te otimal rice of rm : 2;S =2 = 0 and 2;S > =2 = t 2 =2. In te former (latter) case rm serves all consumers (consumers wit x + 2 =4) on its turf. We now turn to te turf of rm, were its otimal strategy is to make any consumer indi erent wenever ossible wit a non-negative rice: 2;S (x; 2 ) = max 0; 2 + t(2x ). Firm serves consumers wit x max =2 2 = (2t) ;. Maximizing wit resect to te ro t max =2 2 = (2t) ; yields te otimal rice of rm : 2;S > =2 = 0 and 2;S =2 = t 2 =2. In te former (latter) case rm serves all consumers (consumers wit x + 2 =4) on its turf. 2;S = t R 0 ( 2x) dx+t 2 + =4 2 =2 = t 4 i =8 and 2;S = t R (2 +)=4 2 =2 + 2x dx = t 4 i =6 are ro ts if =2. 2;S = t R (2 +)=4 0 2 =2 + 2x dx = t 4 i =6 and 2;S = t 2 + =4 2 =2 + t R (2x ) dx = t 4 i =8 are rms ro ts if > =2. Q.E.D. Proof of Lemma 3. s follows from Lemma, we ave to distinguis between te cases (3 2)=2 and > (3 2)=2. ssume rst tat in equilibrium (3 2)=2. Ten and ave to maximize te ro ts +2;s ; = + t 28 i =32 and +2;s ; = + t =6, resectively, were = =2 ( )=2t (if and are not very di erent). Solving simultaneously FOCs we get te rices ;s () = t = (5 + 24) > 0 and ;s () = t = (5 + 24) > 0 for any, and ;s () = (24 )=(0 + 48). Note tat ;s () decreases in, wile ;s (0) = =2 and ;s () = 23=58, suc tat 0 < ;s () < (3 2)=2 for any. SOCs are also ful lled. We get +2;s () = t = 4 (5 + 24) 2i and +2;s () = t = 2 (5 + 24) 2i. To rove tat te rices ;s () and ;s () constitute te equilibrium, we ave to sow 25

28 tat none of te rms as an incentive to deviate suc tat ; > (3 2)=2 olds. ssume tat rm deviates on ;s () t < ;s () t(2 2), in wic case its ro t is +2;s ( ; ;s ()) = + 9t=6, were = =2 ( ;s ())=2t. FOC yields () = 2t( )=(5 + 24) > ;s () t(2 2). Hence, +2;s ( ; ;s ()) gets its maximum at = ;s () t(2 2), were > 0 and! 0. We get +2;s ( ;s () t(2 2); ;s ()) = t = [6(5 + 24)] and +2;s () > +2;s ( ;s () t(2 2); ;s ()) for any, suc tat rm does not ave an incentive to deviate on ;s () t < ;s () t(2 2). Note tat rm does not ave an incentive to deviate on < ;s () t eiter, because in tat case it realizes strictly lower ro ts tan at te rice = ;s ssume now tat rm deviates on t(2 its ro t is +2;s ( ; ;s olds +2;s () t. 2) + ;s () t + ;s (), in wic case ()) = + t=8, were = =2 ( ;s () )=2t. 2) + ;s (), suc tat for any it FOC yields () = t =(5 + 24) < t(2 ( ; ;s ()) +2;s (t(2 2) + ;s ;s (); ;s it olds tat +2;s ave an incentive to deviate on t(2 (); ;s ()), were +2;s(t(2 2) + ()) = t 2 (2 6 2) = [8(5 + 24)]. For any () > +2;s (t(2 2) + ;s (); ;s ()), suc tat rm does not 2) + ;s () t + ;s (). Firm does not ave an incentive to deviate on > t + ;s () eiter, because in tat case it realizes te same ro ts as at te rice = t + ;s (). Hence, te rices ;s () and ;s () constitute te equilibrium. Finally, we sow tat an equilibrium does not exist wit > (3 2)=2, in wic case > t(2 2) + and +2;s ( ; ) = + t=8. FOC yields = + t =2 < + t(2 2) for any, suc tat +2;s ( ; ) gets its maximum at! t(2 2) + and +2;s ( ; ) = t(2 2) + 2 =2 + t=8. However, if rm lim!t(2 2)+ carges some + t =2 < < + t(2 2), ten bot its rst-eriod and second-eriod ro ts increase. Te former increase because tey are maximized at = + t =2 < +t(2 2) for any. Te latter increase because, as follows from Lemma, 2;s ( (3 2)=2) = t(3 2 ) 2 =6 and 2;s ( > (3 2)=2) = t=8, wile t(3 2 ) 2 =6 > t=8 for any < (3 2)=2. Hence, no equilibrium exists wit > (3 2)=2. Q.E.D. Proof of Lemma 4. s follows from Lemma 2, we ave to distinguis between te cases =2 and > =2. ssume tat in equilibrium =2 olds, in wic case +2;S ; = 26

29 + t 4 i were = =2 ; = 4 + t 2 i =6, =8, +2;S = (2t). We get ;S () = t 2 2 = (2 + ), ;S () = t = (2 + ) and ;S () = (2 ) = [2 (2 + )] =2 for any solving simultaneously FOCs. Firms realize ro ts +2;S () = t = 4 ( + 2) 2i and +2;S () = t = ;S 2 ( + 2) 2i. SOCs are ful lled. For ;S () and () to constitute te equilibrium, none of te rms sould ave an incentive to deviate suc tat > =2 olds. ssume tat rm deviates on < ;S (), in wic case +2;S ; ;S () = 4 +t i i =6, were = =2 ;S () = (2t). i FOC yields ;S () = ;S () (4 ) + 2t(2 ) = (8 ). We get ;S () ;S () = 2t (4 ) = [(8 ) ( + 2)] < 0 and if < ;S (), max +2;S ; ;S () = +2;S ;S () ; ;S () = t = 2 (8 ) ( + 2) 2i. We get +2;S () +2;S ;S () ; ;S () = t = 0 for any, suc tat rm does not ave an incentive to deviate. ssume tat rm deviates on > ;S (). Ten +2;S t 4 i =8, were = =2 ;S () ;S ;S () (2 + ) + 2t i = ( + 4). We get (), +2;S 0, suc tat if > ;S +2 ;S () ; ;S () get +2;S () +2;S ;S () ; ;S i = (2t). FOC yields 4 (8 ) ( + 2) 2i > () = + ;S () = () = 2t ( + 2) = > ; ;S () gets its maximum at = ;S () and = t = 4 ( + 4) ( + 2) 2i. We ;S () ; ;S () = t = 4 ( + 4) ( + 2) 2i > 0 for any, suc tat rm does not ave an incentive to deviate. Hence, te rices ;S () and ;S () constitute te equilibrium. Symmetrically, tere exists te equilibrium, were = ;S () and = ;S (). Q.E.D. Proof of Proosition. We start wit te unilateral incentives to invest. ssume tat rm does not invest. If rm does not invest eiter, over two eriods it realizes te ro t +2 () = t ( + ) =2. If it invests, it gets +2;s () = t = 4 (5 + 24) 2i. For any we ave +2;s () +2 () = t = tat rm always invests. 4 (5 + 24) 2i > 0, suc ssume next tat rm invests. If rm does not invest, ten over two eriods it realizes te ro t +2;s () = t = 2 (5 + 24) 2i. If rm invests, ten te ro t is +2;S i () = t = 4 ( + 2) 2i or +2;S j () = t = 2 ( + 2) 2i, deending on te equilibrium. For any it olds 27

30 n o max +2;S i () ; +2;S j () = +2;S j (). We get tat for any, +2;s () +2;S j () = t = > 0, suc tat rm does not invest. Combining te incentives of rms and to invest we conclude tat tere are two asymmetric equilibria were only one of te rms invests. Te equilibrium social welfare over two eriods is SW +2 m () = v(+) t R (24 )=(0+48) 0 xdx t R (24 )=(0+48) ( x)dx tr (3+8)=(5+24) 0 xdx t R (3+8)=(5+24)( x)dx = v( + ) t = 4 (5 + 24) 2i. Consumer surlus is CSm +2 () = SWm +2 () +2;s () +2;s () = v( + ) t = 4 (5 + 24) 2i. Q.E.D. Proof of Lemma 5. Wile making teir rst-eriod decisions, soisticated consumers take into account te equilibrium of te second eriod. s follows from Lemma, we ave to distinguis between te cases (3 2)=2 and > (3 2)=2. Wit U +2 i (x; i ; ) we denote te utility of a consumer x over two eriods if in te rst eriod se buys from rm i = ; and te sare of consumers wo bougt from rm in te rst eriod is. Case : (3 2)=2 < <. We sow tat rices must satisfy t < < t(2 2) and ( ; ) = =2 + =2t. We start wit consumers wit x 3=4, for wom U +2 (x; ; ) = v tx + [v tx t(3=2 2x)]. If a consumer buys at rm in te rst eriod, rm does not learn er reference and as to carge 2;s = 0. Ten U 2 (x; 2;s ) = v tx U 2 (x; 2;s ) = v t ( x) t=2, and a consumer buys at rm in te second eriod uon buying at rm in te rst eriod. Hence, U +2 (x; ; ) = v t ( x) + (v tx). ll consumers wit x 3=4 must buy at rm in te rst eriod, because > (3 2)=2 > 3=4 olds by assumtion. Te inequality U +2 (x; ; ) U +2 (x; ; ) yields te condition t [ 3=2 2x( )] +. Plugging x = 3=4 into te latter inequality we get t=2. Consider now consumers wit 3=4 < x, for wom U +2 (x; ; ) = v tx + [v t ( x) t=2]. If a consumer buys at rm in te rst eriod, ten U 2 (x; 2;s ) = v tx < U 2 (x; 2;s ) = v t ( x) t=2, suc tat a consumer buys at rm in te second eriod too and U +2 (x; ; ) = v t( x) + [v t ( x) t=2]. Comaring U +2 (x; ; ) and U +2 (x; ; ) we conclude tat consumers wit x =2 = (2t) buy at rm and consumers wit x > =2 = (2t) buy at rm in te rst eriod, suc tat ( ; ) = =2 = (2t). Te condition (3 2)=2 < < is ful lled if rices are suc tat t < < t(2 2). 28

31 Case 2: 0 < 3 2 =2. We will sow tat in tis case rices satisfy t(2 2) t(3 2 4)=4 < + t(4 5)=4 and ( ; ) = t(4 5) + 4( ) = [2t(4 3)]. Consider rst consumers wit x, for wom U +2 (x; ; ) = v tx + v tx t(3 2 )=2 t( 2x). If a consumer buys at rm in te rst eriod, ten U 2 (x; 2;s ) = v tx t 5 6 =4 U 2 (x; 2;s ) = v t ( x) t 3 2 =2 for any x =8. Hence, uon buying at rm in te rst eriod a consumer buys at rm in te second eriod and U +2 x; ; = v t( x) + v tx t 5 6 =4. Consumers wit x buy at rm in te rst eriod if U +2 (x; ; ) U +2 olds, wic yields te condition x; ; + t 2 ( ) t + 2 =4. (3) Consider now consumers wit x =8, for wom U +2 (x; ; ) = v t( x) + v tx t(5 6 )=4. If a consumer buys at rm in te rst eriod, it learns er reference and makes er indi erent in te second eriod wenever ossible wit a non-negative rice, suc tat a consumer s utility is always given by U 2 (x; 2;s ) = v t ( x) t 3 2 =2 indeendently of te rm it buys. Hence, U +2 (x; ; ) = v tx+ v t ( x) t 3 2 =2. Comaring U +2 (x; ; ) and U +2 (x; ; ) we conclude tat consumers wit x tat =8 buy at rm in te rst eriod if rices are suc + t 2 ( ) t + 2 =4. (4) Combining (3) and (4) we conclude tat only te rice = +t( 2 )( ) t + 2 =4 satis es bot conditions. Tis rice yields ( ; ) = 4( ) + t(4 5) = [2t(4 3)]. Imosing te constraint 0 < 3 2 =2 we get t(2 2) t(3 2 4)=4 < + t(4 5)=4. We nally sow tat consumers x =8 buy at rm. We ave U +2 (x; ; ) = v t( x) + v t( x) t(3 2 )=2. If a consumer buys at rm in te rst eriod, it learns er reference and makes er indi erent in te second eriod wenever ossible wit a non-negative rice, suc tat a consumer s utility is always given by U 2 (x; 2;s ) = v t( x) t(3 2 )=2 indeendently of te rm it buys. Hence, U +2 (x; ; ) = v tx + v t( x) t(3 2 )=2. Comaring U +2 (x; ; ) and U +2 (x; ; ) we 29

32 conclude tat a consumer buys at rm in te rst eriod if + t( 2x). It is straigtforward to sow tat = + t( 2 )( ) t + 2 =4 satis es te latter inequality for any x wit x =8 buy at rm =8, because < 5=6 olds by assumtion. Hence, consumers It is straigtforward to sow tat ( ; ) = if t and ( ; ) = 0 if + t(4 5)=4. To comlete te derivation of te demand we note tat for any 2 [0; ] it olds tat < 2 2 (3 2 4)=4 2 2 < (4 5)=4, suc tat te demand is given by a corresondence. Q.E.D. Proof of Lemma 6. In te following we will use a( ) := t(2 2) t(3 2 4)=4, b( ) := + t(2 2) + t(3 2 4)=4, c( ) := t(2 2) and d( ) := + t(2 2). We know from Lemma 5 tat consumer demand in te rst eriod is given by a corresondence. We will consider two cases deending on ( ; ) on te interval a( ) < c( ) and will sow tat bot cases yield te same equilibrium. Case. ssume tat ( ; ) = t (4 5) + 4 = [2t (4 3)] if a( ) < c( ). In te following we will consider tree cases deending on. In eac case we will sow tat te equilibrium exists were 3 2 =2, suc tat ;s a( ;s ). We will ten sow tat tis is te unique equilibrium. Case.a). Let < =2. ssume tat in equilibrium ;s a( ) olds, in wic case rms maximize te ro ts +2;s ; = +t 28 i =32 and +2;s ; = + t =6, were ( ; ) = t (4 5) + 4 = [2t (4 3)]. FOCs yield te rices ;s t () = and ;s t () = (5) and ;s () = (24 23) = (48 26). For any it olds ;s () < 3 ;s a( ) is true. ;s also ful lled. Firms ro ts in te rst eriod are ;s 2 =2, suc tat () > 0 and ;s () > 0 old if < =2. SOCs are () = t (24 23) , ;s (26 48) (52 96) () = t

33 Firms ro ts over two eriods are +2;s () = t (3 24) 2, +2;s () = t (3 24) 2. To rove tat te rices in (5) constitute te equilibrium, we ave to sow tat rm () does not ave an incentive to deviate on < a(;s ()) ( > b(;s ())), were > 3 2 =2 olds. ssume tat = ;s +2;s ( ; ;s It must be tat a( ;s (;s ()) = ( ; ;s () and rm deviates on ;s () t < a(;s ()), were i ())+9t=6, ( ; ;s ()) = =2+ ;s () = (2t). ()) > 0, because if a(;s ()) 0, deviation is not ossible. FOC yields ()) = t = [8(24 3)]. We ave (;s ()) > a(;s()) for any, suc tat +2;s +2;s (a( ;s ( ; ;s ()); ;s ()) is maximized at! a(;s ()). We get tat ()) < +2;s ( ;s () ; ;s ()) for any, suc tat rm does not ave an incentive to deviate on ;s () t < a(;s ()). Firm does not ave an incentive to deviate on < ;s () t eiter, because in tat case it realizes a strictly lower ro t tan at = ;s () t. ssume now tat = ;s tat its ro t is +2;s =2 + () and rm deviates on b(;s ( ;s ( ; ;s ()) = ()) < ;s () + t, suc (); ) i +t=8, were ( ;s (); ) = i ;s () = (2t). FOC yields (;s ()) = 3t = [8 (24 3)] > 0 for any. For any < =2 we ave tat (;s +2;s +2;s b( ;s ( ; ;s ;s ()) is maximized at! b(;s () (); ;s ()) < b(;s ()), suc tat ()). We get +2;s ()); ;s () < b( ;s for any, suc tat rm does not ave an incentive to deviate on ()) < ;s () + t. Note nally tat rm does not ave an incentive to deviate on > ;s () + t eiter, because in tat case rm realizes te same ro ts as under te rice = ;s () + t. We conclude tat te rices ;s () and ;s () in (5) constitute te equilibrium, were 3 2 =2 olds. We will sow next tat tis is te unique equilibrium. ssume tat an equilibrium exists wit > 3 2 =2. Note rst tat in equilibrium it cannot be tat < t, because rm realizes ten a strictly lower ro t tan at = t. Hence, rices must satisfy b( ) < + t, in wic case +2;s ( ; ) = ( ; ) + t=8, were ( ; ) = =2 = (2t). FOC yields = + t =2. s < b( ) for any and any, +2 ( ; ) is maximized at = b( ) +, were > 0 and 3

34 ! 0. However, it is always ro table for rm to deviate to te rice = b( ), in wic case bot its rst-eriod and second-eriod ro ts increase. Hence, an equilibrium wit > 3 2 =2 does not exist. Case.b). Let =2 < 6=7. ssume tat in equilibrium ;s a( ;s ) olds. We sowed in Case.a) tat at least one of te rices in (5) is non-ositive. ssume tat in equilibrium ;s wit resect to we get () = 0. Maximizing +2;s ; = +t =6 ;s () = t = (32 28) and (6) ;s () = (6 7) = (8 7). (7) ;s () = 0 and ;s () in (6) satisfy ;s() a(;s()). SOC is also ful lled. For any we ave ;s () <, wile ;s () > 0 and ;s () > 0 old if =2 < 6=7. Firms ro ts in te rst eriod are ;s () = t = and ;s () = 0. +2;s () = t = and +2;s () = t = [6 (8 7)] are ro ts over two eriods. To rove tat te rices ;s () = 0 and ;s () in (6) constitute te equilibrium, we ave to sow tat none of te rms as an incentive to deviate on < a( cannot deviate on < a(;s case its ro t is +2;s ( ; 0) = FOC yields +2 ). s a(;s ) < 0, rm ). ssume tat rm deviates on b(0) < t, in wic (0; ) + t=8 and (0; ) = =2 + = (2t). (0) = t=2 < b(0), suc tat +2;s ( ; 0) is maximized at! b(0) and (b(0); 0) < +2;s () imlying tat rm does not ave an incentive to deviate on b(0) < t. Firm does not ave an incentive to deviate on > t eiter, because in tat case it gets te same ro ts as under and ;s () in (6) constitute te equilibrium. We next sow tat if ;s ssume tat ;s a( ;s = 0. Ten as a(0) < 0, for any ;s = t. Hence, we sowed tat te rices ;s () = 0 ) olds, ten no equilibrium exists wit ;s = 0. we ave ;s ; =2 <, suc tat by increasing its rice sligtly rm gets a ositive ro t in te rst eriod, wile its second-eriod ro t decreases sligtly. We conclude tat if ;s rices ;s () = 0 and ;s Case.a) tat an equilibrium does not exist were ;s a( ;s ) olds, ten te () in (6) constitute te unique equilibrium. s we sowed in < a( ;s ) (;s > 3 2 =2), we 32

35 conclude tat te rices ;s () = 0 and ;s() in (6) constitute te unique equilibrium. Case.c). Let 6=7. ssume tat in equilibrium ;s a( ;s ) olds. We sowed in Case.a) tat at least one of te rices in (5) is non-ositive. ssume tat in equilibrium ;s () = 0. For any 6=7, ;s () in (7) is non-ositive. Hence, we get in equilibrium ;s () = 0, wic yields ;s () = t (5 4) =4 > 0. (8) Firms rst-eriod ro ts are ;s () = 0 and ;s () = t (5 4) =4. Over two eriods rms realize ro ts +2;s () = 25t=32 and +2;s () = t (29 6) =6. To rove tat te rices ;s () = 0 and ;s () in (8) constitute te equilibrium, we ave to sow tat none of te rms as an incentive to deviate on ;s < a( ;s ). s a(;s ) < 0, rm cannot deviate. ssume now tat = 0 and tat rm deviates on b(0) < t, in wic case its ro t is +2;s ( ; 0) = (0; ) + t=8 and (0; ) = =2 + = (2t). FOC yields +2;s (0) = t=2 < b(0), suc tat +2;s ( ; 0) is maximized at! b(0). We get (b(0); 0) < +2;s () imlying tat rm does not ave an incentive to deviate on b(0) < t. Firm does not ave an incentive to deviate on > t eiter, because in tat case it gets te same ro ts as under = t. Hence, we sowed tat te rices ;s () = 0 and ;s () in (8) constitute te equilibrium. Similarly as in Case.b), one can sow tat no equilibrium wit ;s () = 0 exists, wic imlies tat tis is te unique equilibrium wen ;s ;s a( ;s ) olds. s we sowed in Case.a) tat an equilibrium does not exist wit 2 =2), we conclude tat te rices ;s () = 0 and ;s () in < a( ;s ) (;s > 3 (8) constitute te unique equilibrium. Case 2. ssume now tat if a( ) < c( ), ten ( ; ) = =2 + = (2t). We rst sow tat in equilibrium it must old ;s c( ;s ), suc tat ;s < 3 2 =2. ssume tat ;s < c( ;s ) and ;s > 3 2 =2 in equilibrium. Note rst tat in equilibrium it cannot be tat < t, because rm realizes ten a strictly lower ro t tan at = t. Hence, rices must satisfy d( ) < + t, in wic case +2;s ( ; ) = + t=8, were = =2 = (2t). FOC yields = + t =2. s < d( ) for any and any, +2;s ( ; ) is maximized at = d( ) +, were > 0 and! 0. However, it is always ro table for rm to deviate to te rice = d( ), in wic case bot its rst-eriod and second-eriod ro ts increase. Hence, an equilibrium wit ;s > 3 2 =2 does not exist. 33

36 ssume tat in equilibrium ;s c( ;s ), suc tat ;s < 3 2 =2. We rst sow tat no equilibrium exists wit ;s = 0. ssume tat ;s = 0. Ten for any ;s it olds tat ;s c(0) as c(0) < 0, ence, ;s < 3 2 =2 <. Ten if rm increases its rice sligtly, it gets a ositive ro t in te rst eriod, wile its second-eriod ro t decreases sligtly. Hence, an equilibrium wit ;s Note next tat te equilibrium rices ;s = 0 does not exist. and ;s from Case.a)-Case.c) satisfy ;s c( ;s ), wic togeter wit te results derived above imlies tat tose rices are te only candidate equilibria. To rove tat tose rices constitute te equilibrium, we ave to sow tat none of te rms as an incentive to deviate on < c( ), were > 3 2 =2. We sowed in Case tat rm does not ave an incentive to deviate under any. Tis imlies tat rm does not ave an incentive to deviate in Case 2 too, because on d < b rm gets a smaller market sare in te rst eriod tan in Case leading to lower rst-eriod ro ts (wile second-eriod ro ts do not cange due to > 3 2 =2). ;s We sow next tat rm does not ave an incentive to deviate eiter. If 70 ;s 2 72 =2 < 6=7, we sowed in Case.b) tat ;s () = t = (32 28). For any it olds tat c( ;s ()) < 0, suc tat rm cannot deviate on < c(;s ()). If 6=7, we sowed in Case.c) tat ;s () = t (5 4) =4. For any it olds tat ()) < 0, suc tat rm cannot deviate on < c(;s ()) eiter. Consider - c( ;s nally < =2, were te candidate equilibrium is given by te rices (5). ssume tat rm deviates on ;s () t < c(;s ()), in wic case its ro t is i +2;s ( ; ;s ()) = + 9t=6, were = =2 + ;s () = (2t). Te FOC yields (;s ()) = t = [8(24 3)]. We ave (;s ()) > c(;s ()) for any, suc tat +2;s any, +2 (c(;s ()); ;s ( ; ;s ()) < +2 ()) is maximized at! c(;s ()). We get tat for (;s () ; ;s ()), suc tat rm does not ave an incentive to deviate on ;s () t < c(;s ()). Firm does not ave an incentive to deviate on < ;s () t eiter, because in tat case it gets a strictly lower ro t tan at = ;s () t. We conclude tat te rices ;s constitute te unique equilibria for te resective. Q.E.D. and ;s from Case.a)-Case.c) Proof of Lemma 7. s follows from Lemma 2, we ave to distinguis between te cases =2 and > =2. Wit Ui +2 (x; i ; ) we will denote te utility of a consumer x over two eriods if in te rst eriod se buys from rm i = ;. 34

37 Case : =2. We rst assume tat tat tere is an indi erent consumer in te rst eriod, and and are suc tat consumers wit x ; (weakly) refer rm. Consider rst consumers wit x, for wom U +2 (x; ; ) = v tx + [v tx t ( 2x)]. If a consumer buys at rm, rm does not learn er reference and carges 2;S x; = t 2 =2, suc tat U 2 (x; 2;S x; ) = v tx t 2 =2. Firm, in contrast, learns er reference and makes er indi erent in te second eriod wenever ossible wit a non-negative rice, suc tat consumer s utility in te second eriod is always given by U 2 (x; 2;S ) and U +2 (x; ; ) = v t ( x) + v tx t 2 =2. It must old U +2 (x; ; ) U +2 (x; ; ) for any x, wic yields t 2 (2 ) =2. (9) Consider now consumers wit x < 2 + =4, for wom U +2 (x; ; ) = v t( x) + v tx t 2 =2. If a consumer buys at rm, ten rm does not learn er reference and carges 2;S x; = 0, suc tat U 2 (x; 2;S x; ) = v t ( x). Firm, in contrast, learns er reference and makes er indi erent in te second eriod wenever ossible wit a non-negative rice, suc tat consumer s utility in te second eriod is always given by U 2 (x; 2;S x; ) and U +2 (x; ; ) = v tx + [v t ( x)]. It must old (x; ; ) U +2 (x; ; ) for any x < 2 + =4, wic yields U +2 t 2 (2 ) =2. (0) Only te rices = t 2 (2 ) =2 satisfy (9) and (0) simultaneously, wic yields ;S ; = =2 = [t (2 )], () if and are suc tat 0 t (2 ) =2. (2) It is left to ceck tat at te rices (2) consumers wit x 2 + =4 buy at rm in te rst eriod. We ave U +2 (x; ; ) = v t( x) + v t 2 =2 tx. If a consumer buys at rm, rm does not learn er reference and carges 2;S x; = 0 in te second eriod, suc tat U 2 (x; 2;S x; ) = v t ( x). Firm, in contrast, learns a 35

38 consumer s reference and makes er indi erent in te second eriod wenever ossible wit a non-negative rice, suc tat te second-eriod utility is always given by U 2 (x; 2;S U +2 (x; ; ) = v tx x; ) and [v t ( x)]. It must old U +2 (x; ; ) U +2 (x; ; ) for any x 2 + =4, wic yields t 2 =2. Te latter inequality is ful lled for any as = t 2 (2 ) =2, and consumers wit x 2 + =4 buy at rm in te rst eriod. It is straigtforward to ceck tat if in te rst eriod none of te consumers (weakly) refers rm, ten and are suc tat > t (2 ) =2. Case 2: > =2. We rst assume tat tere is an indi erent consumer in te rst eriod, and and are suc tat consumers wit x ; (weakly) refer rm. Note tat tis case is symmetric to Case, suc tat using (), we get te market sare of rm as ;S ; = =2 = [t (2 )], wic yields again () for ;S ; rovided t (2 ) =2 < 0. (3) Combining (2) and (3) we conclude tat ; is given by () if t (2 ) =2 t (2 ) =2. It is straigtforward to ceck tat if in te rst eriod none of te consumers (weakly) refers rm, ten and are suc tat < t (2 ) =2. Q.E.D. Proof of Lemma 8. ssume rst tat ; =2. Ten and ave to maximize te ro ts +2;S ; = + t 4( ) =8 and +2;S ; = + t 4( ) =6, were = =2 = [t (2 )]. FOCs yield ;S () = t = (24 0) > 0, ;S () = t = (24 0) > 0 and 0 < ;S () = (2 7) = (24 0) =2 for any. SOCs are ful lled. Firms realize ro ts +2;S () = t = 2 (5 2) 2i and +2;S () = t = 4 (5 2) 2i. To rove tat te rices ;S () and ;S () constitute te equilibrium, we ave to sow tat none of te rms as an incentive to deviate on <, were ; > =2. ssume tat rm deviates on < ;S (), in wic case its ro t is +2;S ; ;S () = 4 + t i =6, were = =2 ;S () = [t (2 )]. FOC yields ;S () = 4 ;S () + t i = (8 2). We get ;S () ;S () = t (2 ) = (2 5) > 0, suc tat on < ;S (), +2;S ; ;S () gets its maximum 36

39 at! ;S +2;S () +2;S () and +2;S ;S ;S () ; ;S () () ; ;S () = t 2 (4 ) = = t = [2 (2 5)]. We ave 2 (5 2) 2i > 0, suc tat rm does not ave an incentive to deviate. ssume tat rm deviates on > ;S (), in wic case its ro t is +2;S ; ;S () = + t 4 i =8, were = =2 ;S () We get = [t (2 )]. FOC yields ;S () ;S ;S () = 4 ;S () + t i = (8 2). () = 4t (2 ) = [(4 ) (24 0)] > 0, suc tat on > ;S () te ro t of rm gets maximum at = ;S () and +2;S ;S () ; ;S () = t = 2 (4 ) (5 2) 2i. We ave +2;S () +2;S ;S () ; ;S () = t = 4 (4 ) (5 2) 2i > 0, suc tat rm does not ave an incentive to deviate eiter. We conclude tat te rices = ;S and = ;S = ;S () constitute te equilibrium. Symmetrically, tere is te equilibrium wit () and = ;S Proof of Proosition 2. (). Q.E.D. ssume tat rm does not invest. We rst analyze te unilateral incentives of a rm to invest. () If rm does not invest eiter, ten over two eriods it realizes te ro t +2 () = t ( + ) =2. If rm does invest, ten +2;s () = t = 8 (3 24) 2i if ( )=2. We get +2;s () +2 () = t = 8 (3 24) 2i < 0 for any, suc tat rm does not invest. +2;s () = t = if ( )=2 < < 6=7. We ave +2;s () +2 () = t = 32 (7 8) 2i < 0 for any, suc tat rm does not invest eiter. If 6=7, ten +2;s () = 25t=32. We get +2;s () +2 () = (9 6) =32 < 0 for any, suc tat rm does not invest eiter. We conclude tat tere are no unilateral incentives to invest wen consumers are soisticated. We next assume tat rm invests and analyze te incentives of rm to invest too. Consider rst ( )=2. If rm does not invest, its ro t is +2;s () = t = 8 (3 24) 2i. If rm invests, ten its ro t is eiter +2;S i () = t = 2 (5 2) 2i or +2;S j () = 4 (5 2) 2i deending on te equilibrium. It olds t = n o max +2;S i () ; +2;S j () = +2;S j (). We get tat +2;S j () +2;s () = 9t = i 2 < 0 for any ( )=2, suc tat rm does not invest. Consider now ( )=2 < < 6=7. +2;s = t = [6 (8 7)] if rm does not invest. We ave +2;S j () 37

40 +2;s () = t = 6 (8 7) (5 2) 2i < 0 for any ( )=2 < < 6=7, suc tat rm does not invest eiter. ssume nally tat 6=7. If rm does not invest, ten +2;s () = t (29 6) =6. We get +2;S j () +2;s () = t = 6 (5 2) 2i < 0 for any 6=7, suc tat rm does not invest eiter. We conclude tat for any rm does not invest given tat te rival invests. Combining te otimal strategies of rms and we conclude tat tere is te unique equilibrium (in dominant strategies), were none of te rms invests. eac rm carges te rice t and serves alf of consumers. Over two eriods rms realize ro ts +2 i;s SWs +2 () = (+) Ten in eac eriod () = t ( + ) =2 (i = f; g), and social welfare and consumer surlus are v 2t R i =2 0 xdx = (+) (v t=4) and CSs +2 () = SW +2 () t ( + ) = ( + ) (v 5t=4), resectively. Q.E.D. Proof of Proosition 3. Te comarison of rms joint ro ts over two eriods yields () + +2 () 2+2 i;s () = 45t2 ( + 4) = 4 (5 + 24) 2i < 0, suc tat rms are worse +2 ;m ;m o wen consumers are myoic. Te comarison of te discounted sum of consumer surlus in bot cases yields CS +2 m () CS +2 s () = t = (5 + 24) 2. Te latter exression is ositive if > = and (weakly) negative oterwise. Te comarison of te discounted sum of social welfare in bot cases yields SWm +2 () SWs +2 () = t = 4 (5 + 24) 2i < 0, suc tat social welfare is lower wen consumers are myoic. Proof of Proosition 4. We rst note tat if one rm educates consumers, te oter rm is indi erent between te two strategies. We now derive te best resonse of a rm if te rival does not educate. We know tat +2 ;m () > t( + )=2 > +2 ;m () and +2 ;m () + +2 ;m () < t( + ). We introduce te function f(; ) := +2 ;m () + ( ) +2 ;m () and =2 < () <, suc tat f( () ; ) = t( + )=2 for any. It olds tat f(; ) > t( + )=2 if > (), wit te oosite inequality oterwise. Hence, given tat rm does not educate, te best resonse of rm is i) not educate if > (), ii) educate if < (), iii) if = (), rm is indi erent. We introduce next te function g(; ) := ( ) +2 ;m () + +2 ;m () and 0 < () < =2, suc tat g( () ; ) = t(+)=2 for any. It olds tat g(; ) > t(+)=2 if < (), wit te oosite inequality oterwise. Hence, given tat rm does not educate, te best resonse 38

41 of rm is i) not educate if < (), ii) educate if > (), iii) if = (), ten rm is indi erent. s () > (), combining rms best resonses we get te equilibria as stated in Proosition 4. Q.E.D. 39

42 9 References. dams, G. (203) Is Your TV Sying on YOU? It Sounds Like Science Fiction but Many New TVs Can Watc You - Telling dvertisers Your Favourite Sows or Even Filming You on te Sofa. nd Tere s no o Switc! Daily Mail Online, November 26, 203. tt:// 2. ester H., Petrakis E. (996) Couons and Oligoolistic Price Discrimination. International Journal of Industrial Organization;4; Cen Y., Narasiman C., Zang Z. J. (200) Individual Marketing wit Imerfect Targetability. Marketing Science; 20; Cen Y., Iyer G. (2002) Researc Note. Consumer ddressability and Customized Pricing. Marketing Science; 2; Coi C. (203) How Loyalty Programs In uence te Way you So. Te ig Story, May 6, 203. tt://bigstory.a.org/article/ow-loyalty-rograms-in uence-way-you-so. 6. Coudary V., Cose., Mukoadyay T., Rajan U. (2005) Personalized Pricing and Quality Di erentiation. Management Science; 5, Davis G. How Tesco ecame ritain s To Suermarket. MoneyWeek, May 9, tt:// 8. Eliaz K., Siegler R. (20) Consideration Sets and Cometitive Marketing. Review of Economic Studies; 78, FTC (203). ndroid Flasligt Develoer Settles FTC Carges It Deceived Consumers. Federal Trade Commission ress release, December 5, 203. tt:// news-events/ress-releases/203/2/android- asligt-a-develoer-settles-ftc-carges-itdeceived. 0. Fudenberg D., Tirole J. (2000) Customer Poacing and rand Switcing. RND Journal of Economics; 3,

43 . Fudenberg D., Villas-oas J. M. (2005) eavior-ased Price Discrimination and Customer Recognition. Mimeo. 2. Gabaix X., Laibson D. (2006) Srouded ttributes, Consumer Myoia, and Information Suression in Cometitive Markets. Quarterly Journal of Economics; 2, Goldman D. (20) Your Pone Comany is Selling your Personal Data. CNNMoney, November, 20. tt://money.cnn.com/20//0/tecnology/verizon_att_srint _tmobile_rivacy/index.tm. 4. Klemerer P. (995) Cometition Wen Consumers Have Switcing Costs: n Overview wit lications to Industrial Organization, Macroeconomics, and International Trade. Review of Economic Studies; 62; Klosowski T. (203) How Web Sites Vary Prices ased on Your Information (and Wat You Can Do bout It). Lifeacker, January 7, 203. tt://lifeacker.com/ /owweb-sites-vary-rices-based-on-your-information-and-wat-you-can-do-about-it. 6. Kola. (203) How te irline Industry Is Saing Modern Marketing. Vocus Marketing Cloud, ril 8, 203. tt:// 7. Liu Q., Serfes K. (2004) Quality of Information and Oligoolistic Price Discrimination. Journal of Economics & Management Strategy; 3; Liu Q., Serfes K. (2006) Customer Information Saring among Rival Firms. Euroean Economic Review; 50; Ross. (203) Canned Goods not Canned Prices Wit Personalized Pricing. How Grocers Can Imlement a Personalized Pricing Strategy in Four Stes. Canadian Grocer, July 24, 203. tt:// Sa er G., Zang Z. J. (995) Cometitive Couon Targeting. Marketing Science; 4;

44 2. Sa er G., Zang Z. J. (2000) Pay to Switc or Pay to Stay: Preference-ased Price Discrimination in Markets wit Switcing Costs. Journal of Economics and Management Strategy; 9; Sa er G., Zang Z. J. (2002) Cometitive One-to-One Promotions. Management Science; 48; Siller. R. (203) First Degree Price Discrimination Using ig Data. Mimeo. 24. Taylor C. (202) Home Deot cquires Data-Driven Retail Pricing Startu lacklocus. Teccrunc, December 7, 203. tt://teccrunc.com/202/2/7/ome-deotacquires-data-driven-ricing-analytics-startu-blacklocus/. 25. Tisse J.-F., Vives X. (988) On te Strategic Coice of Satial Price Policy. merican Economic Review; 78; Winterman D. (203) Tesco: How One Suermarket Came to Dominate. C News Magazine, 9 Setember 203. tt:// 42

45 PREVIOUS DISCUSSION PPERS 3 aye, Irina and Sai, Geza, Targeted Pricing, Consumer Myoia and Investment in Customer-Tracking Tecnology, February Clemens, Georg and Rau, Holger., Do Leniency Policies Facilitate Collusion? Exerimental Evidence, January Hottenrott, Hanna and Lawson, Cornelia, Fising for Comlementarities: Cometitive Researc Funding and Researc Productivity, December Hottenrott, Hanna and Rexäuser, Sasca, Policy-Induced Environmental Tecnology and Inventive Efforts: Is Tere a Crowding Out?, December Daut, Wolfgang, Findeisen, Sebastian and Suedekum, Jens, Te Rise of te East and te Far East: German Labor Markets and Trade Integration, December 203. Fortcoming in: Journal of Euroean Economic ssociation. 26 Wenzel, Tobias, Consumer Myoia, Cometition and te Incentives to Unsroud dd-on Information, December 203. Publised in: Journal of Economic eavior and Organization, 98 (204), Scwarz, Cristian and Suedekum, Jens, Global Sourcing of Comlex Production Processes, December 203. Fortcoming in: Journal of International Economics. 24 Defever, Fabrice and Suedekum, Jens, Financial Liberalization and te Relationsi- Secificity of Exorts, December 203. Publised in: Economics Letters, 22 (204), auernscuster, Stefan, Falck, Oliver, Heblic, Stean and Suedekum, Jens, Wy re Educated and Risk-Loving Persons More Mobile cross Regions?, December 203. Publised in: Journal of Economic eavior and Organization, 98 (204), Hottenrott, Hanna and Loes-ento, Cindy, Quantity or Quality? Knowledge lliances and teir Effects on Patenting, December Hottenrott, Hanna and Loes-ento, Cindy, (International) R&D Collaboration and SMEs: Te Effectiveness of Targeted Public R&D Suort Scemes, December 203. Fortcoming in: Researc Policy. 20 Giesen, Kristian and Suedekum, Jens, City ge and City Size, November Trax, Micaela, runow, Stean and Suedekum, Jens, Cultural Diversity and Plant- Level Productivity, November Manasakis, Constantine and Vlassis, Minas, Downstream Mode of Cometition Wit Ustream Market Power, November Sai, Geza and Suleymanova, Irina, Consumer Flexibility, Data Quality and Targeted Pricing, November Hinlooen, Jeroen, Müller, Wieland and Normann, Hans-Teo, Outut Commitment Troug Product undling: Exerimental Evidence, November 203. Publised in: Euroean Economic Review 65 (204),

46 5 aumann, Florian, Denter, Pili and Friee Tim, Hide or Sow? Endogenous Observability of Private Precautions gainst Crime Wen Proerty Value is Private Information, November Fan, Ying, Kün, Kai-Uwe and Lafontaine, Francine, Financial Constraints and Moral Hazard: Te Case of Francising, November guzzoni, Luca, rgentesi, Elena, uccirossi, Paolo, Ciari, Lorenzo, Duso, Tomaso, Tognoni, Massimo and Vitale, Cristiana, Tey Played te Merger Game: Retrosective nalysis in te UK Videogames Market, October 203. Fortcoming in: Journal of Cometition and Economics under te title: Retrosective Merger nalysis in te UK Videogames Market. 2 Myrset, Kristian Ove R., Riener, Gerard and Wollbrant, Conny, Tangible Temtation in te Social Dilemma: Cas, Cooeration, and Self-Control, October 203. Hasnas, Irina, Lambertini, Luca and Palestini, rsen, Oen Innovation in a Dynamic Cournot Duooly, October 203. Publised in: Economic Modelling, 36 (204), aumann, Florian and Friee, Tim, Cometitive Pressure and Cororate Crime, Setember öckers, Veit, Hauca, Justus and Heimesoff, Ulric, enefits of an Integrated Euroean Electricity Market, Setember Normann, Hans-Teo and Tan, Elaine S., Effects of Different Cartel Policies: Evidence from te German Power-Cable Industry, Setember 203. Fortcoming in: Industrial and Cororate Cange. 07 Hauca, Justus, Heimesoff, Ulric, Klein, Gordon J., Rickert, Dennis and Wey, Cristian, argaining Power in Manufacturer-Retailer Relationsis, Setember aumann, Florian and Friee, Tim, Design Standards and Tecnology dotion: Welfare Effects of Increasing Environmental Fines wen te Number of Firms is Endogenous, Setember Jeitscko, Tomas D., NYSE Canging Hands: ntitrust and ttemted cquisitions of an Erstwile Monooly, ugust öckers, Veit, Giessing, Leonie and Rösc, Jürgen, Te Green Game Canger: n Emirical ssessment of te Effects of Wind and Solar Power on te Merit Order, ugust Hauca, Justus and Muck, Joannes, Wat Drives te Relevance and Reutation of Economics Journals? n Udate from a Survey among Economists, ugust Jovanovic, Dragan and Wey, Cristian, Passive Partial Ownersi, Sneaky Takeovers, and Merger Control, ugust Hauca, Justus, Heimesoff, Ulric, Klein, Gordon J., Rickert, Dennis and Wey, Cristian, Inter-Format Cometition mong Retailers Te Role of Private Label Products in Market Delineation, ugust Normann, Hans-Teo, Requate, Till and Waicman, Israel, Do Sort-Term Laboratory Exeriments Provide Valid Descritions of Long-Term Economic Interactions? Study of Cournot Markets, July 203. Fortcoming in: Exerimental Economics.

47 99 Dertwinkel-Kalt, Markus, Hauca, Justus and Wey, Cristian, Inut Price Discrimination (ans), Entry and Welfare, June guzzoni, Luca, rgentesi, Elena, Ciari, Lorenzo, Duso, Tomaso and Tognoni, Massimo, Ex-ost Merger Evaluation in te UK Retail Market for ooks, June Carice, Stéane and von Sclienbac, Vanessa, One-Sto Soing as a Cause of Slotting Fees: Rent-Sifting Mecanism, May 202. Publised in: Journal of Economics and Management Strategy, 22 (203), Wenzel, Tobias, Indeendent Service Oerators in TM Markets, June 203. Publised in: Scottis Journal of Political Economy, 6 (204), Coublucq, Daniel, Econometric nalysis of Productivity wit Measurement Error: Emirical lication to te US Railroad Industry, June Coublucq, Daniel, Demand Estimation wit Selection ias: Dynamic Game roac wit an lication to te US Railroad Industry, June aumann, Florian and Friee, Tim, Status Concerns as a Motive for Crime?, ril Jeitscko, Tomas D. and Zang, Nanyun, dverse Effects of Patent Pooling on Product Develoment and Commercialization, ril aumann, Florian and Friee, Tim, Private Protection gainst Crime wen Proerty Value is Private Information, ril 203. Publised in: International Review of Law and Economics, 35 (203), aumann, Florian and Friee, Tim, Cea Talk bout te Detection Probability, ril 203. Publised in: International Game Teory Review, 5 (203), rt. No Pagel, eatrice and Wey, Cristian, How to Counter Union Power? Equilibrium Mergers in International Oligooly, ril Jovanovic, Dragan, Mergers, Managerial Incentives, and Efficiencies, ril Heimesoff, Ulric and Klein Gordon J., argaining Power and Local Heroes, Marc ertscek, Irene, Cerquera, Daniel and Klein, Gordon J., More its More ucks? Measuring te Imact of roadband Internet on Firm Performance, February 203. Publised in: Information Economics and Policy, 25 (203), Rasc, lexander and Wenzel, Tobias, Piracy in a Two-Sided Software Market, February 203. Publised in: Journal of Economic eavior & Organization, 88 (203), ataille, Marc and Steinmetz, lexander, Intermodal Cometition on Some Routes in Transortation Networks: Te Case of Inter Urban uses and Railways, January Hauca, Justus and Heimesoff, Ulric, Google, Facebook, mazon, eay: Is te Internet Driving Cometition or Market Monoolization?, January 203. Fortcoming in: International Economics and Economic Policy. 82 Regner, Tobias and Riener, Gerard, Voluntary Payments, Privacy and Social Pressure on te Internet: Natural Field Exeriment, December 202.

48 8 Dertwinkel-Kalt, Markus and Wey, Cristian, Te Effects of Remedies on Merger ctivity in Oligooly, December aumann, Florian and Friee, Tim, Otimal Damages Multiliers in Oligoolistic Markets, December Duso, Tomaso, Röller, Lars-Hendrik and Seldeslacts, Jo, Collusion troug Joint R&D: n Emirical ssessment, December 202. Fortcoming in: Te Review of Economics and Statistics. 78 aumann, Florian and Heine, Klaus, Innovation, Tort Law, and Cometition, December 202. Publised in: Journal of Institutional and Teoretical Economics, 69 (203), Coenen, Micael and Jovanovic, Dragan, Investment eavior in a Constrained Dictator Game, November Gu, Yiquan and Wenzel, Tobias, Strategic Obfuscation and Consumer Protection Policy in Financial Markets: Teory and Exerimental Evidence, November 202. Fortcoming in: Journal of Industrial Economics under te title Strategic Obfuscation and Consumer Protection Policy. 75 Hauca, Justus, Heimesoff, Ulric and Jovanovic, Dragan, Cometition in Germany s Minute Reserve Power Market: n Econometric nalysis, November 202. Publised in: Te Energy Journal, 35 (204), Normann, Hans-Teo, Rösc, Jürgen and Scultz, Luis Manuel, Do uyer Grous Facilitate Collusion?, November Riener, Gerard and Wiederold, Simon, Heterogeneous Treatment Effects in Grous, November erlemann, Micael and Hauca, Justus, Wic Factors Drive te Decision to oycott and Ot Out of Researc Rankings? Note, November Muck, Joannes and Heimesoff, Ulric, First Mover dvantages in Mobile Telecommunications: Evidence from OECD Countries, October Karaçuka, Memet, Çatik,. Nazif and Hauca, Justus, Consumer Coice and Local Network Effects in Mobile Telecommunications in Turkey, October 202. Publised in: Telecommunications Policy, 37 (203), Clemens, Georg and Rau, Holger., Rebels witout a Clue? Exerimental Evidence on Partial Cartels, ril 203 (First Version October 202). 68 Regner, Tobias and Riener, Gerard, Motivational Cerry Picking, Setember Fonseca, Miguel. and Normann, Hans-Teo, Excess Caacity and Pricing in ertrand-edgewort Markets: Exerimental Evidence, Setember 202. Publised in: Journal of Institutional and Teoretical Economics, 69 (203), Riener, Gerard and Wiederold, Simon, Team uilding and Hidden Costs of Control, Setember Fonseca, Miguel. and Normann, Hans-Teo, Exlicit vs. Tacit Collusion Te Imact of Communication in Oligooly Exeriments, ugust 202. Publised in: Euroean Economic Review, 56 (202),

49 64 Jovanovic, Dragan and Wey, Cristian, n Equilibrium nalysis of Efficiency Gains from Mergers, July Dewenter, Ralf, Jascinski, Tomas and Kucinke, jörn., Hosital Market Concentration and Discrimination of Patients, July Von Sclienbac, Vanessa and Teicmann, Isabel, Te Strategic Use of Private Quality Standards in Food Suly Cains, May 202. Publised in: merican Journal of gricultural Economics, 94 (202), Sai, Geza, argaining, Vertical Mergers and Entry, July Jentzsc, Nicola, Sai, Geza and Suleymanova, Irina, Targeted Pricing and Customer Data Saring mong Rivals, July 202. Publised in: International Journal of Industrial Organization, 3 (203), Lambarraa, Fatima and Riener, Gerard, On te Norms of Caritable Giving in Islam: Field Exeriment, June Duso, Tomaso, Gugler, Klaus and Szücs, Florian, n Emirical ssessment of te 2004 EU Merger Policy Reform, June 202. Publised in: Economic Journal, 23 (203), F596-F Dewenter, Ralf and Heimesoff, Ulric, More ds, More Revs? Is tere a Media ias in te Likeliood to be Reviewed?, June öckers, Veit, Heimesoff, Ulric and Müller ndrea, Pull-Forward Effects in te German Car Scraage Sceme: Time Series roac, June Kellner, Cristian and Riener, Gerard, Te Effect of mbiguity version on Reward Sceme Coice, June De Silva, Daksina G., Kosmooulou, Georgia, Pagel, eatrice and Peeters, Ronald, Te Imact of Timing on idding eavior in Procurement uctions of Contracts wit Private Costs, June 202. Publised in: Review of Industrial Organization, 4 (203), enndorf, Volker and Rau, Holger., Cometition in te Worklace: n Exerimental Investigation, May Hauca, Justus and Klein, Gordon J., How Regulation ffects Network and Service Quality in Related Markets, May 202. Publised in: Economics Letters, 7 (202), Dewenter, Ralf and Heimesoff, Ulric, Less Pain at te Pum? Te Effects of Regulatory Interventions in Retail Gasoline Markets, May öckers, Veit and Heimesoff, Ulric, Te Extent of Euroean Power Markets, ril art, nne-katrin and Heimesoff, Ulric, How Large is te Magnitude of Fixed- Mobile Call Substitution? - Emirical Evidence from 6 Euroean Countries, ril Herr, nnika and Suliet, Moritz, Parmaceutical Prices under Regulation: Tiered Co-ayments and Reference Pricing in Germany, ril Hauca, Justus and Müller, Hans Cristian, Te Effects of Gasoline Price Regulations: Exerimental Evidence, ril 202.

50 46 Stümeier, Torben, Roaming and Investments in te Mobile Internet Market, Marc 202. Publised in: Telecommunications Policy, 36 (202), Graf, Julia, Te Effects of Rebate Contracts on te Healt Care System, Marc 202, Fortcoming in: Te Euroean Journal of Healt Economics. 44 Pagel, eatrice and Wey, Cristian, Unionization Structures in International Oligooly, February 202. Publised in: Labour: Review of Labour Economics and Industrial Relations, 27 (203), Gu, Yiquan and Wenzel, Tobias, Price-Deendent Demand in Satial Models, January 202. Publised in:. E. Journal of Economic nalysis & Policy, 2 (202), rticle art, nne-katrin and Heimesoff, Ulric, Does te Growt of Mobile Markets Cause te Demise of Fixed Networks? Evidence from te Euroean Union, January Stümeier, Torben and Wenzel, Tobias, Regulating dvertising in te Presence of Public Service roadcasting, January 202. Publised in: Review of Network Economics, /2 (202), rticle. Older discussion aers can be found online at: tt://ideas.reec.org/s/zbw/diced.tml

51 ISSN (online) ISN