The Economics of Collective Brands

The Economic of Collective Brand Arthur Fihman Bar-Ilan Univerity Avi Simhon The Hebrew Univerity Irael Finkeltein The Hebrew Univerity Nira Yacouel Ahkelon Academic College April 7, 2014

Abtract We analyze the e ect of a hared brand name, uch a geographical name, on incentive of otherwie autonomou rm to etablih a reputation for product quality. On the one hand, brand memberhip provide conumer with more information about pat quality and therefore can motivate reputation building when the cale of production i too mall to motivate reputation formation by tand alone rm. On the other hand, haring a brand name may motivate free riding on the group reputation, reducing invetment in quality. We identify condition under which collective branding deliver higher quality than i achievable by tand alone rm.

1 Introduction There are many intance in which otherwie autonomou rm, which make independent buine deciion and retain their own pro t, market their product under a hared brand name. Often, the hared brand name i perceived a a badge of uperior quality by conumer, who are willing to pay premium price for them (e.g. Landon and Smith, 1998, and Loureiro and McClukey, 2000, 2003). Example include regional agricultural brand protected by deignation of origin (PDO) and geographical indication (PGI) tatu in the EU uch a champagne bubbly wine, Parma ham and cheee, Roquefort Cheee. In countrie where uch Protected Geographical Statu law are enforced, only product genuinely originating in that region are allowed to be identi ed a uch in commerce. Similarly, the Ja a label i hared by many independent Iraeli orange grower and exporter. Another important example i franchiing which in 2007 accounted for 9.2 percent of total U.S. GDP (Koova and Lafontaine, 2012) and which pan the range from fat food retaurant to accounting and law rm. In a typical buine-format franchiing arrangement, franchiee ell under the common franchie logo, but are otherwie independent buinee which retain their own pro t after paying the chain the correponding fee (typically baed on the outlet ale). Some premium food product, though old by individual producer, hare a common logo. For example, many of Germany top wine producer are member of the VDP wine aociation and carry the VDP logotype. VDP member mut adhere to more tringent tandard than thoe et down in the German wine law. Similarly, otherwie independent member of many pretigiou profeional organization hare a common logo (e.g., the German BFF aociation for profeional photographer in which memberhip i determined through a jury election proce). The fact that collective brand label are aociated with uperior quality ugget that rm which are member of thee brand invet more to maintain brand quality (or at leat are perceived to do o by conumer) and earn higher pro t than they 1

would a tand alone rm. Thi eem urpriing. If conumer perception of the collective brand label quality i jointly determined by their experience with the qualitie provided by di erent individual member, and if the proviion of high quality require cotly invetment, it would eem that each member ha an incentive to free ride on the invetment of fellow member. If o, why are thee brand label perceived a badge of quality? It i true that in ome cae, the perception of uperior quality may be partly attributable to exogenou advantage uch a climate, oil quality, acce to uperior input, technology and o on. However, even when uch natural advantage are preent the achievement of uperior quality preumably alo require the requiite invetment of e ort and other reource. The free riding problem might alo be mitigated to ome extent by monitoring the e ort and invetment of individual member to maintain quality tandard. However, monitoring i cotly and imperfect and i therefore unlikely to eliminate free riding altogether. Thu it would eem that producer have le of an incentive to invet in quality a member of a collective brand than they would a tand alone rm. The purpoe of thi paper i to how how collective branding may lead to higher quality in the market and increae welfare by incentivizing brand member to invet in quality, when they would not do o a tand alone rm. The idea i the following. When product quality i di cult to oberve before purchae and i revealed to conumer only after conuming the product ( experience good ), their perception of quality and the amount they are willing to pay for the product i baed on pat experience with the product - it reputation. Thu the extent to which a rm i able to receive a good return on it invetment in quality depend on how much information conumer have about it pat performance. If rm are mall, relative to the ize of the market, conumer may not have much information about the pat quality of any individual rm. In that cae, an individual rm may be unable to e ectively etablih a robut reputation for quality on it own and conequently ha little 2

incentive to invet in quality. Here collective branding may come to the recue and erve a a vehicle for reputation formation by increaing the relevant information available to conumer. Speci cally, uppoe mall individual rm market their product under a collective brand name, haring a collective reputation, while otherwie retaining full autonomy. Since the collective brand name cover a larger hare of the market than any individual member rm, conumer are better able to ae the reputation of the brand than of individual member. Thi in turn increae the value of a good brand reputation for each member, and may thu incentivize member to invet in quality when they would otherwie not do o. Thi i the reputation e ect of collective branding. But a noted above, branding may alo have an oppoing e ect on invetment incentive. Unle the brand i able to e ectively monitor individual invetment, haring a collective reputation may encourage individual member to free ride on the e ort of other member. Therefore the full e ect of collective branding on invetment in quality i determined by the interaction of thee two oppoing factor - the fact that, on the one hand, a good collective reputation i more valuable than a tand alone reputation, againt the incentive to free ride, on the other. Accordingly, we analyze the e ect of collective branding in two polar cae. In the rt, called perfect monitoring, free riding on the brand reputation i deterred becaue member which fail to invet are cotlely detected and excluded from uing the brand name. Since then only the reputation e ect i operative, a brand member incentive to invet i alway greater than that of a tand alone rm. Moreover, the incentive to invet increae with brand ize (the number of rm which are member of the brand) - the larger the brand, the greater the incentive of each member to invet and therefore the more pro table memberhip i. Thu in thi cae "bigger i better". We how that thi feature alo applie if brand memberhip require cotly authentication of invetment. We nd that, for appropriate parameter thi pro - invetment e ect of collective branding alo applie to the cae of no-monitoring, in which failure to invet cannot reult in excluion from the brand. Speci cally, collective branding can till facilitate 3

invetment if invetment i a u ciently important ingredient for the attainment of high quality - that i, if the di erence between the expected product quality of a rm which invet in quality and one which doen t i u ciently large. However, in contrat to the cae of perfect monitoring, here "bigger i better" only up to a point. Once the brand i u ciently large, the marginal contribution of an individual member invetment to the brand reputation become too mall to override free riding, reducing the brand incentive to invet relative to tand alone rm. Thu, in thi cae the brand ize which maximize rm pro t i large enough to enable ucceful reputation building but mall enough to dicourage individual free riding. Thu one might peculate that a regional brand like Champagne wine owe it ucce not only to unique oil and climatic condition but alo to fortuitou natural boundarie which encompa jut the right number of producer under it brand label. 1.1 Empirical Evidence Caual obervation ugget that collective branding i often oberved in ituation where conumer are unlikely to have much information about individual producer. Thu, for example, the export of agricultural product i often managed by marketing board and tate trading enterprie rather than by the individual producer a foreign conumer are unlikely to recognize individual producer. Similarly, retaurant on highway top, where there i little repeat buine, almot alway belong to well known chain. In the franchiing context, Jin and Lelie (2009) provide evidence that chain retaurant - which hare a collective brand name - maintain better hygiene than non-chain retaurant. In an econometric tudy of the determinant of reputation in the Italian wine indutry, Catriota and Delmatro (2008) how that brand reputation i increaing in the number of bottle produced by the brand and decreaing in the number of individual producer in the brand. Thi i conitent with our analyi. Keeping output xed, an increae in the number of individual producer ha no reputation e ect ince the number of unit whoe quality conumer oberve i unchanged. However, it doe increae the 4

incentive for free riding (which increae with the number of member), and hence lower invetment incentive and reduce the brand reputation. In an experimental tudy, Huck and L½uncer (2009) nd that more eller invet in quality when buyer are informed about the average pat quality of all eller - which correpond to a collective brand in our model - than when they only know the record of the eller from whom they actually buy. However, conitent with our analyi, when the number of eller increae, the average quality decline. Online hiring market alo provide evidence for reputational e ect of collective branding. Stanton and Thoma (2010) nd that employer are willing to pay more to inexperienced online worker (which have yet to etablih individual reputation) a liated with outourcing agencie than to inexperienced independent contractor and that thi advantage diipate over time a employer learn about individual productivity. 1.2 Relationhip to the Literature The centrality of individual rm reputation for quality for their ucce i the theme of a very large literature (ee the urvey article of Bar Iac and Tadeli (2008)). By contrat our concern i to undertand how autonomou rm can form a collective reputation. Tirole (1996) analyze how group behavior a ect individual incentive to invet (behave honetly) when the group ize i xed exogenouly. By contrat, our focu i preciely on the role of the group ize on individual invetment incentive. Our analyi i cloely related to a ubtantial literature on brand extenion or umbrella branding, which refer to the practice of multiproduct rm to ue the ame brand name on otherwie unrelated product in order to ignal quality of experience good to conumer. 1 A eminal paper by Wernerfelt (1988) conider a model of advere election in which a rm ell an old and new product of exogenou quality and etablihe condition under which an umbrella brand ell only high quality product. Choi (1998) 1 Relatedly Rob and Fihman (2005) how that a rm invetment in quality increae with ize and Yacouel (2005) and Guttman and Yacouel (2006) how that larger rm bene t more from a good reputation. 5

conider an in nite horizon ignalling model with advere election in which a rm dicover a new product of given quality in every period, and how that it i le cotly (in term of price ditortion) to ignal high quality to conumer if old product brand name i extended to new product than if product are eparately branded. Cabral (2000) analyze the role of brand extenion in a etting with ongoing learning about exogenou quality when qualitie of old and new product are correlated and how that higher quality eller have tronger incentive to extend their brand. Miklo-Thal (2012) how that if the quality of an exiting product i determined by pat deciion, then brand extenion trengthen the incentive to invet in the quality of a new product only if the exiting product i high quality. More directly related paper in thi literature focu on the role of brand extenion to incentivize invetment in all of the rm product. Anderon (2002), and Cabral (2009) conider a repeated game with moral hazard in which a multi product rm mut repeatedly invet in the quality of each of it product and how that brand extenion can upport high quality equilibria which are not feaible if product are old a eparate brand 2. Cai and Obara (2009) and Hakene and Peitz (2008) conider moral hazard etting when the rm make a once and for all invetment in the quality of both of it product. In a related vein, Dana and Spier (2009) conider a repeated game with imperfect obervability of quality in which bundling di erent product together can incentivize invetment becaue conumer who buy more product from a rm collect more information about it quality and can better monitor it behavior. Hakene and Peitz (2009) explore whether umbrella branding can partially or fully ubtitute for external certi cation of quality and Ramuen (2011) how how a rm with a monopoly on one product may ue umbrella branding to capture the market for a competitive product 3. 2 Anderon (2002) aume aymmetric product, while Cabral (2009) aume ymmetric product but imperfect obervability. 3 Johnon (2013) and Choi and Jeon (2007) alo conider context in which product of di erent rm hare reputation but the iue of brand ize e ect and free riding do not arie. Johnon analyze the relationhip between uptream and downtream rm in the preence of aymmetric information about nal product quality and, peci cally, conider whether quality i better aured if conumer look to 6

Both collective branding and umbrella branding provide rm with greater incentive to invet in quality than if product are branded eparately. The main di erence i that in an umbrella brand a central authority make invetment deciion for each of the brand product and internalize the e ect of each individual product quality on the reputation of the entire brand. By contrat, in a collective brand, individual member are concerned only with the e ect of their invetment deciion on the value of their own product. Therefore, umbrella branding incentivize invetment more than collective branding, but the latter can neverthele upport higher quality than tand alone rm. Another context which addre related iue i the literature on reputation in team (e.g., Che and Yoo, 2001) in which the payo of each team member depend on both her own e ort a well a thoe of other team member. Our analyi can alo contribute to undertanding the role of cooperative. While the conventional approach (e.g., Sexton and Sexton, 1987) view cooperative a a mean of joint integration allowing for the exploitation of cale economie, market power and rik pooling, our analyi ugget an additional important function of cooperative joint ignaling of information. Our approach i alo related to the common trait literature (e.g., Benabou and Gertner, 1993, Fihman 1996), in which an agent behavior reveal information about a common trait that he hare with other agent in the group. 2 The Model: Stand Alone Firm We conider a market for an experience good - conumer oberve quality only after buying, but not at the time of purchae. There are two period, N rik neutral rm and we normalize the number of conumer per rm to be 1. There are two poible product qualitie, low (l) and high (h). Firm are of two type, H and L, which are ditinguihed by their technological ability to produce high quality. An L rm produce high quality with probability b at each period whether or not it invet. An H rm produce high the uptream manufacturer or the downtream retailer for nal product quality aurance. Choi and Jeon conider when a new rm (with no reputation) can facilitate it ability to ignal product quality by employing component produced by a rm with an etablihed reputation (an intance of co - branding). 7

quality with probability b if it doe not invet but if it invet, it produce high quality with probability g at each period, where 0 < b < g 1. In either cae the realized quality at period 2 i independent of it realization at period 1. The cot of invetment i xed at e and invetment i once and for all : Prior to period 1, each rm decide whether or not to invet and that invetment determine the probability with which it produce high quality at period 1 and 2. We denote by N H and N L the total number of H and L rm repectively, N L N H ; and by r = in the market. N H N H +N L the proportion of H rm Each conumer i in the market for one period, demand at mot one (dicrete) unit, and exit the market at the end of the period. Her utility from a low quality unit i zero, from one high quality unit i 1 and her utility from any additional unit i zero. A conumer buy if her expected utility from a unit i greater or equal to the price he pay. We aume that g b > e, o that invetment i e cient. In order to focu on the reputational e ect of collective branding on invetment incentive in the mot direct way, it i convenient to aume that rm have monopolitic market power and can make take it or leave it o er to conumer. Speci cally, if conumer expected utility from a unit of rm i i v i ; rm i 0 price i aumed to be v i. Thu branding ha no e ect on rm pricing power or market hare, and can only a ect rm invetment incentive via reputational conideration. 4 Firm can ditinguih each other type. In contrat, conumer face both advere election and moral hazard; they cannot directly oberve a rm type (H or L) and alo do not oberve if it ha inveted. Let i 2 fl; hg denote the realized quality of rm i at period 1 and let S = ( 1 ; 2 ; :::; N ) be the indutry pro le of realized qualitie at period 1. We aume that at the beginning of period 2, conumer are perfectly informed (e.g., 4 Thi could be becaue conumer have high tranportation cot which e ectively endow rm with local monopoly pricing power. Alternatively, conider a tandard earch model: A conumer know only the price ditribution but not which rm charge what price, i randomly and cotlely matched with one rm and can either buy from that rm or equentially earch for other rm, incurring a poitive earch cot at each earch. A i well known, thee aumption imply that rm have monopoly pricing power (Diamond, 1971). 8

by interacting with conumer of the previou generation) about S and update their belief about rm. A rm pro t i the um of it revenue at period 1 and 2 le the invetment cot, e; if it invet. Let f denote a rm trategy: 5 f : fh; Lg! fi; NIg where I and N I denote inveting and not inveting, repectively. A conumer belief about rm i i the probability with which he believe that the rm i an H rm which ha inveted. 6 Conumer form belief about each rm at each period, where at period 2, belief poibly depend on S: 7 Let B 1 denote conumer belief at period 1, B 1 2 [0; 1] N ; and B 2 (S) be conumer belief at period 2; where B 2 : S! [0; 1] N : uch that: An equilibrium i a trategy f for each rm and conumer belief B 1 and B 2 (S) Each rm trategy f maximize it pro t, given the trategie of all other rm and conumer belief. B 1 and B 2 (S) are conitent with rm trategie. Conumer maximize their expected utility (i.e., they buy if and only if the price i le or equal to the expected value of the good according to their belief). Obviouly L rm don t invet in any equilibrium ince conumer don t oberve invetment and invetment ha no e ect on their quality. Trivially, there alway exit an 5 We do not formally include a rm price a part of it trategy ince we aume that it price alway equal conumer expected utility. 6 A far a a conumer i concerned, an H rm which ha not inveted i equivalent to an L rm ince both produce high quality with the ame probability. 7 We implicitly aume that, ince all conumer have the ame information, they alo form the ame belief about each rm. 9

equilibrium in which no rm invet. 8 The more intereting poibility i the exitence of an invetment equilibrium (IE) in which H rm invet. Suppoe there i an equilibrium in which all H rm invet. Since at period 1 rm have no hitory and ince H rm invet, conumer believe that any rm i an H rm which invet with probability r: Therefore at period 1 the expected utility from any rm - and hence it price - i rg + (1 r)b. At period 2; conumer are informed about S and update their belief. Let Pr(H j i ; S i ) be the poterior probability - and hence conumer belief 9 - at period 2 that a randomly elected rm i i type H when it realized quality at period 1 i i and thoe of the other rm i S i (Sn i ): Then the actual price of rm i at period 2 i g Pr(H j i ; S i ) + b(1 Pr(H j i ; S i )): However, ince S i of coure unknown at the time of invetment, what i relevant for rm invetment trategy i the expected price, a evaluated at the time of invetment. Thi i calculated a follow. Let E S i Pr(H j i ; S i ) be the expected (with repect to S i ) conumer belief at period 2 - a evaluated by rm i at the time of invetment - that rm i i type H, given that it realized quality will be i. Thu: E S i Pr(H j i ; S i ) = X Pr(H j i ; S i ) Pr(S i j i ) = X Pr(H; i ; S i ) Pr( i ; S i ) Pr( i ; S i ) Pr( i ) S i S i = X S i Pr(H; i ; S i ) Pr( i ) = Pr(H; i) Pr( i ) = Pr(H j i ): (1) That i, while conumer actual belief at period 2 will depend on the realization of S i ; their expected belief at the time of invetment doe not: Thu if p( i ) i a rm expected - a evaluated at the time of invetment - econd 8 In thi equilibrium conumer believe that no rm invet, which make it optimal for rm not to invet. 9 For any realization of i ; S i conitent with rm trategy, conumer equilibrium belief mut be conitent with Bayeian updating. 10

period price, conditional on it realized quality being i, p( i ) = ge S 1 Pr(H j i ; S i ) + b(1 E S 1 Pr(H j i ; S i )) = g Pr(H j i ) + b(1 Pr(H j i )) Since an H rm which invet produce high quality with probability g and an L rm produce high quality with probability b; Baye rule give (henceforth we omit ubcript i): and thu: Pr(H j h) = Pr(H j l) = gr gr + b(1 r) (1 g)r (1 g)r + (1 b)(1 r) p(h) = g Pr(H j h) + b(1 Pr(H j h)) (2) = b + (g b) Pr(H j h) = b + (g b)gr gr + b(1 r) and imilarly: p(l) = g Pr(H j l) + b(1 Pr(H j l)) (3) = b + (g b) Pr(H j l) = b + (g b)(1 g)r (1 g)r + (1 b)(1 r) : Denoting by R and R 1 the expected econd period revenue of an H rm that invet and doen t invet, repectively, we have: R = gp(h) + (1 g)p(l) (4) and R = bp(h) + (1 b)p(l) (5) Thu an H rm expected gain from invetment i e R R and thu by (2) - (5): e = (g b) 2 gr gr + b(1 r) (1 g)r : (1 g)r + (1 b)(1 r) Thu: 11

Propoition 1 When rm tand alone an IE exit if and only if e e. In the tand alone etting, rm have only a limited opportunity to etablih a reputation for quality, ince conumer information i limited to one obervation per rm. Hence if e > e ; an IE doe not exit becaue the cot of invetment exceed the individual rm expected return from acquiring a good reputation. 3 Collective Branding In thi ection we how that, in contrat to the tand alone etting, invetment equilibria may exit even when e > e if otherwie autonomou rm market their product under a hared brand name. The idea i that when the product of two or more rm hare a common brand name, conumer may condition their belief about a peci c rm type baed on the pat performance of all the brand member rather than on the rm individual performance. Thu, branding may provide conumer with better information which may in turn increae the incentive of H rm to invet. In order to facilitate the comparion of collective brand with tand alone rm, it i convenient to aume that conumer become aware of rm brand a liation only after the rt period, o that rt period revenue i the ame in both etting. Any e ect of branding on invetment incentive can now only be due to it e ect on econd period revenue. Let } be the et of all the poible partition of the N rm and let P 2 }: P i determined exogenouly. Each element Q 2 P i called a collective brand and each rm i 2 Q aigned to Q by P i called a member of brand Q: Let i (Q) denote rm i 0 pro t a a member of brand Q and let i be it pro t if it tand alone. In thi etting rm trategie and conumer belief at period 2 may depend not only on S but alo on P: That i, f : } fh; Lg! fi; NIg 12

B 2 : } S! [0; 1] N We then de ne a BE (Brand Equilibrium) by P 2 }; f; B 1 and B 2 uch that: Each rm trategy f maximize it pro t, given the trategie of all other rm and conumer belief. B 1 and B 2 (}; S) are conitent with rm trategie. (individual rationality) For each Q 2 P and i 2 Q; i (Q) i : That i, if a rm i aigned to brand Q by P; memberhip in Q mut be at leat a pro table a tanding alone. @i; Q 2 P.t. : 8j 2 Q; i =2 Q; i 2 Q 0 2 P; j (Q [ fig) j (Q); i (Q [ fig) i (Q 0 ), with the inequality trict for at leat one j or i: That i, adding an additional member to brand Q 2 P can not increae both it pro t and the pro t of exiting (aigned) member of Q. For any m 2 f1; :::; N H g; let n m H and nm L be the larget integer N H m ; and the larget integer N L m, repectively. De ne an m partition a a partition coniting of n m H brand, each of which ha exactly m type H member - henceforth called H brand - and n m L brand each of which ha exactly m type L member - henceforth called L brand - and N m(n m H + nm L ) tand alone rm. We hall refer to the number of rm which are member of a brand a the brand ize and de ne a BIE a a BE in which each member of each H brand invet. Let q = nm H n m H +nm L be the proportion of m ize brand which are H. We analyze branding equilibria under two alternative regime. Under perfect monitoring, memberhip in an H brand contitute a binding commitment to invet, uch that a rm which i aigned by P to an H brand and doe not invet i precluded from 13

uing the brand name. 10 The interpretation i that the brand can cotlely detect a member which doen t invet and exclude it from the brand. By contrat, in the nomonitoring regime, memberhip in an H brand cannot be conditioned on invetment. The interpretation i that failure to invet i undetectable and cannot jeopardize brand memberhip. 3.1 Perfect Monitoring In thi ection we analyze collective branding under perfect monitoring. Let e m be the larget value of e for which a BIE exit for an m partition under perfect monitoring. Propoition 2 Correponding to every m 2 f2; :::; N H g (i) e m > e : (ii) e m i trictly increaing in m: Proof of propoition: We contruct a BIE for any m partition. Suppoe all member of all the H brand invet. Let a brand record be the total number of high quality unit produced by all the member of the brand at period 1: Denote the record of brand i of ize m a m i 2 f0; 1; ::::; mg; let S m = ( m 1 ; :::; m n ; m H +nm 1 L n m H +nm L +1 ; :::; 1 N (m 1)(n m H +nm)), and let Sm i (S m n m i ): L Let conumer belief at period 2 be: A tand alone rm or a rm which i a member of a brand of ize 6= m i either type L or type H which ha not inveted. 11 Let Pr(H m j m i ; S m i) be the poterior probability - and therefore conumer belief 12 that, given S m i; brand i of ize m and record m i i an H brand. To implify notation, in the 10 In that cae, we aume that one of the tand alone rm (if there are any under P ), or one of the rm aigned to an L brand i randomly choen to be reaigned to replace the non-invetor. Thu excluding a non-inveting H rm from the brand leave the brand ize and the expected number of high quality unit produced by the brand unchanged, and hence cannot decreae the expected pro t of the remaining brand member which do invet, while it can only increae the pro t of the replacement rm. 11 With repect to brand of ize 6= m thi i an out of equilibrium belief. 12 For a brand of ize m; any record m i on the equilibrium path and conumer belief about uch a brand mut be conitent with Bayeian updating. 14

remainder of the proof we omit the ubcript and upercript of m i when thi doe not lead to any ambiguity. A completely analogou argument to (1) implie that conumer expected (with repect to S m i) belief - evaluated at the time of invetment - that a brand with record i an H brand i given by: Pr(H m j ) = qg (1 g) m qg (1 g) m + (1 q)b (1 b) m (6) Thu at the time of invetment, the expected revenue (price) of each member of an H brand at period 2, conditional on the brand realized record being ; i given by p m () : p m () = g Pr(H m j ) + b(1 Pr(H m j )) = b + (g b) Pr(H m j ) (7) and thu it unconditional expected revenue at period 2 i: R m = mx m g (1 g) m p m () (8) Analogouly, the expected revenue of each member of an L brand of ize m at period 2 i: R m L = mx m b (1 b) m p m (): (9) Since conumer believe that tand alone rm are either type L or type H which don t invet, the econd period revenue of any tand alone rm i b. Conider an L rm which i a member of an L brand. A a brand member it expected pro t i R m L and a a tand alone rm it pro t i b < RL m ; where the inequality follow from (7) and (9). Thu brand memberhip i more pro table for L rm than tanding alone. Conider an H rm which i a member of an H brand. A a brand member, it invet and it expected pro t i R m e. If it doen t invet, it mut tand alone (ince memberhip in the H brand i contingent on invetment) and it pro t i b. Thu brand memberhip i more pro table than tanding alone if R m b e: 15

Conider a tand alone rm. If it join one of the L brand, the brand ize will increae to m + 1; and the pro t of every exiting member will be b (ince conumer will not pay more than b to a rm which i a member of a brand of ize 6= m), while otherwie it pro t i R m L > b. By the ame reaoning, if it join one of the H brand, the revenue of every exiting member will decreae from R m to b. Thu the equilibrium condition are ati ed if R m b e: To prove the propoition it thu remain to characterize e which ati e the condition R m b e. Thi i achieved by uing the following lemma, proved in the appendix. Lemma 1 For every m 1; R m i increaing and R m L i decreaing with m. Let " m R m R m L : By equation (4) - (9), R1 = R and R 1 L = R. Hence by Lemma 1, and the de nition of e it follow that for every m 2: " m = R m R m L > R 1 R 1 L = R R = e : Let e m = " m : Thu, R m b > e for e e m : Thi complete the proof of part (i) of the propoition. Part (ii) then follow immediately from Lemma 1. Remark 1: Although we do not formally require, a an equilibrium condition, that member of H brand earn greater pro t when the brand collectively invet than if no member invet, it follow immediately from the de nition of " m in the preceding proof that our equilibrium contruction do indeed atify thi enible criterion. Thu under collective branding with perfect monitoring, there are multiple brand ize which can upport invetment in equilibrium when e > e : A the preceding propoition etablihe, thee may be ranked in term of their e ect on invetment: The larger i the brand ize, m; the greater i the range of invetment cot for which invetment i utainable in equilibrium. In particular, the larget invetment cot under which invetment i utainable correpond to the brand ize N H where all H rm are in the ame brand. In thi equilibrium, "bigger i better" in the ene that the larger i N H ; 16

the larger the range of invetment cot which can upport equilibrium invetment. The ame obervation applie to the relationhip between brand ize and rm pro t: A hown in the proof of the propoition, the larger the equilibrium brand ize, the greater the H rm pro t and the lower the L rm pro t. Thi ugget that the equilibrium brand ize m = N H i upported by more plauible conumer belief than m < N H. Speci cally, a i hown in the proof of the propoition, equilibria in which m < N H require that conumer believe that a brand of ize larger than m i either type L or type H which doen t invet: But, it i preciely the H rm which would pro t, while L rm would loe, if the brand ize increaed, a long a conumer believed that a brand ize > m with a record greater or equal to that of a brand of ize m i at leat a likely to invet. Thu, conumer belief which aociate larger brand ize with lower quality eem omewhat unpalatable. By contrat, conumer appropriately aociate a brand ize larger than N H with lower quality becaue uch a brand mut include at leat ome L rm. The ame reaoning ugget that equilibria in which brand are of di erent ize would imilarly be baed on le plauible conumer belief. Speci cally, in an equilibrium in which H brand are of di erent ize, the maller H brand would be le pro table and could pro tably increae in ize unle conumer implauibly aociate larger brand ize with lower quality. Although the preceding argument ugget a theory of mega brand, thi concluion mut be tempered once the aumption of perfect monitoring i relaxed, a the following ection how. 3.2 No-Monitoring We now turn to examine the extent to which the analyi of the previou ection applie in the cae of no-monitoring. In thi etting failure to invet cannot prevent a rm from uing the brand label and thu rm have le of an incentive to invet than in the perfect monitoring regime. Neverthele, the following propoition etablihe that if g 17

i u ciently large, collective branding can till incentivize invetment when tand alone rm will not invet. Let e m be the larget value of e for which a BIE exit for an m partition under no-monitoring. Propoition 3 Under no-monitoring, for every m 2 f2; :::; N H g there i g(m) < 1 uch that if g g(m); e m > e : Proof: For any m partition, let the rm trategie and conumer belief be the ame a decribed in the proof of propoition 2. Then exactly the ame argument a in the proof of propoition 2 imply that the equilibrium condition are ati ed for all tand alone rm and member of L brand. Conider a member of an H brand. If it invet it revenue (given that the other m 1 member invet) i R m given by (8). However, in contrat to the cae of perfect monitoring, here it ha the option of remaining in the H brand without inveting. If it doen t invet, then it revenue i: 13 R m 1 = mx 1 m 1 g (1 g) m 1 [(1 b)p m () + bp m ( + 1)] (10) If it tand alone, it revenue i b < R m 1 where the inequality follow from (7) and (10). Let e" m R m R m 1: Thu the equilibrium condition are ati ed if e e" m : The following lemma how that a imilar reult to Lemma 1 applie under no monitoring in the pecial cae g = 1: Lemma 2 Under no- monitoring, if g = 1; e" m i trictly increaing in m for m 1: By equation (4) - (10), R 1 = R and R 1 1 = R. Hence e" 1 = R 1 R 1 1 = e : Thu it follow from the lemma that if g = 1; then e" m > e for all m > 1: By equation (6) - (8) and (10), e" m i continuou in g; implying that there i g(m) < 1, uch that for g g(m); e" m > e : Finally, let e m = e" m : Thi complete the proof. 13 m 1 g (1 g) m 1 i the probability that the other, m 1 inveting rm, produce high quality unit. With probability 1 b the rm which doen t invet produce low quality in which cae the brand produce high quality unit and each member receive the price p m (): With probability b the m-th rm produce high quality and the price i p m ( + 1). 18

The intuition behind Propoition 3 i that the incentive to free ride on the invetment of other brand member re ect the advere e ect of a ingle low quality obervation on the brand reputation. If g i u ciently large, even a ingle low quality unit ha enough of a negative e ect on conumer belief to deter free riding. However, thi i true only a long a the brand ize i not "too large". Once the brand ize i u ciently large, the e ect of a ingle low obervation on the brand reputation i too mall to deter free riding. Therefore, in contrat to the cae of perfect monitoring, under no-monitoring it i not generally true that bigger i better. In fact, the following propoition how that under no-monitoring, for u ciently large m; a BIE for an m partition doe not exit for e e. Propoition 4 Under no-monitoring, for every g < 1, there i m(g) uch that for m m(g); e m e : Proof: In the Appendix. Thu, if em denote the brand ize which maximize e m - the brand ize for which a BIE exit for the larget range of invetment cot - then, em < N H if N H i u - ciently large, in contrat to the cae of perfect monitoring. Alo, in contrat to perfect monitoring, if bm i the equilibrium ize which i mot pro table for H rm, then bm > em if N H i u ciently large, a the example directly below illutrate. 14 Recall that in the cae of perfect monitoring it wa argued that N H i a more plauible equilibrium brand ize than maller brand ize. Thu by a completely analogou argument, under no-monitoring the ame hold true for bm: Example In gure 1, R m and R m 1 are ketched for the parameter b = 0:4; g = 0:95; N H = 10, N L = 30 and e = 0:14. e m i repreented by the ditance between R m and R m 1: In thi 14 Thi i becaue em i the m which maximize R m R m 1 while the mot pro table brand ize for a given e i the larget m for which R m R m 1 i till e: 19

1 0.9 Revenue per firm 0.8 0.7 0.6 0.5 R m R m 1 0.4 1 2 3 4 5 6 7 8 9 10 Number of brand' member m example 15, e = 0:12, BIE exit for 2 m 5 and em = 3 (where ~e 3 = 0:19 > e = 0:12): The equilibrium brand ize which maximize H rm pro t i m = 5: By contrat, under perfect monitoring, a we know from the previou ection, both e m and H rm pro t i maximized when m = N H = 10. 4 Umbrella brand Umbrella branding refer to the practice of multiproduct rm to market otherwie unrelated product under the ame brand name in order to ignal quality. How do the incentive of collective brand to invet in reputation compare with thoe of umbrella brand? To addre thi quetion in our etting, conider an m partition each element of which i now a multiproduct rm which make invetment deciion for, bear the invetment cot of and own the the pro t of each member (product). Thu, if the 15 (n H ; n L ; q) equal (10,30,0.25), (5,15,0.25), (3,10,0.23), (2,7,0.22), (2,6,0.25), (1,5,0.17), (1,4,0.2), (1,3,0.25), (1,3,0.25), (1,3,0.25), for m = 1; 2; :::; 10, repectively. Note that R m i almot at between m = 5 and m = 6 (increaing from 0:862 to 0:865) becaue of the harp decline in q between thoe two value. 20

umbrella brand i ize m; and the price of each of it member (product) i p; the brand revenue i pm: We compare the umbrella brand invetment incentive with thoe of the collective brand under no-monitoring 16. In the cae of collective brand under no-monitoring, the highet invetment cot for which a BIE exit for an m partition i e m = R m R m 1: If the umbrella brand of ize m invet in all it member, then it econd period expected pro t i m(r m e). For the ame reaon, if it invet in only m 1 of it product, it pro t i m(r m 1 e) + e: Thu a BIE exit for umbrella brand of ize m if: m(r m e) m(r m 1 e) e = m(r m R m 1) e = me m e 0 Thu, while a BIE exit for collective brand only if e e m, in the cae of umbrella brand it exit for e me m : Thu umbrella branding incentivize invetment more than collective branding. The intuition for thi i traightforward. In the cae of both collective brand and umbrella brand, a low quality realization of one member reduce the reputation of the entire brand. In the cae of the collective brand, individual member are only concerned about how thi a ect the value of their own product. By contrat, the umbrella brand internalize the e ect of it invetment in each individual member (product) on the reputational value of the brand entire product line. 5 Monitoring cot We have conidered two polar cae of collective brand; perfect monitoring, in which member of H brand are committed to invet, and imperfect monitoring, in which brand member invet only if invetment i individually optimal. Conider an intermediate cae in which the brand cannot cotlely detect failure to invet and, accordingly, memberhip 16 The appropriate comparion i to no-monitoring becaue under perfect monitoring brand member have no dicretion with repect to invetment deciion while the owner of the umbrella brand can decide in which product to invet. 21

in an H brand require a rm to incur a xed monitoring cot c to verify that it invet - for example by hiring a reliable external auditor to certify it invetment 17. Then, a brand member pro t i R m e c while the pro t from tanding alone i b: Thu, a BIE exit for the m partition if R m (e + c) > b. Thu, ince R m increae with m; invetment incentive and H rm pro t increae with m, jut a in the cae of perfect monitoring without monitoring cot. Thi alo ugget that under monitoring cot there i a minimal brand ize - the brand mut be large enough for reputational gain aociated with increaed ize to cover monitoring cot in addition to invetment cot. 6 Franchiing Franchiing hare ome feature of umbrella brand and ome feature of collective brand. The franchior collect a hare of each franchiee revenue - and thu bene t from the invetment of each outlet - but franchiee bear invetment cot. In practice, franchior tend to monitor franchiee quite cloely, by contractually requiring that the ervice be in accordance with the pattern determined by the franchior, through eld upport, external ervice audit, peer review and conumer feedback (Spinelli Jr, Roenberg, Birley, 2004), all of which ugget that quality aurance i cotly to the franchior. Thu, if the franchior incur a monitoring cot c for each franchiee that it monitor and get a fraction of franchiee revenue, it pro t i m(r m c) which, ince R m i increaing, increae with m: Thi ugget that, a in the cae of collective brand with perfect or cotly monitoring, the franchior pro t increae with the number of franchiee and that the number of franchiee mut be large enough for reputational gain to cover monitoring cot. Indeed, leading franchie chain are huge and eem to trive for unlimited growth. For example, in the US alone, there are over 20,000 Subway, 14,000 McDonald, 7000 Pizza Hut, 11000 Starbuck and 13000 H&R Block tax preparation location. However, it hould be noted that the number of chain outlet or location can greatly exaggerate 17 Alternatively and equivalently, the cot c i hared by all brand member. 22

the number of "brand member" ince franchiee often own multiple unit. Indeed, the policy of many large chain i to actively encourage franchiee to take on multiple outlet. For example, Domino Pizza and Subway o er reduced fee for franchiee that acquire further unit (ee http://www.buinefranchie.com/pecial-feature/multiple). According to NatWet/BFA Franchie Survey 2008, one fth of franchiee own multiple unit, with an average of even unit each. Thi policy might be deigned to reduce monitoring cot. Firt, owner of multiple unit have more of an incentive to internalize the e ect of their invetment on the brand reputation than owner of ingle unit (particularly if the outlet owned are in cloe geographical proximity). Second, it may be cheaper for the franchior to monitor owner of multiple unit than ingle unit owner. For example, the former can be e ectively monitored by retaliating againt all it unit if the quality of one randomly ampled unit i defective, while in the cae of ingle unit owner, it i neceary to monitor each unit individually. 18 7 Concluding Remark It ha been hown that collective branding can lead to higher quality than i attainable by tand alone rm. Intitution uch a marketing board and tate trading enterprie are often viewed a mean to foter colluion and obtacle to e cient market and on thee ground have been targeted by free market advocate in WTO negotiation. Our analyi ugget that to the contrary, by enhancing reputational incentive, uch intitutionalized collective brand may increae e ciency and welfare by enabling higher product quality than would be attainable in their abence. 19 18 Moreover, there i ome evidence that monitoring by franchior i le than perfect, poibly to ave on monitoring cot. For example, Jin and Lelie (2008) how that within a chain, company owned retaurant tend to have better hygiene than franchiee owned retaurant, uggeting at leat ome free riding by franchiee on the chain reputation. Relatedly, Ater and Rigby (2012) how that chain outlet at location in which repeat buine i infrequent tend to be company owned, poibly to ave on monitoring cot at location in which individual incentive to free ride are particularly trong. 19 An alternative poition expreed in defene of STE i that they provide economie of cale in production and promotion. 23

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[35] Wernerfelt, B. 1988. Umbrella Branding a a Signal of New Product Quality: An Example of Signalling by Poting a Bond. The Rand Journal of Economic 19(3): 458-466. [36] Yacouel N. 2005. Reputation, Firm and Social Norm. Ph.D. Diertation, Bar- Ilan Univerity. 8 Appendix 8.1 Proof of Lemma 1 By equation (6) - (8) where R m = b + (g b) = b + (g b) = b + (g b) mx m mx m mx m g (1 g) m g (1 g) m q g (1 g) m q q + (1 g (1 g) m k m x m b (1 b) m g (1 g) m and k m g (1 g) m q + b (1 b) m (1 q) q)x m q q + (1 q)x m Let S be a binomial random variable with the parameter (m; g): Let X m bs (1 b) m S g S (1 g) m S and K m q q + (1 q)x m Note that E(X m+1 j X m ) = g bs+1 (1 b) m S g S+1 (1 g) m S + (1 g) bs (1 b) m+1 S g S (1 g) m+1 S = bxm + (1 b)x m = X m implying that X 1 ; X 2 ; X 3 ; ::: i a martingale. Since X m 0, K m i a trictly convex function of X m ; then by Jenen Inequality, EK m+1 > EK m : Hence, R m+1 = b+(g b) m+1 X m + 1 g (1 g) m+1 k m+1 > b+(g b) 27 mx m g (1 g) m k m = R m

which prove that R m i increaing with m. Subtitute equation (6) and (7) into (9) yielding mx m RL m = b + (g b) b (1 b) m g (1 g) m q g (1 g) m q + b (1 b) m (1 q) mx m = b + (g b) g (1 g) m qx m qx m + (1 q) Since qx m qx m +1 q i a concave function of X m ; by Jenen Inequality qx m+1 E qx m+1 + 1 q < E qx m qx m + 1 q implying which prove that R m L R m+1 L = b + (g b) < b + (g b) m+1 X mx m + 1 g (1 g) m+1 qx m+1 m qx m+1 + 1 q g (1 g) m qx m qx m + 1 q = Rm L i decreaing with m. Thu completing the proof. 8.2 Proof of Lemma 2 Proof: When g = 1; the m 1 inveting rm produce high quality with certainty. If the mth rm doen t invet it produce high quality with probability b, in which cae it revenue (and that of every other member of the brand) are R m. With probability 1 b it produce low quality in which cae = m 1 and, by equation (6) and (7) Pr(H m j m 1) = 0 and p m () = b. Hence, R m 1 = br m + (1 b)b: It follow that e" m = R m R m 1 = (1 b)(r m b): Since by Lemma 1 R m i increaing with m, it follow that e" m i increaing with m. 28

8.3 Proof of Propoition 4 The proof i uing the following Claim. Claim R m = mx 1 m 1 g (1 g) m 1 [gp m ( + 1) + (1 g)p m ()] (11) Proof of the Claim: Let 0 be the number of high quality unit produced by any given group of m 1 member of an H brand of ize m. Since the mth rm invet, it produce high quality with probability g and low quality with probability 1 g: Hence, the brand produce 0 +1 high quality unit and receive a price of p m ( 0 +1) with probability g and produce 0 high quality unit and receive a price of p m ( 0 ) with probability 1 g. Since the probability that m 1 member produce 0 high quality unit i m 1 0 g 0 (1 g) m 1 0 it follow that R m = mx 1 which prove the Claim. m 1 Uing equation (10) and (11) e" m = R m R m 1 = (g b) g (1 g) m 1 [gp m ( + 1) + (1 g)p m ()] mx 1 m 1 g (1 g) m 1 [p m ( + 1) p m ()] Subtituting for p m () from equation (6) and (7) and recalling from the proof of Lemma 1 that x m b (1 b) m g (1 g) m : mx 1 e" m = (g b) 2 Subtituting yield m 1 g (1 g) m 1 q(1 q)(x m x m +1) q + (1 q)x m +1 [q + (1 q)x m ] : x m x m +1 = b (1 b) m g (1 g) m b +1 (1 b) m 1 g +1 (1 g) m 1 = b (1 b) m 1 g (1 g) m 1 mx 1 e" m = (g b) 2 1 b 1 g 1 b b m 1 q(1 q) b (1 b) m 1 1 g g q + (1 q)x m +1 [q + (1 q)x m ] : 29 b g

Hence, and ince lim m!1 x m = 1 and P m 1 m 1 b (1 b) m 1 = 1 it follow that lim e" m = 0 m!1 and the lemma follow immediately. 30