Referrals in Search Markets

Transcription

1 eferrals in Searc Markets Maria Arbatskaya y and Hideo Konisi z May 0, 0 Abstract Tis aer comares te equilibrium outcomes in searc markets a la Wolinsky (984) wit and witout referrals. Altoug it seems clear tat consumers would bene t from referrals, it is not at all clear weter rms would unilaterally rovide information about cometing o ers since suc information could encourage consumers to urcase te roduct elsewere. In a model of a orizontally di erentiated roduct and sequential consumer searc, we sow tat valuable referrals can arise in te equilibrium: a rm will give referrals to consumers wose ideal roduct is su ciently far from te rm s o ering. We allow rms to rice-discriminate among consumers, and consumers to misreresent teir tastes. It is found tat te equilibrium ro ts tend to be iger in markets wit referrals tan in te ones witout, even toug tere is a continuum of equilibrium rices wit referrals. Under a certain arameter range, referrals lead to a Pareto imrovement. Keywords: orizontal referrals, consumer searc, information, matcing, referral fees. JEL numbers: C7, D4, D8, L. We are articularly indebted to two anonymous referees of te journal and te editor Yossi Siegel for teir invaluable comments and suggestions. We also tank Eric asmusen, egis enault, articiants of seminars at Boston College, Emory University, Georgia Institute of Tecnology, IEB at Kobe University, and articiants at te International Industrial Organization Conference, te Soutern Economic Association Meetings, and te Midwest Economic Teory Meetings. y Corresonding Autor: Deartment of Economics, Emory University marbats@emory.edu z Deartment of Economics, Boston College ideo.konisi@bc.edu

2 Introduction We often observe referral ractices in industries were consumers urcase goods and services infrequently, or else te roduct caracteristics are di cult to assess. Examles include rofessional services in areas of law, accounting, real estate, and ealt care, as well as secialized services and ig-tec electronic roducts. As a result, in tese industries a tyical consumer needs to conduct a costly searc in order to nd te roducts tat matc er tastes. In contrast, rms know te industry well, and tey gater information on goods and services rovided by teir cometitors simly by engaging in teir everyday business and articiating in business grous. Troug conversations wit teir customers, rms can also ascertain te customers references and inform tem about were tey can nd te roducts tey are looking for. In suc industries, referrals can reduce consumer searc costs and imrove matcing outcomes. However, in te absence of referral fees, a rm does not want to refer a consumer to anoter seller if tere is a cance for te rm to sell its roduct to te consumer. Ten, a natural question arises of weter or not tere is any economic motive to making referrals witout referral fees. Under wat circumstances would rms inform consumers about roducts o ered by oter rms? Giving referrals can be a way to build goodwill wit otential customers. 3 It is also a way to build referral relationsis wit business contacts. Te recirocity in referral relationsis can be furter suorted by rofessional grous and associations tat romote networking between members of a rofession for te urose of excanging customer leads. eferral clubs aim seci cally to rovide a structured and ositive environment for businesses to ass referrals to one anoter (e.g. Gold Star eferral Clubs and eferral Key). eferrals a ect consumers searc beavior, and as a result, rms ricing beavior as well. In tis aer, we rst investigate te e ects of referrals on equilibrium rices, ro ts, Sales clerks in retail markets may also o er referrals. Tis aens wen a consumer searcing for a suitable roduct (a digital camera, a iece of furniture, and a collection item) does not nd it in a store, asks for referral, and is referred to a store tat sells it. To avoid otential con icts of interest in referral activity, rofessional associations in law, accounting, and real estate regulate referrals by establising codes of onor, wic may roibit te ayment of referral fees. 3 One may argue tat a store s sales clerk cooses to rovide a valuable referral to a consumer urely out of goodwill. However, if being elful to customers in tat way is a norm for sellers, ten we would like to know te imact of suc a norm on te market outcome.

3 and consumer welfare. Ten, we move on to te fundamental questions about te economic reasons for referrals to arise in searc markets: Wy are referrals made? How can te social norm for a rm to refer oorly matced otential consumers to te best-matcing cometitors arise in an equilibrium? We sow tat te social norm of making referrals can bene t rms, and tis rovides an exlanation for existing referral ractices in various industries. To analyze te role of referrals in searc markets we introduce referrals into a model of cometition between rms roducing a orizontally di erentiated roduct. Te roduct sace is a unit circle, wit rms evenly and consumers uniformly distributed over it. Consumer utility from a roduct decreases as a mismatc increases between a rm s roduct and te consumer s ideal roduct. A consumer can engage in sequential searc by randomly samling roducts at a constant marginal searc cost. Uon a visit to a rm, te consumer learns te features of te roduct o ered by te rm. Te basic set u is as in Wolinsky s symmetric oligoolistic rice cometition model (Wolinsky, 984), excet tat we introduce eterogenous consumer valuation for te roduct in order to endogenize consumer market articiation. We ten evaluate te e ect of referrals in suc markets. We allow rms to refer consumers wo visit tem to oter sellers. A rm does not ave to rovide consumers wit referrals if te rm would rater sell tem its own roduct. However, wen a rm knows tat a consumer would not urcase its roduct, it may as well refer er to anoter rm. In tis aer, we assume tat wen indi erent, a rm always refers a consumer to te best-matcing roduct. Since te model is rater comlicated, we rst derive equilibria wit and witout referrals in te bencmark model of no rice discrimination by rms and no misreresentation of locations by consumers. We relax tese assumtions in te main model and comare equilibria wit and witout referrals in tis eras more realistic case. Te results are interesting. In te bencmark model, te symmetric equilibrium wit or witout referral is unique (Proositions and resectively). Te norm of referring consumers to te best-matcing cometitors increases rices, and rms tend to earn more ro ts in te referral equilibrium tan in equilibrium witout referrals (Proosition 3). Tis result can be understood as follows. Wen a rm refers consumers to te rival rm o ering tem te igest utility, te referring rm is actually weakening te incentives of te rival rm 3

4 to cut rices. eferrals make te rival s demand more inelastic and tus tey function as a ro-collusive device. Tis suggests tat altoug referrals rovide consumers wit valuable information tat decreases searc costs and imroves roduct matc, consumers may be worse o in te resence of referrals. 4 We sow tat indeed for su ciently low searc costs relative to te degree of roduct eterogeneity, consumers refer markets witout referrals. At te same time, referrals can lead to a Pareto imrovement in searc markets (Proosition 3). In contrast, in te main model wit consumer reference misreresentation and rm rice discrimination, a consumer may coose to reort er location trutfully or to misreresent it in order to get a referral, deending on te distance between te roduct sold by te rm se visits and er ideal one (Proosition 4). 5 Altoug te symmetric random searc equilibrium (witout referrals) is unique, tere is a continuum of symmetric referral equilibria wit di erent rices (Proosition 4). Tis indeterminacy of equilibrium comes from a kinked demand function generated by consumers reference misreresentation. Somewat surrisingly, under most arameter values and referral equilibrium rices, rms are still better o in te referral equilibria tan in te random searc equilibrium (Proosition 5). In articular, if te otimal equilibrium rices are cosen, rms always refer te referral equilibrium for any arameter values tat assure te existence of te equilibria (Proosition 5). Tat is, te tendency for rms to refer te establisment of referral ractices in te industry is robust, and tis exlains wy referrals arise in many industries, even in te absence of referral fees. We nd tat wen searc costs are not too low, consumers tend to be better o in te resence of referrals. We also nd tat deending on te arameter values and te equilibrium rice, te random searc equilibrium can Pareto-dominate or be Pareto-dominated by te referral equilibrium (Proosition 5). Given di erences in oinion about referral olicies and teir rominence in many industries, it is eras surrising tat tere is not muc economic teory on te toic. One 4 Suc a negative externality on consumers from imroved information was rst demonstrated by Anderson and enault (000) in an economy wit orizontally di erentiated searc goods. 5 Proositions 4 and 5 deal wit te referral equilibria under reference misreresentation, yet witout rice discrimination. Proosition 6 sows tat as long as consumers can misreresent teir references, te equilibrium is intact even if rms can rice-discriminate among consumers based on teir reorted references. 4

5 excetion is a study by Garicano and Santos (004), wic examines referrals between vertically di erentiated rms (vertical referrals). Due to comlementarity between te values of oortunities and rms skills, e cient matcing involves assigning more valuable oortunities to ig-quality rms. Te autors sow tat at referral fees can suort e cient referrals from ig-quality to low-quality rms but not vice versa. Te moral azard roblem arises because a low-quality rm as an incentive to kee te best oortunities to itself rater tan refer tem to a ig-quality rm. 6 However, te model does not allow te rms clients to conduct searces on teir own. In contrast, we do not deal wit te moral azard roblem in tis aer. Instead, we focus on te role of orizontal referrals in searc markets were consumers can always randomly visit a rm and at a cost learn about te rm s roduct and rice. Te rest of te aer is organized as follows. Section outlines te fundamental features of our basic environment. Section 3 considers rice cometition between rms selling a orizontally di erentiated roduct in searc markets witout referrals and describes te random searc equilibrium tat arises in te model. In Section 4, we analyze searc markets wit referrals and derive te referral equilibria in suc markets, rst assuming tat consumers cannot misreresent teir locations and ten relaxing tis assumtion. Section 5 comares te referral and random searc equilibria. In Section 6, we sow tat te results of te main model carry over to te case of rice discrimination based on reorted consumer locations and in te resence of referral fees. Section 6 o ers concluding comments. Te Aendix contains all te roofs. Te Basic Environment We model cometition between rms tat roduce a orizontally di erentiated roduct closely following Wolinsky (983, 984, 986). 7 We assume tat tere is a large number of 6 For an early study on te e ects of fee slitting on referrals in ealt care see Pauly (979). An emirical study by Surr (990) on referral ractices among lawyers examines te roortion of cases referred between lawyers, as deendent on te value and nature of a claim, advertising activity, and oter factors. 7 Te closest model (esecially our random searc case) is Wolinsky (984), but e assumes xed rice in te aer for te sake of simlicity of te analysis. Te market rice is endogeneously determined in Wolinsky (983) in a similar satial model, toug te analysis is only brie y described tere. Wolinsky (986) o ers te most toroug analysis on te determination of oligoolistic rice, toug e assumes away satial structure in tat aer, relying on i.i.d. random willingness-to-ay by consumers. We analyze a 5

6 rms, n, of wic locations are symmetrically located (equidistant) on a circle of unit circumference and roducing te roduct of te location at a zero marginal cost. As te number of rms goes to in nity, rms will be distributed uniformly over te circle. For analytical simlicity, ignore integer roblems assuming tat consumers regard te distribution of rms is uniform over te unit circle. 8 Tere is unit mass of consumers er rm, and eac consumer as a unit demand and is caracterized by a valuation of te roduct (willingness-to-ay) and references over te orizontally di erentiated roducts. Consumers ideal ositions are uniformly distributed over te unit circle. Indeendently of satial references, eac consumer as a value v for er ideal roduct (te roduct tat is a erfect matc wit er tastes). Altoug Wolinsky (984) assumes tat v is common to all consumers, we assume tat v is uniformly distributed over an interval [0; ] in order to determine te equilibrium consumer articiation endogenously in te model. Eac consumer s ideal osition and valuation are indeendently distributed (double uniform distribution over te surface of a cylinder wit unit circumference wit unit eigt), and se knows er v and er ideal osition on a circle. As a result, consumers decide if tey articiate in te market based on er value of v (endogenous articiation decision). Firms know te ositions on te circle of all oter rms in te industry, wereas consumers do not know wic rms o er wic roducts. Wen a consumer visits a rm, se learns of te rm s osition and its rice, wile te rm learns of te consumer s ideal roduct (tastes). Te rm remains uncertain about te consumer s willingness-to-ay even after er visit. Tis assumtion catures te idea tat rms may nd it easier to extract information about a consumer s ideal roduct tan about te consumer s willingness-to-ay for te ideal roduct. Consider a consumer wose roduct valuation is v and wo learns tat te rm s roduct is located at distance x from er ideal osition. Let te consumer s utility for te rm s roduct (gross of rice and searc costs) be u(x; v) = v x, were > 0 is te taste arameter tat denotes te degree of roduct eterogeneity and x reresents te disutility a consumer receives from consuming a roduct located at a distance x in te roduct sace variant of te model in Wolinsky (984) using te analysis in Wolinsky (986). 8 We follow te aroac taken by Wolinsky (983, 984). 6

7 from te consumer s ideal roduct. For examle, a ig corresonds to markets were consumers feel strongly about roduct caracteristics, e.g. color, weigt, or design. Te case of = 0 corresonds to a omogeneous roduct market. Consumer searc is sequential, wit a constant marginal cost of searc c > 0, common across consumers. Eac consumer cooses weter to initiate searc, and a consumer wo decides to searc can always coose not to buy te roduct of te rm samled and continue to searc for anoter roduct. We assume tat consumer searc is random wit relacement. 9 Tat is, at eac ste of te sequential searc rocess, a consumer samles rms roducts randomly, but se does not samle te same roduct more tan once, and se can always recall reviously samled roducts. We assume tat wen indi erent between searcing or not, consumers do not searc. A rm s referral olicy can be conditional on consumer location. At te same time, rms are assumed to set nondiscriminatory rices in te bencmark model wit or witout referrals. Wen a rm refers a customer to anoter rm, te customer can costlessly follow te referral. Tis is consistent wit te idea tat searc costs come mainly in te form of learning about roduct caracteristics, and terefore referrals substantially lower consumers searc costs. Te assumtion is not crucial, toug. We also assume tat wenever a rm knows tat it cannot sell its own roduct to a consumer given its own rice and oter rms rices, and tus is indi erent weter to rovide a referral or not and were to refer te consumer, it refers te consumer to te best-matcing rm. Tis assumtion of onest referrals resolves rms indi erence and is in te sirit of te onor codes adoted in markets for rofessional services. Note tat onest referrals are in fact incentive comatible in te sense tat rms do not gain by deviating unilaterally from te equilibrium in wic onest referrals are suorted. 0 We start in Section 3 wit te analysis of rice cometition in a random searc market witout referrals. We assume tat rms set nondiscriminatory rices, and we ten derive 9 We assume searc wit relacement in order to ave an invariant distribution of rms as searc roceeds for te case of a nite number of rms. As Wolinsky (984) correctly states, as te number of rms goes to in nity, it becomes irrelevant weter samling rocess is wit or witout relacement. 0 Suose a rm were to deviate and refer a dearting consumer to a oorly matcing rm. Te consumer would follow te referral because se exects it to be valuable in te equilibrium. Ten, se would eiter urcase te referred roduct, or if se learns tat te roduct is of oor matc, se would engage in additional random searc. Tus, te consumer would not urcase te disonest rm s roduct anyway. 7

8 te equilibrium rice tat caracterizes te unique symmetric (ure-strategy) equilibrium wit consumer articiation, wic we call te random searc equilibrium. 3 andom Searc In tis section, we assume tat rms do not make referrals, and so te only way for consumers to receive information about a roduct s location and rice is to engage in sequential random searc. We will suort te equilibrium wit a symmetric rice by following Wolinsky s (984, 986) tecniques. To nd te equilibrium in te random searc model, we assume tat all rms excet rm i carge rice and tat consumers rationally exect te common rice level, and we ten derive te best-resonse rice for rm i in a market wit an arbitrary large number of rms. By setting te best-resonse rice equal to, we obtain a symmetric equilibrium in te monoolistically cometitive market. To allow for te ossibility of an equilibrium wit consumer articiation, we assume c, and later we will sow tat tis condition is necessary for te existence of a symmetric 4 equilibrium wit consumer articiation (Proosition ). For analytical simlicity, we ignore te integer roblem due to niteness of rms, so consumers regard rms locations are uniformly distributed. Wen consumers articiate in te market, rm i s ro t deends on te otimal stoing rule for a consumer engaged in random sequential searc. Lemma derives te otimal stoing rule (similar to Wolinsky 986: te roof is omitted). Lemma. Assume tat c. Wen all rms excet rm i set a common rice and rm 4 i sets a rice i, ten te otimal stoing rule for a consumer engaged in random searc is to sto searcing at rm i if and only if rm i s roduct is witin distance x( i ; ) = x + We could ave taken te niteness of n seriously by analyzing an n- rm searc market, but tis would greatly comlicate te analysis because te distribution of unsamled roducts canges as searc roceeds. Following Wolinsky (984), we assume away tis ossibility by letting n be very large (see footnote on age 76 in Wolinsky (983) for a justi cation of te aroac). For very large n we can also ignore te ossibility of a consumer not being able to nd a rm located witin te critical distance x. Note tat tere is always a symmetric equilibrium witout consumer articiation in te market. In suc an equilibrium, all rms carge a roibitively ig rice, and consumers do not searc correctly execting te market rice to be very ig. Tis is an equilibrium because consumers only receive rice information by engaging in searc, and if a rm were to deviate by reducing its rice it would not be able to convey te rice information to consumers. Hence, no deviation is ro table. 8 i ()

9 from er ideal roduct, were x = c is te critical distance in te symmetric equilibrium. If in case all rms are searced in te above manner wile could not nd any roduct tat is close enoug to satisfy te condition, ten coose te rm tat o ers te igest net surlus as long as it is nonnegative, max j (v x j j ) 0. In a symmetric equilibrium, te robability tat a consumer stos er searc at rm i is x = c because te otimal stoing rule tells er to sto searcing once se samles a roduct witin distance x on bot sides of er ideal roduct on te circumference. For examle, if rm i were to set a di erent rice, i 6=, it could ten a ect consumers searc beavior somewat. If rm i were to surrise consumers by carging a iger rice, rm i would romt more consumers to continue random searces. Note tat in a symmetric random searc equilibrium, it is strictly dominated for rm i to set a rice i suc tat x( i ; ) > or x( i; ) < 0. In case x( i ; ) >, wic occurs wen i is below x, all consumers wo visit rm i buy tere since i s o er is better tan engaging in furter random searc, and a rm could increase its rice sligtly witout losing any customers. In case x( i ; ) < 0, wic occurs wen i is above + x, no consumer would urcase rm i s roduct, but rm i could sligtly reduce its rice to generate ositive sales and ro ts. Tus, we can restrict our attention to i ( x ); + x. To derive rm i demand wen it sets a rice i and all oter rms carge, we need to rst nd te robability tat a consumer samles rm i on a kt random draw, stos searc to buy rm i s roduct, and ten sum over all k, k n. Te robability of drawing rm i as te kt rm is n for a consumer, since all rms are symmetric and at eac ste in te sequential searc, te next store is cosen randomly wit equal robability and witout correlation. 3 Te robability tat a consumer searces at least k times is ( x ) k (wic, in accordance wit te otimal stoing rule, is te robability tat all revious k draws were farter tan distance x = c on bot sides from er ideal osition). If rm i carges i, te robability tat a consumer urcases at rm i uon te visit is x( i ; ). Note tat rms are located in equi-distanced manner. As a result, wit 3 Wit n rms, rm i is selected rst wit robability =n. It is selected on a second draw if it is not selected rst (robability =n), and if it is selected as te second rm among te remaining n rms (robability =(n )). Tus, te robability of rm i being selected on te second draw is also =n. Similarly, we can sow tat rm i is selected on te kt draw wit robability =n (see Wolinsky, 986). 9

10 a very large n, eac consumer nds a rm tat is close enoug to er osition before all n rms ave been exausted. 4 Tus, rm i s demand er searcer is ed i n ( i ; ) = nx ( x ) k x( i ; ) () n k= = ( x ) n x( n ( x i ; ): ) Te last term of te demand function is te case were consumers searced all rms wile none of te rms o er To nis te derivation of rm i s demand function, we need to nd te measure of searcers. Let v denote te critical valuation for market articiation, wic is te valuation of te consumer indi erent between initiating searc and staying outside te market. Only consumers wit valuations v [v ; ] enter te market. Since tere is unit mass of consumers er rm, te total measure of searcers is n( function is v ), and rm i s demand ( x Di n ( i ; ) = ( v ) n ) x( ( x i ; ): (3) ) For zero marginal costs, te ro t function of rm i is ten n i ( i ; ) = i D n i ( i ; ) in te n- rm market. In te limit as n!, rm i s ro t function becomes i ( i ; ) = lim n i ( i ; ) = ( v ) i + i : (4) n! c A rm s rice does not a ect consumers market articiation decisions and tus does not a ect te number of consumers wo visit te rm. Tis is because consumers decisions to engage in searc are based on rice exectations, not on te actual rices set by rms. Terefore, te measure of searcers does not deend on i, and rm i cooses i to maximize te exression in te square brackets in (4). Te roerties of te unique random searc equilibrium and comarative statics results are stated in Proosition. Proosition. Consider te limit case of n!. Tere exists a unique symmetric random searc equilibrium if and only if c min 4 ; 4. Te equilibrium rice is = c, critical valuation for market articiation is v = c, and ro ts are = ( v ). 4 In Wolinsky (986), demand function as a second term tat is comosed by te demand by consumers wo searc all rms witout satisfying te criterion described by te otimal stoing rule. Tis is because in Wolinsky s model tere is only n times to try searcing. In our model (wit relacement: in order to reserve stationary distribution), we may visit te same rm again and again randomly. So, even if te number of rms is n, te number of searc can be muc larger until all rms ave been exausted. 0

11 Te equilibrium rice increases and consumer market articiation decreases in searc cost, c, and roduct eterogeneity,. Pro ts can increase or decrease in c and. Condition c 4 is necessary for sustaining sequential consumer searc in a symmetric equilibrium. 5 Te oter condition c 4 is needed to guarantee tat te equilibrium rice is not roibitively ig. If tis condition is violated, ten v = c >, and all consumers exect a negative ayo and stay away from te market. Te comarative statics analysis of Proosition sows tat, as exected, te equilibrium rice in te random searc equilibrium increases wit searc cost and roduct eterogeneity. Interestingly, te equilibrium ro ts may increase or decrease wit c and deending on teir levels. Te equilibrium ro ts increase in c and for su ciently low levels of te arameters, c <. For oter values of c and, te decline in market articiation is 6 not comensated for by te iger rice associated wit larger c and. In oter words, for c, sellers refer to oerate in searc markets wit lower searc costs and lower 6 4 roduct eterogeneity. Intuitively, if searc cost c goes u, ten te ro ts may go down desite a iger equilibrium rice because te rice increase reduces equilibrium consumer articiation. Janssen et al. (005) and Konisi (005) similarly nd tat te equilibrium ro ts are in uenced by tese two e ects. [Figure ere] Te equilibrium consumer decisions to engage in searc, buy at a rm located at a distance x, or engage in sequential searc are illustrated in Figure. Only consumers wose roduct valuations are at least v = c engage in searc. Consumers visiting a rm located witin distance x = c from teir ideal ositions buy te roduct, wile oters 5 Wen c > 4, tere is no symmetric ure-strategy equilibrium wit consumer articiation in te random searc model. Wen c > 4, te otimal stoing rule in a symmetric equilibrium is for a consumer to always sto searcing regardless of te roduct found since for suc arameter values x = c >. However, witout sequential searc, rms ave an incentive to raise rices above te exected rice level, and terefore a symmetric equilibrium wit consumer articiation does not exist wen c > 4. Tis tye of non-articiation equilibrium is described in Stiglitz (979) and is also reminiscent of te Diamond aradox (Diamond, 97). However, suc an equilibrium is rater uninteresting, and we will restrict arameter values to focus on equilibria wit consumer articiation.

12 continue to searc. Figure also deicts te exected utility of a consumer wo rst draws a roduct located at distance x from te consumer. 4 Searc wit eferrals Te goal of tis section is to analyze searc models wit referrals and no referral fees. In te model, rms simultaneously set uniform rices and coose referral olicies. Our focus is again on te symmetric ure-strategy equilibria in wic all rms use te same rice and referral olicy. We will sow tat since a rm refers a consumer if and only if te consumer would oterwise leave te rm to engage in random searc, rm i s referral rule is caracterized by te same critical distance as te consumers stoing rule. Hence, a symmetric referral equilibrium is described by a common rice and a referral rule x, suc tat if te distance between a consumer s ideal roduct and a rm is greater tan x, te rm refers te consumer to te best-matcing rm. We derive te unique symmetric equilibrium wit consumer articiation, (, x ), wic we call te referral equilibrium. Firms do not observe consumer locations but tey know te locations of all roducts. Given tat rms do not ave an incentive to refer consumer located close to tem, consumers may want to misreresent teir locations in order to receive a referral. Tis suggests tat te model tat allows consumers to strategically maniulate teir references may be referable. However, for te sake of clarity of resentation, we start in Section 4. wit te bencmark case of referrals wit no consumer maniulation. Ten, in Section 4. we analyze te main case of referrals wit consumer misreresentation. Te latter is signi cantly more comlicated wit qualitatively di erent caracteristics suc as indeterminacy of te market equilibrium rice. 4. No misreresentation of references In tis section, we allow rms to rovide referrals to consumers. We assume tat tere are no referral fees and tat a rm (saleserson) can observe a customer s ideal osition x from aving a conversation wit er, but cannot observe er willingness-to-ay v. Terefore, te referral tat a rm o ers its customer can only be conditioned on te observed consumer s ideal roduct. We continue to assume in te bencmark model tat rms carge

13 nondiscriminatory rices, but we will relax tis assumtion in Section 6. In te model, rms simultaneously set nondiscriminatory rices and referral olicies, wile consumers old rational exectations and select te otimal stoing rule for teir sequential searc wit costless and erfect recall of roducts and referrals. In a searc market wit referrals, a consumer cooses weter to start a random searc given er roduct valuation v; after eac draw te consumer learns te rm s roduct and decides weter to follow te rm s referral if it is given, continue random searc, urcase te best examined item, or leave te market witout urcasing any roduct. Our focus is again on symmetric ure-strategy equilibria (i.e., equilibria in wic rms coose te same rice and referral olicy). As discussed in Section, we assume tat rms referrals are onest in te sense tat wenever a rm knows tat it cannot sell its own roduct to a consumer at te given rices, it refers er to te best-matcing rm. A rm would ten refer a consumer if and only if te consumer s ideal osition is su ciently far away, so tat te consumer refers engaging in furter random searc to buying at te rm. Te otimal stoing rule in sequential searc wit referrals is for a consumer visiting rm i to sto searcing at rm i if and only if rm i s roduct is witin distance x ( i ; ) from er ideal roduct. Since a rm refers a consumer if and only if te consumer would oterwise leave te rm to engage in additional random searc, rm i s referral rule is caracterized by te same critical distance as te consumer stoing rule. Te symmetric equilibrium referral rule states tat if te distance between a customer s osition and a rm is more tan x = x (; ), te rm refers te consumer to er best-matcing rm. Hence, a symmetric referral equilibrium can be caracterized by a air (, x ). To nd te equilibrium (, x ), consider rm i coosing an arbitrary rice i, and suose tat all oter rms set a common rice and referral rule x. Te otimal referral tresold x ( i ; ) for rm i is based on te location of a consumer wo is indi erent between buying from rm i at rice i and continuing to searc at random among rms carging. Lemma derives te equilibrium referral rule x and otimal stoing rule x ( i ; ) for a consumer engaged in searc wit referrals. Lemma. Assume tat c 4. Suose rm i sets a rice i and oter rms set a common 3

14 rice and use referral rule x. Te otimal stoing rule for a consumer engaged in searc wit referrals is to sto searcing at rm i if and only if rm i s roduct is witin distance x ( i ; ) = x + i from er ideal roduct, were x = 4 (c=) is te equilibrium referral rule. [Figure ere] Figure illustrates te otimal consumer searc and rm i s referral olicy, assuming tat rm i sets a rice i and oter rms set a common rice and use referral rule x. A consumer randomly cooses te rst rm to visit, say, rm i, located at distance x from er ideal osition. Wen te distance between te consumer and rm i is greater tan x ( i ; ), as in te case of consumer B, te consumer is referred by rm i to te best-matcing rm ( rm j), and se as to decide weter to buy at rm i, follow te referral, continue random searc, or leave te market. Wen rm i is located witin distance x ( i ; ) from te consumer s ideal osition, as in te case of consumer A, te consumer does not receive a referral and as to eiter buy at rm i, continue random searc, or leave te market. In te symmetric equilibrium, a consumer follows te referral and buys at rm j wen rm i is located farter away tan x = x (; ), and se buys at rm i immediately oterwise. In case c >, te otimal stoing rule in a symmetric equilibrium is for a consumer 4 to always sto searcing regardless of te roduct found. Tis is te same as in te case of no referrals. Tus, consumers searc at most one rm, and since referrals are given only to consumers wo would oterwise engage in additional random searc, consumers do not receive referrals. Hence, just as in te model witout referrals, a symmetric equilibrium wit consumer articiation does not exist in searc markets wit referrals wen c > =4. Next, we calculate te demand function of rm i assuming tat oter rms coose a symmetric rice and give referrals to customers located farter tan x. We can restrict our attention to i + x rice outside tis interval. In case i < +x ; + x because it is strictly dominated for rm i to, we ave x ( i ; ) >, and all consumers wo visit rm i buy tere since i s o er is better tan engaging in furter random searc 4

15 or following te referral. But ten rm i would rater set a sligtly iger rice. In case i > + x, we ave x ( i ; ) < 0, and no consumer visiting rm i urcases its roduct. Moreover, v i < v x olds for any v, and even consumers wo are referred to rm i do not urcase from it. Tus, demand for rm i in tis case is zero, and rm i would bene t by reducing its rice to generate ositive demand and ro ts. For i + x ; + x, consumers located at x x ( i ; ) [0; ] buy from rm i. Assuming rm i follows te otimal referral olicy x ( i ; ), its demand er searcer is were x = ed n i( i ; ) = = n n x ( i ; ) + n n + ( i) n ( x ) ; (5) 4 (c=) and te number of rms n is very large. Te rst term reresents demand from consumers wo visit rm i rst, wile te second term reresents demand from consumers wo visit oter rms rst and are ten referred to rm i. Let v denote te critical valuation for market articiation, wic is te valuation of te consumer wo is indi erent between initiating sequential searc and staying outside te market in te referral equilibrium. Since tere is unit mass of consumers er rm, te total measure of articiating consumers is n( v ), and rm i s demand function is Di( n i ; ) = ( v) + ( i) : (6) Hence, wen rm i sets a rice i and all rms are exected to set rice and use referral rule x, rm i s ro t function in te limit as n! is i ( i ; ) = lim i D n n! i( i ; ) = ( v) i + ( i) : (7) As before, a rm s rice does not a ect consumers market articiation decisions and, terefore, ( v ) does not deend on i. Given tis, rm i cooses i to maximize te exression in te square brackets in (7). In Proosition we describe te unique ure-strategy symmetric equilibrium wit consumer articiation, wic we call te referral equilibrium. 5

16 Proosition. Consider te limit case of n!. Tere exists a unique symmetric referral equilibrium if and only if c 4 and eiter or c 3=4 =. Te equilibrium rice is =, referral rule is x = market articiation is v = + x, and ro ts are = ( 4 (c=), critical valuation for v ). eferral intensity decreases wit consumer searc cost and increases wit roduct eterogeneity. Te equilibrium rice is erfectly insensitive to searc cost, wereas it increases as roduct eterogeneity increases. Consumers market articiation and ro ts decrease wit searc cost, c, and tey can increase or decrease wit roduct eterogeneity,. According to Proosition, te symmetric referral equilibrium exists if and only if c 4 and eiter or c 3=4 =. Te inequality c 4 is necessary for sustaining sequential consumer searc in a symmetric equilibrium. Te second condition obtains from 4 (c=), wic is equivalent to v, were v = + x = 4 (c=) is te critical valuation for market articiation. Figure 3 illustrates te equilibrium consumer decisions and te exected consumer utility for di erent realizations of v and x. Only tose consumers wose roduct valuations are at least v engage in searc. Consumers visiting a rm located witin distance x buy te roduct, wile oters follow te rm s referral and buy from te referred seller. [Figure 3 ere] Wy does searc cost c not matter in te determination of rice in tis case? By lowering its rice, rm i can increase its sales only troug an increase in te retention rate x ( i ; ) = x ( i )= of consumers wo visit rm i rst. However, a cange in te retention rate, wic equals =, is not a ected by searc cost c since sequential searc never takes lace in te equilibrium. Tus, in searc markets wit referrals te equilibrium rice is determined only by eterogeneity arameter. We can see an analogy wit te Diamond aradox (Diamond 97): in bot cases, sequential searc does not occur, and te equilibrium rice is indeendent of te level of searc cost (as long as it is ositive). In te current model, owever, tere is still cometition among rms trying to retain initial customers, and te monooly rice does not revail as te equilibrium rice. 6

17 Proosition 3. Wenever bot random searc and referral equilibria exist, we ave and x x. All consumers are better o in te referral equilibrium if and only if c 0:09, i.e. searc cost is not very low relative to roduct eterogeneity. Tus, c 0:09 guarantees tat rms earn more ro ts in te referral equilibrium, and te referral equilibrium Paretodominates te random searc equilibrium. 4. Misreresentation of references In te bencmark case, we assumed tat rms can correctly identify consumers ideal locations. However, a consumer wose true location is outside a rm s referral region but close to te referral border x (say, x, were > 0 is small) as an incentive to reort er osition to be x + " so tat se can receive a referral, were " > 0 is arbitrarily small. Altoug suc maniulation would result in an imerfect referral, it is bene cial as long as x >. To cature te ossibility of consumer maniulation, we will assume tat () as before, rms know oter rms ositions, but tey cannot observe te location of a consumer wo visits tem, and tat () altoug consumers cannot tell rms ositions rior to teir visits, tey can immediately identify a rm s osition uon a visit to te rm. Maintaining te assumtion of nondiscriminatory ricing, we obtain results similar to tose of te bencmark model. Figure 5 illustrates te equilibrium referrals obtained by consumers deending on teir distance from a samled rm ( rm i). equilibrium rms rovide referrals for anybody outside of [ farter tan x Consumers located in te region [ x ; x In te symmetric ]. Consumers located from rm i trutfully reort teir location and obtain erfect referrals. x ; x ) [ ( x ; x ] ave an incentive to misreresent teir osition in order to receive an imerfect referral. Tese consumers reort teir location to be x at x + " (were " > 0 is arbitrary small) in order to receive a referral to a rm located x + ", wic is less tan from teir ideal osition. Firm i can sell its roduct only to new (not referred by oter rms) consumers in region [ x ; x ]. However, by symmetry, rm i receives referrals from oter rms on average of te measure of customers equivalent to [ x ; x ) [ ( x ]. ; x [Figures 5 and 6 ere] 7

18 Figure 6 illustrates consumer decisions in te referral equilibrium wit consumer misreresentation and te equilibrium utility enjoyed by consumers, as deendent on te distance from te rst rm tey visit. Lemma can be modi ed by relacing te equilibrium referral rule x = wit x = Proosition 6. 4c= 8c=. We refer to tis statement as Lemma 3 and use it to rove Lemma 3. Assume tat c 8. Suose rm i sets a rice i and oter rms set a rice and use referral rule x. Te otimal stoing rule for a consumer engaged in searc wit referrals is to sto searcing at rm i if and only if rm i s roduct is witin distance x B ( i ; ) = x + i from er ideal roduct, were x = 8 (c=) is te symmetric equilibrium referral rule. Note tat unlike in Lemma, consumers urcase a rm s roduct in te equilibrium only if tey are located witin distance x B (; ) = x from te rm. Altoug tis aears to be a minor modi cation, te demand curve can be kinked in tis case deending on te assumtion of. Tis is coming from te imerfect referral demand. On te one and, if i >, ten some imerfect referral consumers may leave rm i to engage in furter searc. 6 On te oter and, if i <, ten all imerfect referral consumers clearly urcase te rm s roduct. However, since te measure of consumers arriving at a rm deends only on exected rater tan actual rice. Tat is, consumers wit imerfect referral are simly leasantly surrised, and te rice cutting does not generate additional demand from any referred consumers because rice cutting cannot increase te number of consumers wo visit te rm by referrals. Tis asymmetry causes a kinked demand curve, wic results in a continuum of symmetric equilibrium rices, as described in Proosition 6. Proosition 4. Suose tat consumers can misreresent teir locations. Consider te limit case of n!. Wen c ; and eiter 4 or c 4 3, tere exists a continuum of symmetric referral equilibria wit rices 8 (c=), critical valuation for market articiation v [ ; ], referral rule x 4 = = + x, and ro ts 6 Perfectly matced referred consumers urcase roduct anyway unless i is muc iger tan, since te matc is erfect. 8

19 = ( v ). eferral intensity is lower in te case of consumer misreresentation, and it decreases wit consumer searc costs and increases wit roduct eterogeneity. We could comare te referral equilibria witout and wit reference misreresentation outlined in Proositions and 6 resectively. Te main di erences are tat under misreresentation of consumer references te total referral activity is lower, some referrals are imerfect, and tere is a range of rices suorted in te referral equilibrium. Figure 7 illustrates ow te region of arameter values for wic te referral equilibrium exists would contract in te resence of maniulative consumers. [Figure 7 ere] 5 Comarison of te andom Searc and eferral Equilibria In tis section we will comare te regions of teir existence of te equilibria,and welfare roerties of te random searc and referral equilibria under reference misreresention. Since tere is a continuum of equilibria in te referral case, te comarison of equilibria is involved. In te following roosition and gure, for eac ossible referral equilibrium rice [ ; ], we identify te range of arameter values under wic equilibrium exists. 4 Figure 7 illustrates Proosition 3 by sowing te regions of arameter values of and c for wic te random searc and referral equilibria exist. Wen = (te igest equilibrium rice), te range for te referral equilibrium is a subset of te one for random searc equilibrium, but tis is not te case for oter equilibrium rices. Te random searc equilibrium exists for any level of roduct eterogeneity, rovided searc cost is su ciently low. In contrast, a referral equilibrium may exist only for a su ciently low eterogeneity arameter,. As roduct eterogeneity aroaces te critical level of, te market collases because te equilibrium rice = for consumers, regardless of te magnitude of searc cost. aroaces unity and tus becomes roibitively ig Intuitively, wen te roduct is igly eterogeneous, rms ave greater market ower to set ig rices in te random searc and referral equilibria, wic discourages consumers 9

20 market articiation. Even for a very ig, a random searc market would not close down for a su ciently low searc cost, since te low searc cost imoses cometitive ressure on rms in te market. In te referral equilibrium, rices are not a ected by searc costs, and te searc market wit referrals does not oen for >. We next comare te random searc and referral equilibria in te region of arameter values for wic bot of tem exist. Consumer surlus is directly related to te value of te marginal consumer te consumer wo is indi erent between entering and staying out of te market. 7 We use te critical values for market articiation v and v to sow tat v v, and terefore all consumer tyes are better o and market articiation is larger in te referral equilibrium, as long as searc cost is not very low relative to roduct eterogeneity. We furter sow tat for relatively ig searc cost, te referral equilibrium Pareto-dominates te random searc equilibrium. Tat is, te ex ante exected ayo s of eac consumer and eac rm in te referral equilibrium are iger for some agents and at least as ig for oter agents tan in te random searc equilibrium. Proosition 5. Denote te rices in te random searc equilibrium (SE) and referral equilibrium (E**) by and, resectively.. For any rice [ 4 ; ], tere exists a referral equilibrium if and only if (i) c 8, and (ii) eiter 4( ) or c ( (4=) ( 8 )). As decreases, te arameter range tat assures te existence of E** exands monotonically. Te arameter range tat assures te existence of SE includes te one tat assures te existence of E** wit te igest rice =, but tis is not te case for a lower rice. exist.. Consider te arameter range in wic bot random searc and referral equilibria a) If c 6, ten 4 and for any [ ; ], 4. If < c, ten 6 8 ( ; ) and te referral equilibrium rices can iger or lower tan te random searc 4 equilibrium rice. b) Consumers refers E** to SE if searc cost c is ig relative to roduct eterogeneity 7 To see tis, suose a critical valuation for market articiation in a searc market is bv. Te exected utility of a consumer wo values te roduct at v bv is EU(v) = v bv, and consumer welfare is bv EU(v)dv = ( bv). Terefore, bv fully determines te exected utility of any consumer and te total consumer welfare. Higer consumer market articiation is equivalent to iger consumer bene ts. 0

21 . As te referral equilibrium rice goes u, te arameter range tat consumers refer E** to SE srinks, and consumers always (weakly) refer SE to E** wit =. c) Firms always refer E** to SE for an otimally cosen rice [ 4 ; ]. Tese results are not surrising. If searc cost c is very low, consumers surely refer te random searc equilibrium, since te random searc equilibrium rice is low wile te referral equilibrium rice is insensitive to c. If searc cost is not very low, te referral equilibrium is favored by consumers; and since te equilibrium rice is iger in te referral equilibrium tan in te random searc equilibrium, rms favor tis equilibrium as well. Te referral equilibrium Pareto-dominates te random searc equilibrium wen te gain to consumers due to iger matcing quality and lower searc costs is iger tan te loss due to increased rice. From te welfare ersective, referrals andle te information roblem of matcing buyers and sellers but lead to iger rices in searc markets. Te reason te equilibrium rices are iger under referrals is tat in te referral equilibrium, a fraction x = 4 (c=) of consumers are referred to teir best-matcing roducts. Not surrisingly, te rm faces a more inelastic demand. 8 Te fact tat rices are iger in te referral equilibrium tan in te random searc equilibrium indicates tat rms bene t more tan consumers from te resence of referrals. Tat is, if consumer welfare is iger under referrals, ten rms nd tem bene cial as well, but te reverse is not true. It could be te case tat rms nd te referral equilibrium more ro table, wile te referrals make consumers worse o. 9 Since rms usually enjoy iger ro ts in te referral equilibrium, it sould be selected over te random searc equilibrium by rms and rofessional associations wenever bot equilibria exist. We next study ow social welfare deends on te arameters of te searc model. We 8 ecall tat rm i s demand is roortional to + i and + i c in searc markets wit and witout referrals, resectively. Hence, for c 4, rm i s demand is more inelastic in a searc market wit referrals. 9 Altoug rms usually would bene t from establising onest referrals, tere are some arameter values for wic ro ts are lower in te referral equilibrium tan in te random searc equilibrium. For tese arameter values, it must be tat consumer market articiation is lower (and consumers are worse o ) because te referral equilibrium rice is iger. Terefore, te referral equilibrium can be Pareto dominated by te random searc equilibrium.

22 de ne social welfare as a sum of consumer welfare and ro ts. According to footnote 0, consumer welfare is bv EU(v)dv = bv (v bv) dv = ( bv), wic is only a function of te critical valuation for market articiation bv. Te social welfare in te searc model wit and witout referrals is ten a function of rice and bv: W (; bv) = ( bv) + ( bv) : (8) Proosition 5 summarizes te comarative statics results for social welfare in te random searc and te referral equilibria. Proosition 5. Social welfare in te random searc and referral equilibria is iger wen searc cost is lower. Te e ect of roduct eterogeneity on social welfare is negative in te random searc equilibrium, and it is ambiguous in te referral equilibrium. Te comarative statics results for te random searc equilibrium indicate tat social welfare is iger in markets wit low searc costs and low roduct eterogeneity. Similarly, for te referral equilibrium, social welfare is iger in markets wit low searc costs, but te e ect of roduct eterogeneity on social welfare is ambiguous. Te results are quite intuitive. An increase in searc cost does not a ect te equilibrium rice, but it reduces referral intensity and market articiation. Terefore, iger searc costs are detrimental from te oint of view of bot te consumer and social welfare. In contrast, iger roduct eterogeneity stimulates referral activity and can imrove social welfare desite a rice increase. 6 Extensions 6. Price Discrimination by Firms Next, we consider te ossibility of rice discrimination by rms. In te main analysis, we assumed tat rms must carge te same (uniform) rice to all consumers, even toug rms can observe a consumer s referred location and refer te consumer to te most suitable roduct. Te reader may wonder weter rms would try to use teir information about consumer location to rice-discriminate between consumers based on te distance, x, between te consumer s ideal osition and te rm s roduct. We will address tis ossibility by assuming tat rms can engage in suc rice discrimination. Tat is, we let eac rm i