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Selling Your Product Through Competitors’ Outlets:Channel Strategy When Consumers Comparison ShopSridhar Moorthy, Yongmin Chen, Shervin Shahrokhi Tehrani

To cite this article:Sridhar Moorthy, Yongmin Chen, Shervin Shahrokhi Tehrani (2018) Selling Your Product Through Competitors’ Outlets: ChannelStrategy When Consumers Comparison Shop. Marketing Science

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MARKETING SCIENCEArticles in Advance, pp. 1–15

http://pubsonline.informs.org/journal/mksc/ ISSN 0732-2399 (print), ISSN 1526-548X (online)

Selling Your Product Through Competitors’ Outlets: ChannelStrategy When Consumers Comparison ShopSridhar Moorthy,a Yongmin Chen,b Shervin Shahrokhi TehraniaaRotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada; bDepartment of Economics, University ofColorado at Boulder, Boulder, Colorado 80309Contact: moorthy@rotman.utoronto.ca (SM); yongmin.chen@colorado.edu (YC); s.shahrokhi13@rotman.utoronto.ca,

http://orcid.org/0000-0001-5244-9705 (SST)

Received: December 4, 2015Revised: December 16, 2016; May 31, 2017Accepted: June 9, 2017Published Online in Articles in Advance:January 10, 2018

https://doi.org/10.1287/mksc.2017.1063

Copyright: © 2018 INFORMS

Abstract. This paper develops a new rationale for decentralization in distribution chan-nels: providing a one-stop comparison shopping experience for consumers. In our duopolymodel, when consumers are knowledgeable about their brand preferences, each manu-facturer would distribute through its own vertically integrated retail outlets only. Whensome consumers are unsure about their brand preferences, however, it may be optimal forone of the manufacturers to also distribute through its competitor’s outlets. The result-ing equilibrium has several interesting properties. First, only one of the manufacturerschooses to add competitor-outlet distribution, not both—even when the manufacturersare symmetric. Second, themanufacturer distributing through its competitor’s outlets alsodistributes through its own outlets, i.e., its distribution strategy is a hybrid strategy, com-bining vertical integration and decentralization. Third, when the manufacturers’ brandsare asymmetric, it is the weaker brand that has a stronger incentive to pursue hybrid dis-tribution. Fourth, the competitor’s outlets in question welcome the new brand, even whenno consumer would actually buy the new brand—a case of pure showrooming. Theseresults highlight the linkages between distribution strategy, shopping efficiency, and retailformats. Shopping costs and consumers’ uncertainty about their own brand preferencescreate a demand for multibrand retailing, and in pursuing this demand, manufacturersmay eschew the efficiency advantages of vertical integration in favor of hybrid distribu-tion. However, the fact that only one of the manufacturers chooses to do so suggests thatthis strategy also has weaknesses, which we discuss in the paper.

History: Ganesh Iyer served as the senior editor and Greg Shaffer served as associate editor for thisarticle.

Funding: This research was supported by the Social Sciences and Humanities Research Council ofCanada via [Grants 410-2005-0824 and 435-2013-0704] to the first author.

Keywords: distribution channels • retailing • shopping behavior

1. IntroductionThe channel strategy question, whether to go to mar-ket directly, through own outlets, or indirectly, throughindependent outlets, has played out in the marketingliterature as largely a trade-off between two forces, onebeing double marginalization. Independent manufac-turers and retailers optimize over parts of the valuechain, not the whole value chain, leading to marginbuildup, too-high retail prices, and too-low demand.Vertical integration can eliminate this externality bygetting rid of one of the margins. However, there is asecond force, going in the other direction, that arguesfor preserving the second margin. This is the strategicvalue of decentralization: independent middlemen caninsulate manufacturers from direct competition at theretail level (McGuire and Staelin 1983, Coughlan 1985,Moorthy 1988, Choi 1991).In this paper we highlight a third force, consumer

shopping efficiency, thatmay also push amanufacturer

toward decentralization. The connection between dis-tribution strategy and shopping efficiency may not beimmediately obvious. It arises because each is linkedto retail format—whether retailers are single brand ormultibrand.1 Shopping efficiency and retail format arelinked because consumers who are unsure about theirbrand preferences would like to resolve their uncer-tainty by visiting as few stores as possible, preferablyone, where they can compare brands side by side. Thiscreates a demand for multibrand stores. On the otherhand, retail format and distribution strategy are linkedbecause pure vertical integration implies single-brandretailing, while multibrand retailing requires at leastsome decentralization.

In our model there are two manufacturers sellingone product each, potentially substitutable in demand.Absent consumer uncertainty about brand preferences,pure vertical integration would prevail: each manu-facturer would distribute its product only through its

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Figure 1. (Color online) Four Generic Distribution Structures

Manufacturer A

Retailer A

Manufacturer A

Retailer A

Manufacturer B

Case 2�Manufacturer B

Retailer B

Case 1(status quo)

Retailer B

Manufacturer A

Retailer A

Manufacturer A

Retailer A

Case 2

Case 3

Manufacturer B

Retailer B

Manufacturer B

Retailer B

own retail outlets.2 With consumer uncertainty aboutbrand preferences, however, it may be optimal for oneof the manufacturers to add distribution through itscompetitor’s outlets. The resulting equilibrium has sev-eral interesting properties. First, only one of the manu-facturers chooses to add competitor-outlet distribution,not both—even when the manufacturers are symmet-ric. Second, the manufacturer distributing through itscompetitor’s outlets also distributes through its ownoutlets, i.e., its distribution strategy is a hybrid strat-egy combining vertical integration and decentraliza-tion (Case 2 in Figure 1 illustrates). Third, when themanufacturers’ brands are asymmetric, it is the weakerbrand that has a stronger incentive to pursue hybriddistribution. Fourth, the competitor’s outlets in ques-tion welcome the new brand, even when no consumerwould actually buy the new brand—a case of pureshowrooming. Thus the paper provides a rationale forhow a store may benefit from showrooming evenwhenthe product being showroomed has no sales.These observations dovetail nicely with contempo-

rary developments in retailing. Whereas 50 years agoretailerswerebackward integrating intomanufacturingvia private labels, nowmanufacturers are forward inte-grating into retailing via e-commerce. It is rare to seea manufacturer who does not sell its products directlyto the public through its website. Indeed, several man-ufacturers, for example, Microsoft and Apple, operatenot only online stores but also brick-and-mortar stores.Asymmetric hybrid distribution strategies of the sortstudied in this paper seem to accompany thesedevelop-ments. Consider, for example, Microsoft’s distributionstrategy for its Surface-branded line of laptops/tablets.Microsoft’s stores sell these products, of course, butthese stores also sell competingproductsmadebyAsus,Dell, and Lenovo. However, these other manufactur-ers’ online stores only sell their own brands—they donot sell Surface. The eReader market provides anotherexample. Here Amazon and Barnes and Noble have

backward integrated into manufacturing with theirKindle and Nook brands. However, while Amazonpractices pure vertical integration, selling Kindle onlythrough its own stores, Barnes and Noble has chosento sell Nook through its own stores as well as throughAmazon.com. Finally, in the world of media, where 20years ago Chipty (2001) reported that integrated cabletelevision operators tended to exclude rival programservices, nowRoos et al. (2015) find several examples ofnewswebsites “linking” and “excerpting” competitors’stories.

The one-stop comparison shopping motivation fordecentralization is a key idea of this paper. It has thepower to link distribution strategy to a retailing format,explain hybrid distribution strategies, and provide anew rationale for showrooming. To our knowledge,these ideas are new to the literature. In McGuire andStaelin (1983), Coughlan (1985), and Moorthy (1988),for instance, manufacturers’ distribution options arelimited to pure vertical integration or pure decen-tralization through third-party retailers. Furthermore,retailers are constrained to be single-brand retailers.Choi (1991) considers both single-brand and multi-brand retailing, but ends up arguing for single-brandretailing. Shopping considerations play no role in anyof these papers. Consumers are represented in reducedform, as a demand function; they know what theywant, where to buy it from, and what price to pay, allbefore leaving home.3

By contrast, in ourmodel, consumers decidewhetherto shop, where to shop, and which brand to buy. Andthey search for prices. Their decisions depend on theirshopping costs, brand preferences, and knowledge ofbrandpreferences, andwemodel heterogeneity in all ofthese dimensions. The last of these is critical. What weare trying to capture is the reality that some consumersknow, before they start shopping, which brand theyprefer, while others discover their brand preferencesduring the shopping process. Modeling this difference

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allows us to bring out a central idea of this paper—thatthe one-stop comparison shopping benefit provided bymultibrand retailers is useful to some consumers, butnot to others.In Section 2 we present our model and develop

some preliminary results that facilitate our subsequentanalysis. Particularly noteworthy is the simplicity ofthe equilibrium-price characterization. This is a con-sequence of our search model. Section 3 examines thebaseline case where all consumers are assumed to beknowledgeable about their brand preferences. In thiscase, vertical integration is a dominant strategy foreach manufacturer, neither manufacturer distributesthrough its competitor’s outlets, and each retailer issingle brand. We get into our model proper in Sec-tion 4. Here we analyze a symmetric version of themodel, where each manufacturer has an equal numberof loyal consumers. Despite the symmetry, any equi-librium involving hybrid distribution is asymmetric:only one of the manufacturers adopts hybrid distri-bution; the other sticks to pure vertical integration.The fact that both manufacturers do not adopt hybriddistribution underscores its limitations. One is canni-balization: the inefficient competitor channel may can-nibalize the efficient own channel. The other draw-back is what we call the “strengthening-the-competitoreffect.”While hybrid distribution increases the numberof uncertain consumers shopping—which both man-ufacturers welcome—it also strengthens the competi-tor’s brand at the expense of the manufacturer’s own.Once a competitor has been strengthened this way, itdoes not pay for it to return the favor!

We extend the analysis to asymmetric manufactur-ers in Section 5. Here, one brand has more loyal con-sumers than the other. In this context we ask whichmanufacturer—the one with the stronger brand or theone with the weaker brand—has a stronger incentiveto pursue hybrid distribution. Our first result is thateven small asymmetries in brand strength have a bigeffect on uncertain consumers’ shopping behavior. Thestronger manufacturer’s position improves, the weakermanufacturer’s position deteriorates, and the numberof uncertain consumers shopping increases relative tothe symmetric case. Second, while both brands canpursue hybrid distribution in equilibrium—just not atthe same time—the weaker brand has a stronger incen-tive. This is because, of the three effects describedabove, two of them favor the weaker brand goingthrough the stronger brand’s store.

In Section 6 we discuss the robustness of our resultsto alternative assumptions. We note that our searchmodel for prices leads to monopoly retail prices inequilibrium. Other ways of competing—such as withadvertised retail prices—will lead to different prices.However, this will not necessarily change our mainresults because those results do not depend on the

absolute level of prices, and their dependence evenon relative prices is only marginal. Rather, the maindriving force is uncertain consumers’ preference forone-stop shopping at a multibrand store. We also dis-cuss what happens when the manufacturers’ retail-ing operations have independent strengths and weak-nesses other than their store brands. For example, onemanufacturer’s stores might provide a better shoppingexperience in the sense of Iyer and Kuksov (2012),or one manufacturer’s stores might carry more prod-uct categories than the other (compare, for example,Macy’s stores with Levi’s stores). When such exoge-nous retail-level asymmetries are overlaid on the store-brand asymmetry, it is no longer the case that theweaker brand necessarily has a stronger case to pursuehybrid distribution. In fact, it could be the other wayaround.

2. ModelTwo manufacturers, A and B, with brands A and B,competing in the same product category, have todecide whether to add distribution through their com-petitor’s stores. The status quo is that each manu-facturer is vertically integrated, distributing throughits own stores only (Case 1 in Figure 1). The deci-sion to add a competitor channel would represent ahybrid distribution strategy: the manufacturer wouldbe vertically integrated through its own stores anddecentralized through its competitor’s stores. Table 1summarizes each firm’s strategic options and Figure 1illustrates the resulting channel structures.4 In the sta-tus quo, all retail outlets are single-brand outlets; in allother channel structures, there are multibrand outlets,either one (Cases 2 and 2′) or two (Case 3).5

To focus on the demand-side considerations driv-ing distribution strategy, we simplify the supply side.All costs, manufacturing and retailing, are assumedaway. In addition, adding an additional distributionchannel is assumed to not involve additional costs.6Issues such as retailing expertise are also suppressed.The firms interact as follows. They choose distributionstrategy first, then wholesale price (if necessary), andfinally, retail price(s) for the brand(s) they carry in their

Table 1. Distribution Strategies

Firm B’s distribution strategy

Via own Via own andstores only competitor’s stores

Firm A’s distribution strategy

Via own stores only Case 1 Case 2(status quo)

Via own and competitor’s Case 2′ Case 3stores

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stores. We apply the usual subgame-perfect criterionfor equilibrium: for every channel structure andwhole-sale price(s) (when chosen), retail prices must be inequilibrium; for every channel structure, wholesaleprice(s) (when chosen) must be in equilibrium antic-ipating the equilibrium retail prices to follow; finally,the channel structure must be in equilibrium anticipat-ing the equilibriumwholesale (when chosen) and retailprices to follow (McGuire and Staelin 1983, Moorthy1988). Besides these standard requirements, we imposetwo additional conditions dictated by our unique set-ting. First, we require that competitor-outlet distribu-tion not make the competitor worse off. This simplyrecognizes that distributing through the competitor’sstores requires the competitor’s cooperation; a com-petitor would never allow another brand into its storesif its profit declined as a result. Second, we require thatany equilibrium involving hybrid strategies must makethe manufacturer(s) pursuing such a strategy strictlybetter off than the status quo. This simply recognizesthat complexity has its costs—even though we do notmodel it explicitly. In the real world, it would be hard tojustify adding an additional distribution channel with-out showing a profit improvement.On the demand side, we have a unit mass of con-

sumers, each of whom demands D(p) units of oneproduct (either brand A or brand B); D( · ) satisfiesstandard properties: D(p) > 0, D′(p) < 0 for p < v̄ <∞;D(p) ≡ 0 for p ≥ v̄. Consumers differ in their brandpreferences: a fraction α will consider brand A only,a fraction β will consider brand B only, and a frac-tion γ � 1 − α − β will consider both, being indiffer-ent between the two. Consumers in the first (respec-tively, second) group will buy brand A (respectively, B)as long as its price does not exceed v̄, whereasconsumers in the third group will buy whicheverbrand is cheaper. This way of representing consumers’brand preferences has a long history in marketing(Narasimhan 1988, Simester 1997, Lal and Villas-Boas1996, and Chen et al. 2001). In this literature, thefirst group would be called brand-A loyalists, the sec-ond group would be called brand-B loyalists, and thethird group would be called switchers.Wewill examine two variants of thismodel: onewith

symmetric brands, α � β � (1 − γ)/2 ∈ (0, 1/2), in Sec-tion 4, and the other with asymmetric brands, 0 < α <β < 1− γ ∈ (0, 1), in Section 5. To facilitate the compar-ison between the two, we will fix γ, and work withα′ and β′, the fractions of A- and B-loyals within thepopulation of loyalists, i.e.,

α′ � α/(1− γ), β′ � β/(1− γ), α′+ β′ � 1.

In the symmetric model, α′ � β′ � 1/2; in the asymmet-ric model, 0 < α′ < 1/2 < β′ < 1.Up to now our demand side has been more or less

standard. Now we come to the novelties. We assume

that shopping is costly: it takes a cost t > 0 to visit astore.7 One store visit costs t, two store visits cost 2t,and so on. Furthermore, consumers differ in thesecosts: t has a distribution function H( · ) on [0, θ], θ > 0,with H(0) � 0, H(θ) � 1, and H′(0) � 0. This model ofshopping costs may be seen as a reduced form of thewell-known Hotelling model—instead of distinguish-ing between consumers’ geographical locations x (typi-cally assumed to be distributed uniformly on [0, 1]) andunit transportation costs c (typically assumed to be thesame across consumers), we are simply amalgamatingthe two into t � cx. However, there are some key dif-ferences. In the standard Hotelling model, transporta-tion costs simply represent the costs of procuring aproduct with known characteristics. The procurementangle applies here, too, but our shopping costs do dou-ble duty, serving as search costs as well, as discussedbelow.

All consumers know the distribution structure of themarket, i.e., they knowwhether they are in Case 1, 2, 2′,or 3. However, they need to search, by visiting stores,to find out the retail prices. In addition, some of themneed to visit stores to learn their brand preferences—whether they are brand-A loyalists, brand-B loyalists,or switchers. Denote by λ the fraction of consumerswho need to learn their brand preferences by visit-ing stores; we will refer to them as “uncertain con-sumers.” The remaining fraction, 1 − λ, know theirbrand preferences even before they begin shopping,i.e., these people do not need to visit a store to findout whether they are brand-A loyalists, brand-B loy-alists, or switchers. We call them knowledgeable con-sumers. Other than this difference, knowledgeable anduncertain consumers are alike; in both groups, frac-tions α and β of them are brand-A and brand-B loy-alists, respectively, and the remaining are switchers.In particular, retailers cannot tell them apart; so theycannot price discriminate between knowledgeable anduncertain consumers.

The brand-preference learning process for uncer-tain consumers is conceptualized as follows. First, weassume that examining both brands is necessary to dis-cover brand preferences. Second, we assume that alluncertain consumers who begin the brand-preferencelearning process complete it, regardless of the pricesthey find along the way. Implicit in the first assump-tion is the idea that brands are uncorrelated: learn-ing about one does not provide information about theother.8 The second assumption decouples the brand-preference learning process from the price learningprocess. It amounts to saying that knowing whetherone is a brand-A loyalist, brand-B loyalist, or a switcher,is sufficiently important to these uncertain shoppersthat they will want to resolve their uncertainty com-pletely, by visiting two stores if necessary, even if thefirst brand searched is available at an attractive price.9

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The price learning process is a sequential search pro-cess with a costly initial visit and costly recall (Bayeet al. 2006, Janssen andParakhonyak 2014). Consumers’search strategy—which store to visit first, and what todo next—is based on their knowledge of what brand(s)are sold in each store and their expectations of theretail prices, which, in the case of stores carrying decen-tralized brands, requires conjectures about wholesaleprices. In equilibrium, expected prices match actualprices.

We are now ready to lay down some notation anddefine the key parameters. Let

y(p)�∫ v̄

pD(x) dx

denote a consumer’s surplus after buying a brandpriced at p (t, the shopping cost does not figure in thiscalculation because it is sunk at this point). With priceexpectation pe , therefore, a consumer will go shoppingif and only if her shopping cost does not exceed y(pe).Note that y′(p)�−D(p) < 0.Consider first a decentralized bilateral monopoly.

Given a fixed endowment of consumers and a whole-sale price w, such a retailer would choose retail pricep(w) to solve

maxp(p −w)D(p), (1)

and the manufacturer, anticipating the retailer’s pric-ing decision, would choose w to solve

maxw

wD(p(w)). (2)

Assume these maximization problems are well be-haved and yield unique solutions, p(w) ≤ v̄ for w ≤ v̄,and wd ∈ (0, v̄). Define

pm�p(0), pd�p(wd), t(w)�y(p(w)), (3)tm�y(pm), td�y(pd), ti�tm−td , (4)

Hm�H(tm), Hd�H(td), Hi�H(ti), (5)

πm�pm D(pm), πw(p)�(p−w)D(p), δd�wd D(pd)πm

. (6)

Absent shopping considerations, a vertically inte-grated firmwouldmaximize pD(p), the “channel profitfunction,” which would result in pm as the optimalretail price, and πm as its profit. In a decentralizedbilateral monopoly, by contrast, the manufacturer’soptimal wholesale price would be wd , the retailer’soptimal retail price would be pd , and their respec-tive profits would be wdD(pd) and πwd

(pd). Thus δd ,the fraction of vertically integrated profit a decentral-ized manufacturer realizes, is a measure of the double-marginalization distortion built into D.10Backing up to the shopping decision, tm (respec-

tively, td) is simply the shopping cost at which a con-sumer expecting pm (respectively, pd) is just indifferent

between shopping and not shopping. We will assumeθ > tm , so that, even in a vertically integrated channel,not all consumers would shop. Then our assumptionsimply 0 < td < tm < θ. Finally, the H function convertsmarginal shopping costs into fractions shopping.

We begin our analysis with a series of lemmas thatplay an important role in the sequel. The first of thesesays that in a decentralized bilateral monopoly, givenour regularity conditions, as the double-marginaliza-tion distortion approaches zero, retail price and con-sumer surplus approach their vertically integratedcounterparts.

Lemma 1. (δd→ 1)⇔ (pd→ pm)⇔ (td→ tm).The next two lemmas describe equilibrium retail and

wholesale prices (where applicable).

Lemma 2. In all distribution structures, equilibrium retailprices are pm for vertically integrated products and p(w) fordecentralized products with wholesale price w.

Lemma 2 is essentially a restatement of Diamond’s(1971) paradox, adapted to our context. The price equi-librium is unique and it involves monopoly pricing.The fact that the retailers are competing for switchers,and in some channel configurations for brand-loyalistsas well, and the fact that some consumers are search-ing for price only and others are searching for priceand brand preferences, makes no difference. The onlyadditional wrinkle is “category management” consid-erations within a multibrand store—how to optimallyprice the vertically integrated product vis-à-vis thedecentralized product. This decision bears on whetherswitchers will be induced to buy the store brand orthe competitor’s brand. The answer from Lemma 2is resoundingly clear: steer switchers to your ownbrand.11 The reason is, on the vertically integratedproduct, the retailer gets all of a maximized channelprofit; on the decentralized product, it gets only theretail share of a smaller channel profit.

Lemma 3. In all distribution structures with hybrid dis-tribution strategies, the equilibrium wholesale price throughthe competitor channel will be wd .

This lemma simply reflects the fact that consumers’shopping decisions are based on expected retail prices,hence expectedwholesale prices. Since actual wholesaleprices are not observed, the only wholesale price thatsatisfies rational expectations is the monopoly whole-sale price wd . Putting Lemmas 2 and 3 together, equi-librium retail prices of vertically integrated and decen-tralized products will be pm and pd , respectively.

3. The Benchmark Case: λ � 0It is useful to begin with an analysis of what wouldhappen in ourmodel if all consumers were knowledge-able about their brand preferences before shopping.

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Consider Case 1 first. By Lemma 2, all products arepriced at pm . Since tm is the consumer surplus corre-sponding to this price, all consumers with shoppingcosts t ≤ tm will shop. Among those shopping, brand-A loyalists will go straight to store A and buy theirfavorite brand there, brand-B loyalists will go straightto store B and buy their favorite brand there, andswitchers will divide themselves evenly between thetwo stores. Suppose manufacturer B considers deviat-ing to Case 2. Its wholesale price in the hybrid strat-egy will be wd > 0, and by Lemma 2, retail prices atstore A will be pm for brand A and pd > pm for brand B.Nobody will buy brand B at store A. So consumerswill behave exactly as in Case 1: brand-A loyalists willcontinue to buy brand A at store A, brand-B loyalistswill continue to buy brand B at store B, and switcherswill continue to divide themselves evenly between thetwo stores. There will be no change in the number ofshoppers, and manufacturer B will make exactly thesame profit as in Case 1. Similar arguments apply fordeviation to Case 2′, and to Case 3 (from Case 2 orCase 2′). Note that whether brands are symmetric orasymmetric has no bearing on these conclusions.

In other words, in none of the channel structuresdoes amanufacturer pursuing hybrid distribution ben-efit from such a strategy. Status quo, therefore, is theunique equilibrium.

Proposition 1. When all consumers are knowledgeable, sta-tus quo is the unique equilibrium.

The message from Proposition 1 is that it is impos-sible to improve on pure vertical integration in ourmodel when consumers are already knowledgeableabout their brand preferences before shopping. Sincethese consumers can one-stop shop even at a single-brand store, they have no use for a multibrand store.The presence of uncertain consumers is therefore nec-essary to motivate multibrand stores and hybrid distri-bution strategies.

4. Distribution Strategy When BrandsAre Symmetric

Our analysis of equilibriumdistribution strategieswithuncertain consumers is split into parts. In this section,we will examine the case of symmetric brands: α �

β � (1 − γ)/2. In Section 5, we will examine the caseof asymmetric brands: α , β. This separation is neces-sary because uncertain consumer behavior differs fun-damentally between the two cases; the case β � α+ ε isnot the same as α � β, no matter how small ε is.

In what follows, we will analyze the three genericdistribution structures in turn and then ask which ofthem prevails in equilibrium.

Case 1: Each Manufacturer Sells Only Through ItsOwn OutletsKnowledgeable consumers visit only one store andthe marginal knowledgeable shopper has a shoppingcost tm , as discussed in Section 3. Uncertain consumersneed two store visits to figure out their brand prefer-ences. Since both stores are single-brand stores, and thebrands are symmetric, it is immaterial which store theyvisit first. At the conclusion of the second store visit,they may discover either that they are done with shop-ping (because they are that store brand’s loyalists orswitchers) or that a third store visit is required (becausethey are the other store brand’s loyalists). Therefore,for an uncertain consumer with shopping cost t, theexpected surplus from shopping is

1+ γ2 (y(pm) − 2t)+

1− γ2 (y(pm) − 3t)

� tm −5− γ

2 t .

The marginal uncertain consumer indifferent betweenshopping and not shopping is therefore12

t1u �

25− γ tm . (7)

Note that t1u < tm : fewer uncertain consumers are

willing to shop than knowledgeable consumers. Thismakes sense because the shopping process is morearduous for the former. Let Hm denote H(tm) and H1

udenote H(t1

u); these are the proportions of knowledge-able and uncertain consumers who shop. Case 1 profitfor each manufacturer is therefore

π1∗j � (1/2)[(1− λ)Hm + λH1

u]πm , j � A,B. (8)

Case 2 (2′): Manufacturer B (A) Sells ThroughOwn and A’s (B’s) Outlets; Manufacturer A (B)Sells Only Through Its OutletsSince Cases 2 and 2′ aremirror images of each other, wewill only examine Case 2. As already discussed in Sec-tion 3, for knowledgeable consumers, nothing changesfrom Case 1 to Case 2. Uncertain consumers, however,behave differently. They first have to decidewhich storeto visit, the multibrand store A or the single-brandstore B. If the former, their brand-preference learningis over; however, depending on what is learned, a sec-ond store visit may still be called for. If they discoverthemselves to be brand-A loyalists or switchers, thenthe shopping process is definitely over. On the otherhand, if they discover themselves to be brand-B loyal-ists, then they have to decide whether to buy brand Bat store A or at store B, which depends on the price dif-ference pd − pm and their shopping cost (low shoppingcost consumers may go to store B while high shoppingcost consumers stay in store A). By contrast, if the firstvisit is to store B, then a visit to store A is required

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just to complete the brand preference learning process,after which the shopping process is the same as above.From this, it is immediate that visiting store A first domi-nates visiting store B first for all uncertain consumers.Uncertain consumers’ expected surplus from shop-

ping is therefore

1+γ2 (y(pm)− t)+

1−γ2 (max{y(pm)−2t , y(pd)− t}). (9)

Setting this equal to zero and solving for t yields themarginal uncertain shopper in Case 2

t2u � max

{2tm

3− γ ,1+ γ

2 tm +1− γ

2 td

}. (10)

Now,

2tm

3− γ ≤1+ γ

2 tm +1− γ

2 td ⇐⇒td

tm≥

1− γ3− γ . (11)

Therefore,

t2u�

1+γ

2 tm+1−γ

2 td iftd

tm≥

1−γ3−γ

2tm

3−γ iftd

tm<

1−γ3−γ .

(12)

So, depending on whether td/tm ≥ (1 − γ)/(3 − γ)or not, uncertain consumers’ shopping behavior lookslike Figure 2(a) or 2(b). In either case, all uncertainshoppers visit store A first, and if they discover them-selves to be brand-A loyalists or switchers, then theybuy brand A and they are done. It is the shoppingbehavior of uncertain shoppers who discover them-selves to be brand-B loyalists that distinguishes the twofigures. When td/tm ≥ (1 − γ)/(3 − γ), some of theseconsumers—those with t < ti—choose to buy brand Bat store B, while others—those with t ≥ ti—choose tobuy brand B at store A itself. On the other hand, whentd/tm < (1−γ)/(3−γ), then all of these shoppers chooseto buy brand B at store B—a case of “pure showroom-ing”: store A carries brand B but does not sell any of it!Why would store A carry a brand on which it has nosales? This is related to the broader question ofwhethermanufacturer A benefits from having brand B in itsstores.

Should Manufacturer A Accept Brand BInto Its Stores?With respect to knowledgeable consumers, it is obviousthat it makes no difference; nothing changes for theseconsumers between Cases 1 and 2. So it comes downto uncertain consumers. Lemma 4 is key.

Lemma 4. t2u > t1

u .

More uncertain consumers shop in Case 2 than inCase 1, because in Case 2 there is a multibrand store,whereas in Case 1 both stores are single-brand stores.Having amultibrand store allows uncertain consumersto figure out their brand preferences in one store visitinstead of two. Greater shopping efficiency translatesto more shopping. For manufacturer A, the owner ofthe only multibrand store in Case 2, this provides adirect benefit in terms of more brand-A loyalist sales.Yet there is an additional knock-on benefit. Brand Anow captures all uncertain switchers versus only halfof them in Case 1. Together, these two benefits are enoughto justify accepting brand B into its stores even if consumersdo not actually buy brand B there (as in Figure 2(b)). Tothe extent there are sales of brand B in store A, as inFigure 2(a), that is just additional gravy. In otherwords,it makes sense for manufacturer A to carry brand B inits stores.Lemma 5. Each manufacturer would be willing to acceptthe competitor’s brand into its stores. The hybrid strategies inCases 2 and 2′ are therefore feasible deviations from Case 1.Lemma 5 speaks to how two lay intuitions about

competition and showrooming may go astray. One isthe common idea that more competition cannot be agood thing for the store’s own brand. This intuitionis based on the assumption that switchers will moveto the competitor’s brand when given the opportunityto do so. As our analysis reveals, however, it does notnecessarily have to happen this way; it is the storethat manages the competition between the store brandand the competitor’s brand—via retail pricing. Thoseprices can be set to deliver switchers to the store brand(Lemma 2). And it makes sense to do so because onthe store brand the retailer captures all of the verticallyintegrated channel profit stream, whereas on the com-petitor’s brand it captures only a fraction of the smallerdecentralized channel profit stream.

The second intuition that Lemma 5 casts doubt onis the idea that showrooming cannot be a good thingfor the stores subject to it. Yes, it is correct to say thatif consumers use a store only as a showroom and buynothing from it—in the short-term or in the long-term—then it is not a good thing for the store. Yet that is notwhat is happening in our model. It is the prospect ofusing a multibrand store as a one-stop showroom thatinduces all uncertain consumers to stop there first, andencourages more of them to shop. A larger propor-tion of these consumers—(1+γ)/2—end up buying thestore brand than the competitor’s brand. Even thosewho end up buying the competitor’s brand bring rev-enue to the store, either directly, via the profit stream(pd−wd)D(pd) (as in Figure 2(a)) or, indirectly, by boost-ing the number of uncertain consumers who shop (asin Figure 2(b)). In the latter case, the mere presence ofthe competitor’s brand boosts the number of uncertainconsumers shopping at the store from t1

u/2 to t2u .

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Figure 2. Shopping Behavior of Uncertain Brand-B Loyalists After Visiting Store A in Case 2

0 ti tu2 �

0 titu2tu

1 �

Buy brand B in store B Buy brand B in store A

(a) When td/tm ≥ (1 − �)/(3 − �)

Buy brand B in store B

(b) When td/tm < (1 − �)/(3 − �)

Will Manufacturer B Go Through Brand A’s Stores?Using (11), manufacturer B’s profits in Case 2 is,

π2∗B �

[1−λ

2 Hm +λ2 (1−γ)min{Hi ,H

2u}

]πm

+λ2 (1−γ)[max{0,H2

u −Hi}]wdD(pd)

�

[1−λ

2 Hm +λ2 (1−γ)

· (min{Hi ,H2u}+ δd max{0,H2

u −Hi})]πm .

13 (13)

By contrast, manufacturer B’s profits in Case 1 is

π1∗B �

[1− λ

2 Hm +λ2 H1

u

]πm .

Therefore,

π2∗B −π1∗

B �λ2 H1

u

·[(1−γ)

(min{Hi ,H2

u}H1

u+δd

max{0,H2u−Hi}

H1u

)−1

]πm ,

and, given λ > 0,

π2∗B > π

1∗B ⇔ 1−γ >

H1u

min{H2u , δdH2

u + (1− δd)Hi}. (14)

As γ→ 1, the left-hand side of the inequality ap-proaches zero and the right-hand side approachesH( 12 tm)/[δdH(tm)+ (1− δd)H(ti)] > H( 12 tm)/H(tm) > 0.14Therefore, the inequality can never be satisfied as γ→1.In other words, as brand loyalty vanishes, neither man-ufacturer has an incentive to deviate unilaterally frompure vertical integration to hybrid distribution—eventhough doing so would increase the number of uncer-tain consumers shopping.15 The reason is, such a movestrengthens the competitor’s stores and brand at theexpense of the manufacturer’s own stores and brand.

All uncertain consumers stop at the competitor’s storefirst, which results in all uncertain switchers being lostto the competitor.

By contrast, as γ→ 0, the left-hand side of (14) ap-proaches 1. This seems to favor a deviation to hybriddistribution, but a conclusive verdict depends on thesize of the right-hand side. If td/tm < (1 − γ)/(3 − γ),then the right-hand side is H1

u/H2u , which is less than 1

per Lemma 4. For td/tm ≥ (1−γ)/(3−γ), the right-handside is H1

u/(δdH2u + (1 − δd)Hi), which is not obviously

less than 1 because ti may not be greater than t1u . For

td/tm ≤ (3−γ)/(5−γ), however, ti ≥ t1u and H1

u/(δdH2u +

(1 − δd)Hi) < 1. Therefore, for td/tm ≤ (3 − γ)/(5 − γ),as γ→ 0, manufacturer B will deviate to Case 2 fromCase 1. Finally, if td/tm > (3−γ)/(5−γ) and δd ≈ 1, thenthe right-hand side approximates H1

u/Hm < 1 andman-ufacturer B will deviate to Case 2 as γ→ 0.16 Therefore,we get the following:

Proposition 2. In the symmetric model, a manufacturerwill deviate from the status quo to hybrid distribution if andonly if λ > 0 and (14) is satisfied. His preference for hybriddistribution increases in λ and δd , but decreases in γ. Inparticular, if λ > 0 and(a) γ is large enough, then each manufacturer will prefer

the status quo;(b) γ is small enough, and either td/tm ≤ (3− γ)/(5− γ)

or δd ≈ 1, then each manufacturer will prefer to deviate tohybrid distribution.

How does augmenting own outlets with competitoroutlets help amanufacturer such as B? All of the value-add comes from expanding the market of uncertainshoppers. However, this is not an unalloyed blessing.Inequality (14) captures, and Figure 2(a) and 2(b) illus-trate, the central trade-offs. On the positive side, anyincrease in uncertain shoppers represents an increasein brand-B sales (via brand-B loyalists). Besides, whentd/tm < (1 − γ)/(3 − γ), each of these new consumersbrings the entire vertically integrated profit stream

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with her. On the negative side, there are two effects.One is a possible reduction in the number of consumersbuying brand B at store B. This happens when ti < t1

uin Figure 2(a), i.e., when td/tm > (3 − γ)/(5 − γ). Thisis a cannibalization effect: hybrid distribution causes theinefficient competitor-channel to cannibalize the effi-cient own-channel. The cannibalization effect is lessdamaging as δd → 1, i.e., as the efficiency of the com-petitor channel improves. The second negative effect ofhybrid distribution is the loss of uncertain switchers tobrand A: in Case 1, brand B was getting half of them; inCase 2 it is getting none. We call this the strengthening-the-competitor effect.17 Note that the improvement incompetitor fortunes is not the main concern here—B does not necessarily begrudge A’s good fortune.Rather, what is concerning about this effect is that someof these customers used to be B’s customers in Case 1.Both negative effects become larger, and the positiveeffect becomes smaller, as γ increases. Therefore, forlarge γ, deviating to hybrid distribution is not profitincreasing. On the other hand, a small γ increases thepositive effect, while reducing the negative effects—especially when coupled with δd close to one—therebyimproving the case for hybrid distribution. While thenumber of uncertain consumers, λ, does not figurein (14), it obviously plays a crucial role in justifying adeviation to hybrid distribution. In fact, both λ > 0 andγ < 1 are necessary to justify such a deviation.Note that under the conditions of Proposition 2(b)

not only does manufacturer B prefer Case 2, so doesmanufacturer A. In fact, Case 2 would not have beenfeasible without manufacturer A’s acquiescence. Itis not hard to see where the win-win comes from:both manufacturers benefit when more uncertain con-sumers shop.18 Roos et al. (2015, p. 1) provide empir-ical support for the win-win in their study of severalcelebrity news sites. They conclude that the “linking”and “excerpting” of competitors’ news stories “are ben-eficial to both the linking and linked sites, as well asconsumers.”

Case 3: Both Manufacturers Sell Through Own andCompetitor OutletsWhen a hybrid channel structure such as Case 2 orCase 2′ beats pure vertical integration, one mightbe tempted to conclude that the symmetric chan-nel structure—both firms pursuing hybrid distribution(Case 3)—would be the natural outcome of the game.However, this conclusion would be wrong. Case 3 can-not be an equilibrium distribution structure. The argu-ment is as follows. First, Cases 2, 2′, and 3 are all equiv-alent from knowledgeable consumers’ point of view.Second, all these cases result in the same number ofuncertain shoppers: t3

u � t2u � t2′

u . Third, the dividingline, ti , between loyalists who shop for their favoritebrand at the own store versus at the competitor’s store,

is also the same. What is different about Case 3 isuncertain shoppers’ first-visit behavior. In Case 3 theseconsumers divide themselves evenly between the twomultibrand stores whereas in Cases 2 and 2′ they all goto the sole multibrand store. This results in each brandgetting half of all uncertain switchers in Case 3, versusall going to brand A in Case 2 and all going to brand Bin Case 2′. Deviating from Case 2 (respectively, Case 2′)to Case 3 is therefore unprofitable for manufacturer A(respectively, B).

Proposition 3. Case 3 cannot be an equilibrium channelstructure, i.e., neither manufacturer would adopt a hybriddistribution strategy when its competitor already does so.

Proposition 3 offers a novel intuition for marketing.We noted earlier that competitor-outlet distribution inCases 2 and 2′ is driven by a “win-win”: both manufac-turers have a common interest in providing a one-stopcomparison shopping experience for uncertain con-sumers. Proposition 3 says that there are limits to howfar the win-win can go. The reason is, when a firm pur-sues a hybrid distribution strategy, it is simultaneouslystrengthening its competitor’s retail outlets and brand,while weakening its own.19 While it may pay one firmto do so, it does not pay both firms to do so. For exam-ple, in going from Case 1 to Case 2, manufacturer Bis increasing the fraction of uncertain consumers whobuy brand A (from (1/2)H1

u to ((1 + γ)/2)H2u). A move

bymanufacturer A to Case 3 would amount to “return-ing B’s favor.” Not only does manufacturer A have noincentive to do so, the preceding argument shows thatit actually has a disincentive. The bottom line is, hav-ing two multibrand outlets operating simultaneouslydoes not increase the number of uncertain consumersshopping, but it does nullify the competitive advan-tage a firm gets by operating the only multibrand storein town. A symmetric model does not necessarily leadto symmetric distribution strategies in equilibrium!

Putting Propositions 2 and 3 together, the followingproposition summarizes the equilibria in the symmet-ric model.

Proposition 4. In the symmetric model, the equilibriumchannel structure is either Case 1, or both Cases 2 and 2′, asper the conditions of Proposition 2.

5. Distribution Strategy When BrandsAre Asymmetric

The symmetric model is instructive in laying barethe fundamental incentives driving decisions to dis-tribute through competitor outlets, but its very sym-metry obviates answering some interesting managerialquestions. For instance, it cannot answer a basic ques-tion: Are some firms more likely to pursue competitor-outlet distribution than others? In this section, weexplore this issue. One manufacturer’s brand, say B,

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will be assumed to be stronger than the other; it willhave more loyal consumers: β > α > 0. This requiresγ < 1. To facilitate comparison with the symmetricmodel, we will fix γ and change β′ from β′ � 1/2 to1/2 < β′ < 1; correspondingly, α′ � 1 − β′ will changefrom 1/2 to 0 < α′ < 1/2. Now Cases 2 and 2′ will notbe mirror images of each other. To distinguish betweenthe two it will be useful to normalize the discus-sion in terms of whether the stronger brand (denotedby “S”) or the weaker brand (denoted by “W”) pursuescompetitor-outlet distribution. Some additional nota-tion will come in handy. Firm-specific quantities willhave the subscript S or W to identify the firm in ques-tion (corresponding quantities in the symmetric modelwill continue to use subscripts A and B). For quantitiescommon to both firms, the superscript “a” will identifythe asymmetric case; for instance, the marginal uncer-tain consumer in Case 2, denoted by t2

u in the sym-metric model, will be denoted by t2a

u in the asymmetricmodel.Much of the previous analysis goes through un-

changed. Retail prices continue to be pm and pd forthe vertically integrated and decentralized products,respectively, and the wholesale price for the latter isstill wd . The shopping behavior of knowledgeable con-sumers does not change. In fact, the only thing thatchanges is the behavior of uncertain consumers,mainlyin Case 1. Yet these changes do differentially affect theincentives to pursue hybrid distribution for manufac-turers S and W .

Case 1: Each Manufacturer Sells Only Through ItsOwn Retail OutletsWith symmetric brands, uncertain consumers were in-different between going to retailer A or to retailer Bfirst; with β′ > α′ > 0, it is optimal for them to go to retailerW first because there is a higher probability that theywill end up as brand-S loyalists than as brand-W loy-alists.20 After the second store visit, to store S, con-sumers who discover themselves to be brand-S loyal-ists or switchers will stay put; only those who discoverthemselves to be brand-W loyalists will return to storeW . Uncertain consumer shopping thus becomes moreefficient; expected consumer surplus from shoppinggoes up

(β′(1− γ)+ γ)(y(pm) − 2t)+ (α′(1− γ))(y(pm) − 3t)� tm − (α′(1− γ)+ 2)t ,

which implies

t1au �

tm

α′(1− γ)+ 2>

tm

(1/2)(1− γ)+ 2� t1

u .

As β′→ 1/2, t1au → 2tm/(5− γ) � t1

u ; there is continuitybetween the symmetric and asymmetric models with

respect to the number of uncertain consumers shop-ping. However, the same cannot be said for the shareof uncertain switchers each brand gets. In the symmet-ric model, each brand received an equal share of thoseswitchers; in the asymmetric model, brand S capturesall uncertain switchers—and this is true even if theasymmetry is arbitrarily small.

From this it is obvious that manufacturer S is betteroff than manufacturer W

π1∗S �

[(1−λ)

(β′(1−γ)+

γ

2

)Hm +λ(β′(1−γ)+γ)H1a

u

]πm

>

[(1−λ)

(α′(1−γ)+

γ

2

)Hm +λα′(1−γ)H1a

u

]πm

�π1∗W .

Note that limβ′↓1/2 π1∗S � π1∗

B + (λγ/2)(H1u)πm > π1∗

A −(λγ/2)(H1

u)πm � limβ′↓1/2 π1∗W .

Case 2: S Sells Through Own and W’s RetailOutlets; W Sells Only Through Its Own OutletsThis case remains substantially the same as in the sym-metric model. Uncertain consumers still want to visitthe multibrand store first and Figure 2(a) and 2(b) stilldescribe what happens next (replacing store A withstore W and brand B with brand S). The marginaluncertain shopper is given by

t2au �

(α′(1− γ)+ γ)tm + β′(1− γ)td

if td/tm ≥ β′(1− γ)/(1+ β′(1− γ)),

tm/(1+ β′(1− γ))if td/tm < β

′(1− γ)/(1+ β′(1− γ)),

(15)

and t1au < t2a

u .21 Finally, store W continues to welcomebrand S unconditionally.

Using (15), manufacturer S’s profit in Case 2 is

π2∗S �

[(1− λ)

(β′(1− γ)+

γ

2

)Hm + λβ′(1− γ)

· (min{Hi ,H2au }+ δd max{0,H2a

u −Hi})]πm .

Therefore,

π2∗S − π1∗

S

� λ(β′(1− γ)+ γ)H1au

[β′(1− γ)

β′(1− γ)+ γ

·(

min{Hi ,H2au }

H1au

+ δdmax{0, H2a

u −Hi}H1a

u

)− 1

]πm ,

and, given λ > 0,

π2∗S >π

1∗S

⇔β′(1−γ)

β′(1−γ)+γ >H1a

u

min{H2au ,δdH2a

u +(1−δd)Hi}. (16)

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This looks much the same as in the symmetricmodel, except the left-hand side of the inequality issmaller. Therefore, ceteris paribus, it is harder for manufac-turer S to justify deviating to hybrid distribution than it isfor either manufacturer to do so in the symmetric model. Thisis to be expected. When brands are asymmetric, uncer-tain consumers’ shopping in Case 1 are already moreefficient. Therefore, a multibrand store in Case 2 canonly increase the number of uncertain shoppers by somuch. Moreover, manufacturer S’s position in Case 1 isalready quite strong, as it captures all uncertain switch-ers. Moving to Case 2 only weakens manufacturer S’srelative position. In other words, the strengthening-the-competitor drawback of hybrid distribution loomslarger. Finally, the cannibalization effect is also morelikely; the td/tm-threshold that sets off cannibalizationis lower: (1+ α′(1− γ))/(2+ α′(1− γ)) < (3− γ)/(5− γ).

Case 2′: W Sells Through Own and S’s RetailOutlets; S Sells Only Through Its Own OutletsNow uncertain consumers want to visit store S first asit is the multibrand store. Figure 2(a) and 2(b) continueto describe what happens next if we replace brand Bwith brand W and brand A with brand S. Analogousto Case 2, the marginal uncertain shopper is given by

t2′au �

(β′(1− γ)+ γ)tm + α′(1− γ)td

if td/tm ≥ α′(1− γ)/(1+ α′(1− γ)),

tm/(1+ α′(1− γ))if td/tm < α

′(1− γ)/(1+ α′(1− γ)).

(17)

Note that

(β′(1−γ)+γ)tm+α′(1−γ)td>(α′(1−γ)+γ)tm+β

′(1−γ)td ,

tm

1+α′(1−γ) >tm

1+β′(1−γ) , andα′(1−γ)

1+α′(1−γ) <β′(1−γ)

1+β′(1−γ) .

Hence t2′au > t2a

u . The uncertain consumer market ex-pands evenmore when the weaker brand goes throughthe stronger brand’s store. The reasons are twofold.First, in the Figure 2(b) scenario, uncertain consumershopping is more efficient—there is a smaller proba-bility that a second store visit will be required. Second,in the Figure 2(a) scenario, where the marginal uncer-tain consumer is staying at the first store visited, theprobability of buying at pm instead of pd is higher.Man-ufacturer W ’s profit in Case 2′ is

π2′∗W �

[(1− λ)

(α′(1− γ)+

γ

2

)Hm + λα′(1− γ)

· (min{Hi ,H2′au }+ δd max{0,H2′a

u −Hi})]πm ,

and

π2′∗W − π1∗

W � λα′(1− γ)H1au

·[(

min{Hi ,H2′au }

H1au

+ δdmax{0, H2′a

u −Hi}H1a

u

)− 1

]πm .

Therefore, given λ > 0,

π2′∗W >π1∗

W ⇔ 1>H1a

u

min{H2′au , δdH2′a

u +(1−δd)Hi}. (18)

For td/tm ≤ (1 + α′(1 − γ))/(2 + α′(1 − γ)) or δd ≈ 1,the inequality is satisfied—regardless of γ. In Case 2,by contrast, we needed the auxiliary condition γ→ 0to justify hybrid distribution under the same circum-stances. The size of the switcher segment does notplay as big a role in the weaker brand’s justificationof hybrid distribution because uncertain switchers arelost either way; neither in Case 1 nor in Case 2′ cantheweaker brand obtain these consumers. (By contrast,in going from Case 1 to Case 2, the stronger brandwas losing all of the uncertain switchers.) Absent astrengthening-the-competitor loss, one of the down-sides of hybrid distribution is eliminated. A canni-balization effect can still occur when td/tm > (1 + α′ ·(1 − γ))/(2 + α′(1 − γ)) in Figure 2(a). Then ti < t1a

uand some efficient vertically integrated revenue (frombrand-W loyalists) is replaced by inefficient decentral-ized revenue. When δd ≈ 1, however, this effect is alsonullified, and only the expansion of the uncertain con-sumer market remains. Then the case for hybrid distri-bution by the weaker brand becomes unassailable.

Is the Stronger or the Weaker Brand More Likely toDeviate to Hybrid Distribution?Comparing (16) and (18), the left-hand side of (18) isbigger and the right-hand side is smaller. Therefore,the following proposition is immediate.

Proposition 5. Whenever the stronger brand is willing todeviate from the status quo to hybrid distribution, so will theweaker brand.

The implication of Proposition 5 is that the weakerbrand has a stronger case for hybrid distribution thanthe stronger brand. To understand why, recall that amove to hybrid distribution has advantages and disad-vantages for themanufacturer doing so. The advantageis the creation of amultibrand store,whichmakes shop-ping more efficient for uncertain consumers, encour-aging more of them to shop, netting additional brandloyalists in the process. The disadvantages have todo with possible “strengthening-the-competitor” and“cannibalization” effects. The competitor is strength-ened when uncertain switchers who were hithertopatronizing the manufacturer in question (at its ownstore) now switch to the competitor at its (the competi-tor’s) store. Cannibalization happens when uncertainbrand loyalists who were hitherto buying the manu-facturer’s brand in its own store, generating verticallyintegratedprofit streams, nowbuy it at the competitor’sstore, which nets only a part of an inefficient decentral-ized revenue stream.

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Simply put, the advantages are bigger, and the disad-vantages are either the same or smaller, when it is theweaker brand that initiates the move. On the positiveside, a multibrand store at the stronger brand’s loca-tion is a more powerful magnet for inducing uncertainconsumers to shop. On the negative side, first, thereis effectively no strengthening-the-competitor effectwhen the weaker brand deviates to hybrid distribu-tion, whereas it is at its highest when the strongerbrand deviates to hybrid distribution. Second, the can-nibalization effect is essentially a wash no matter whoinitiates hybrid distribution: in both cases the td/tm-threshold is the same.

Case 3: Both Manufacturers Sell Through Own andCompetitor OutletsCase 3 in the asymmetric model replicates Case 2′.All uncertain shoppers stop at the stronger brand’smultibrand store first, and all uncertain switchers buybrand S. Brand W ’s store is multibrand in name only;nobody buys brand S in W ’s store. In fact, nobody usesW ’s store even as a showroom for brand S—the onlyuncertain consumers visiting W ’s store are brand-Wloyalists. Manufacturer S is indifferent between Case 3and Case 2′, so Case 3 cannot arise in equilibrium.

6. RobustnessThe models examined so far succeed in demonstrat-ing three things. First, a hybrid distribution strategy ofdistributing through competitor’s outlets while main-taining own outlets can be justified on the basis of pro-viding for the different shopping needs of two typesof consumers—those who know what they want evenbefore they begin shopping and those that rely on theshopping process to inform themselves about brandpreferences. Second, while it may pay one manufac-turer to practice hybrid distribution for this reason,it does not pay for the other to follow suit—even ina perfectly symmetric model. Third, a manufacturerwith a weaker brand has more to gain from pursu-ing hybrid distribution than a manufacturer with astronger brand. In this section we discuss how robustthese findings are to alternative specifications of ourmodel.

Price EquilibriumOne thing that made our model tractable was the sim-ple characterization of equilibrium retail andwholesaleprices that it enabled (Lemmas 2 and 3). Specifically,by assuming that consumers had to search for pricessequentially, retail prices turned out to be monopolyprices (Stahl 1996). In fact, given H′(0)�0, this was theonly equilibrium possible. While assuming H′(0)> 0would allow other retail price equilibria to emerge,monopoly prices will continue to be one equilibrium.Moreover, any of the other equilibria—as long as prices

stay above marginal costs—will not change our conclu-sions. This is because our arguments about the valueof hybrid distribution do not depend on the absolutevalue of retail prices, and to the extent they depend onrelative retail prices, they do so onlyminimally, namely,that decentralized prices are higher than vertically inte-grated prices. For instance, it was this difference thatallowed us to assert that a switcher would favor thestore’s own brand over the competitor’s brand when astore carries both.

Decentralized product prices being higher than ver-tically integrated product prices is a robust conse-quence of double marginalization in a decentralizedchannel.22 Any model of retail price competition willdeliver that feature. And as long as it does, our argu-ments will go through. For instance, if we replace oursearch model for prices with advertised retail prices,the resulting equilibriumwill be amixed-strategy equi-librium as in Lal and Villas-Boas (1996). However, itwill still be the case that the distribution of prices ofthe vertically integrated product is first-order stochas-tically dominated by the distribution of prices of thedecentralized product, and the advantages and disad-vantages of hybrid distribution will remain.

Other Sources of Retailer DifferencesIn the real world, store-brand differences are not theonlydifferences that differentiate retailers. For instance,some retailers carry a small number of categories (e.g.,Barnes and Noble) while others carry many categories(e.g., Amazon.com). Some retailers are known for theirretailing expertise (e.g.,Macy’s)while others areknownfor theirmanufacturing expertise (e.g., Levi.com). Con-sumer choices about where to shop are guided by thesedifferences as well as the store-brand differences wehave chosen to focus on.What impactwould these otherdifferences have on our results?

It is instructive to ask this question in the context ofour symmetric model because in that model the storebrands are symmetric. Suppose retailer A is a strongerretailer than retailer B. Then even in Case 1, consumerswill not be indifferent between the two stores. Specif-ically, knowledgeable switchers will gravitate towardstore A, and even brand-B loyalists might do the sameif the model allowed for a trade-off between retailerpreferences and product-brand preferences. Further-more, uncertain consumers will want to finish theirbrand-preference-learning at A’s store. Together, allthese effects will give A an advantage over B even inCase 1. This will make it more likely that brand Bwould want to deviate to hybrid distribution ratherthan brand A. Instead of Cases 2 and 2′ being equallylikely, now Case 2 is more likely.

Now consider a situation where the brands are notsymmetric. If the stronger retailer also possesses thestronger store brand, our prediction in Proposition 5

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will be reinforced. On the other hand, if the strongerretailer possesses the weaker product brand, our pre-diction in Proposition 5might be reversed—for no faultof the proposition. An example of the former situationis our eReader example from Section 1. Here Amazon’sKindle is not only the stronger product brand, Ama-zon is also the stronger retailer. So it is not surprisingto see that Nook is sold at Barnes and Noble as wellas at Amazon, but Kindle is only sold at Amazon. Anexample of the latter situation occurs in the jeans cate-gory where Levi’s brand of jeans are sold at Levi.comas well as at Macy’s, but Alfani, Macy’s house brand, issold only at Macy’s. Here it is the stronger brand that isdoing hybrid distribution, not the weaker brand—theopposite of what our theory predicts. Yet it is easy torationalize why this is so: Macy’s is a much strongerretailer than Levi’s.Factors other than store brand that make one re-

tailer a more attractive shopping destination than theother introduce independent motivations for pursuingcompetitor-outlet distribution that operate on top ofour motivation. They may reinforce our motivation, orthey may fight it; but they do not negate it. As longas λ > 0, there will be consumers who prefer one-stopcomparison shopping, and there will be demand fora multibrand store. As long as this demand exists, amanufacturer will need to consider hybrid distributionin the way our theory suggests.

7. ConclusionIn this paperwehave examined a special formof decen-tralization, distribution through competitors’ outlets,and argued that it should be seen not as a decentraliza-tion strategy, but rather as a strategy to change the retail-ing format—from single-brand retailing to multibrandretailing. Multibrand retailing facilitates one-stop com-parison shopping, which benefits consumers uncertainabout their brand preferences, encouraging more ofthem to shop. This is beneficial not only to the manu-facturer seeking such distribution but also to the storereceiving the new brand—even if it ends up not sell-ing any of it. By supplementing own-outlet distribu-tionwith competitor-outlet distribution—whatwehavecalled hybrid distribution—a manufacturer can com-bine the efficiency advantages of own-outlet distribu-tion with the one-stop comparison shopping advan-tages of competitor-outlet distribution, targeting eachto a different type of consumer—those who know theirbrand preferences versus those who do not know theirbrand preferences.However,despite its appeal, hybriddistribution isnot

a panacea. In fact, in our model only one of the manu-facturers chooses to do so in equilibrium. The reason is,hybrid distribution, while providing one-stop compar-ison shopping opportunities to uncertain consumers,also strengthens the competitor’s outlets, which has the

effect of driving switchers to the competitor’s brand.From the competitor’s point of view, therefore, recipro-cating hybrid distribution would amount to nullifyingits competitive advantage.

What sort of manufacturer is likely to pursue hybriddistribution? Within the parameters of our model, amanufacturer with a weaker brand has a stronger casefor doing so than a manufacturer with a strongerbrand. Of course, as we discussed in Section 6, this con-clusion needs to be tempered by the limitations of ourmodel in which store patronage is solely a function ofthe number, and strengths, of the brand(s) it carries ina given category. A more general model in which storechoice is also a function of other attributes, such asthe number of product categories carried or quality ofservice provided, could overturn these prescriptions.Nevertheless, a central message of this paper is likely toendure. A manufacturer with a strong brand can lever-age its strength into retailing by opening stores, whichhave the potential of turning into one-stop compar-ison shopping destinations when competing brandsdistribute through them, making them stronger still.

AcknowledgmentsThe authors thank the associate editor and the entire reviewteam for their comments, criticisms, and suggestions. ScottFay, Michael Gordy, Ravi Jain, Sandeep Juneja, Tanjim Hos-sain, Nitin Mehta, Andrew Rhodes, and participants at theUTDallas FORMS Conference in 2015 and theMarketing Sci-ence Conference in 2013 also provided useful commentary.

AppendixProof of Lemma 1δd � wd D(pd)/pm D(pm) and wd D(pd) ≤ pd D(pd) ≤ pm D(pm).Therefore, if δd→1, wd D(pd)→pm D(pm) and hence pd D(pd)→pm D(pm). Since pD(p) has a unique maximizer in pm , thelemma follows. �

Proof of Lemma 2Consider Case 1 first. If all consumers are knowledgeable,this is a straightforward sequential price-search model, withonly switchers searching. Clearly, both manufacturers charg-ing pm , consumers expecting that, and consumers with t ≤ tmshopping one store and no further, is an equilibrium. Withuncertain consumers in the mix, the argument is slightlymore complicated. These consumers make two store visitsjust to discover their brand preferences. This presents anopportunity for either manufacturer to show a price lowerthan pm to switchers who visit its store first in the hope of lur-ing some of them back after their second store visit. However,because H′(0)� 0� H(0), the gain in revenue from additionalswitchers is exactly balanced by the loss in revenue fromthe lower price;23 then, considering the loss in revenue fromknowledgeable consumers, uncertain loyalists, and uncertainswitchers whose second store visit is to “this” store, lower-ing price below pm is strictly worse. Is there another equi-librium? Since H′(0) � 0 � H(0), Proposition 4.4(a) of Stahl(1996) assures that there is not. The basic argument is thatany candidate equilibrium with prices below the monopolyprice is susceptible to revenue-increasing price increases.

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In Case 2, both brands are sold in store A, and brand Bis sold in store B. Within store A, given a wholesale pricew > 0 for brand B, retailer A’s profit function per unit of storetraffic is {

(α+ γ)π(pA)+ βπw(pB) if pA ≤ pB ,

απ(pA)+ (β+ γ)πw(pB) if pA > pB .(A.1)

Since π( · ) is maximized by pm and πw( · ) by p(w), and pm <p(w) for w > 0, only the first case of (A.1) obtains: all switch-ers in store A buy brand A. Hence, retailer A charging pm andp(w) for brands A and B, retailer B charging pm for brand B,and consumers expecting those prices is a retail price equi-librium, for essentially the same reasons as in Case 1. Thekey difference is that in Case 2 all uncertain consumers visitstore A first. This presents an opportunity for store A to lowerbrand-B’s price below p(w) to induce more brand-B loyal-ists to purchase brand B in store A. However, the revenuegains from thismaneuver are exactly balanced by the revenuelosses, for the reason explicated in endnote 23. The argumentfor uniqueness also replicates. Finally, Case 3 follows analo-gously. �

Proof of Lemma 4It is straightforward that t1

u � 2tm/(5 − γ) < 2tm/(3 − γ) � t2u

when td/tm < (1 − γ)/(3 − γ). When td/tm ≥ (1 − γ)/(3 − γ),then t2

u � tm(1+ γ)/2+ td(1− γ)/2. Then t2u − t1

u � (1/2)[tm(1+4γ − γ2)/(5− γ)+ td(1− γ)]. The numerator of the first termis positive for γ ∈ [0, 1], which finishes the proof. �

Endnotes1When we say “single-brand” and “multibrand” retailing, we meansingle-brand and multiple-brand retailing within a category. A single-brand retailer in our terminology may carry several brands acrosscategories. For example, Aldi is a retailer with (generally) one brandin each category—its private label. However, that brand happens tobe called Crofton in kitchenware and Sea Queen in frozen shrimp.2 In other words, the model has been designed to suppress the tra-ditional strategic motivation for decentralization—the second forcediscussed in the opening paragraph.3Some recent work deviates from this stark paradigm. Gu and Liu(2013) examine how shopping behavior within a store affects retail-ers’ shelf layouts, and Iyer and Kuksov (2012) study the optimumretail investment in shopping experiences—things like music, light-ing, and ambience. By contrast, the focus of our inquiry is manufac-turers’ distribution strategies, and we consider consumers’ shoppingbehavior both within and across stores; our shopping experiences—one-stop versus multistop shopping—are the endogenous result ofmanufacturers’ distribution decisions, not retailers’ manufacturer-independent decisions.4One can imagine an additional strategic option: closing one’s ownoutlets and distributing through the competitor’s outlets exclusively.However, as we note in endnote 13, such a strategy is dominated bythe hybrid strategy.5Multibrand retailing is necessarily two-brand retailing in our two-manufacturer model. However, our arguments extend easily to n > 2manufacturers.6We will insist, however, that a more complex distribution systemjustify its complexity. More on this in Section 2.7Wedo not take a position onwhether the stores are online or offline.That is, we are assuming that even online shopping is costly—if not indistance traveled, then at least in time. In online shopping, “visitingstores” should be interpreted as “visiting retailer websites.”

8 In an earlier version of this paper, we assumed otherwise—thatexamining one brand was enough to learn about the other. Theadvantage of this formulation is that it makes the price-learningprocess identical between knowledgeable and uncertain consumers.However, the main results do not change qualitatively.9An integrated model of brand-preference learning and price learn-ing would allow the two searches to be aborted midway based onwhatever is learned up to that point (Wolinsky 1986, Anderson andRenault 1999). For instance, after examining a brand in a store, a con-sumer may discover that (a) she has a high reservation price for it,and (b) it is priced low. She may then be tempted to take the “birdin hand” and forgo the opportunity to learn about her reservationprice for the other brand or its price. To assess the costs and benefitsof doing so, the consumer must have priors on her reservation pricefor the other brand. Our maintained assumption amounts to sayingthat those priors are sufficiently optimistic that complete learning ofbrand preferences is always warranted.10 If two-part tariffs were practicable—they generally are not (Iyerand Villas-Boas 2003)—then even a bilateral monopoly would oper-ate efficiently (Moorthy 1987), and there would be no point in treat-ing pure vertical integration as the status quo. A single multibrandstorewould be optimal—even in the absence of uncertain consumers;see Proposition 1.11This pricing strategy is often referred to as “shielding” the private-label brand (Quelch and Harding 1996, p. 100).12Throughout the paper, superscripts refer to the cases, small lettersubscripts identify consumer type (e.g., uncertain consumers), andcapital-letter subscripts identify the firms.13This expression makes clear why going through competitors’ out-lets exclusively, without own outlets, is dominated by the hybridstrategy. The first term becomes (1 − γ)δd Hdπm/2, the second termdisappears, and the third term becomes (λ/2)(1 − γ)δd H2

uπm . Fig-ure 2(b) disappears and in Figure 2(a) all brand-B loyalists buy brandB at store A. Finally, the number of uncertain consumers shopping issmaller whenever td/tm < (1− γ)/(3− γ).13This expression makes clear why going through competitors’ out-lets exclusively, without own outlets, is dominated by the hybridstrategy. The first term becomes (1 − γ)δd Hdπm/2, the second termdisappears, and the third term becomes (λ/2)(1 − γ)δd H2

uπm . Fig-ure 2(b) disappears and in Figure 2(a) all brand-B loyalists buy brandB at store A. Finally, the number of uncertain consumers shopping issmaller whenever td/tm < (1− γ)/(3− γ).14To see this, note first that as γ→ 1, t1

u→ 12 tm and t2

u→ 12 (1+ γ)tm +

12 (1− γ)td (because the upper condition governs in (12)). Second, asγ→ 1, ( 1

2 (1+ γ))tm + ( 12 (1− γ))td→ tm .

15This may explain the growing success of nearly-100% private-labelgrocery stores such as Aldi and Trader Joe’s. Their success coin-cides with the decreasing brand loyalty of consumers in the low-involvement categories grocery stores typically carry.16To see this, note that for δd ≈ 1, td ≈ tm (per Lemma 1), hencet2

u �12 tm(1+ γ)+ 1

2 td(1− γ) ≈ tm , ti ≈ 0, and H1u/(δd H2

u + (1− δd)Hi) ≈H1

u/Hm < 1.17Examples of both effects are seen in the results reported by Atheyand Mobius (2012) based on their study of browsing behavior on thenews aggregator site Google News.18This argument also shows that if two-part tariffs were practica-ble, then the optimal channel structure would degenerate to a singlemultibrand store, either A or B; both manufacturers would willinglyabandon their own stores in favor of going through their competitor’sstore. The reason is, two-part tariffs enable w � 0 in the competitorchannel, which results in pd � pm , td � tm , and t2

u � tm—making theuncertain shopper market the largest it can be. Moreover, half of theuncertain switchers buy the competitor’s brand in the multibrandstore. Each manufacturer gets half of the channel profits, just as in

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Case 1, but the channel profits are larger with the expansion of theuncertain consumer market.19As Manjoo (2015) notes, “The modern Microsoft breaks all theserules: its Surface devices compete with PCs made by other Windowshardwaremakers. Its non-Windows applications, like the iOS versionof Office, improve the Apple devices that compete withMicrosoft andits Windows hardware makers.” (Emphasis added.)20 In previous versions of this paper we assumed that a single storevisit was enough to learn brand preferences. Then, in Case 1 of theasymmetric model, it was optimal to visit the stronger store first.However, despite this difference, the subsequent results remainedsubstantially the same.21To see this, note that tm/(1 + β′(1 − γ)) > tm/(2 + α′(1 − γ)) � t1a

ualways. For td/tm < β′(1 − γ)/(1 + β′(1 − γ)), therefore, the state-ment is true. For td/tm ≥ β′(1 − γ)/(1 + β′(1 − γ)), also, since t2a

u �

(α′(1−γ)+γ)tm +β′(1−γ)td ≥ tm/(1+β′(1−γ)), the statement is true.22Of course, double marginalization could be eliminated with two-part tariffs (Moorthy 1987). However, that would make the case forcompetitor-outlet distribution overwhelming. As we noted in end-note 18 it would then be a dominant strategy for both manufacturersto distribute through a single multibrand store.23 If p is the lower price shown to these switchers, the fraction luredback is some portion of λγH(pm − p), yielding additional revenuesproportional to pD(p)H(pm − p). The derivative of this with respectto p at pm is exactly zero.

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