Slotting Allowances and Conditional Payments

Transcription

1 Slotting Allowances and onditional Payments Patrick Rey Jeanine Thal Thibaud Vergé ay 2005 Abstract We analyze the competitive effects of upfront payments made by manufacturers to retailers in a contracting situation where rival retailers offer contracts to a single manufacturer. As Bernheim & Whinston (1998), who look at a situation in which competing manufacturers offer contracts to a single retailer, we find that the resulting equilibrium outcome maximizes industry profits. Yet, while non-contingent two-part tariffs suffice to implement the monopoly outcome in the situation considered by Bernheim & Whinston, more complex contracts are required here to eliminate all contracting externalities from common agency. Two-part tariffs that are contingent on common agency versus exclusivity may for example yield common agency but can never sustain the monopoly outcome. Once upfront slotting allowances are added, however, the monopoly outcome can be restored. This suggests that slotting allowances, as widely observed in the contracts between manufacturers and large distributors, may be detrimental to consumer and total welfare. keywords: vertical contracts, slotting allowances, buyer power, common agency JEL classification codes: L14, L42 University of Toulouse (IDEI and Gremaq), prey@cict.fr University of Toulouse (Gremaq), JeanineThal@gmail.com University of Southampton, T.Verge@soton.ac.uk 1

2 1 Introduction In recent years, payments made by manufacturers to retailers have triggeredheateddebates. 1 Especially when dealing with supermarket chains, manufacturers often make upfront payments at the time when a supply contract is signed, or at the beginning of each year. Examples include listing fees that must be paid to become or remain a potential supplier, and slotting allowances or pay-to-stay fees that are required for accessing the retailer s shelf. The economic literature on slotting allowances has first focused on the manufacturers incentives to propose such payments. Large manufacturers might for example use slotting allowances to exclude smaller competitors from scarce shelf space, 2 or to dampen retail competition. 3 Yet, in the grocery industry, for example, the general perception is that bargaining power has shifter towards large multiples in recent years. 4 When dealing with smaller manufacturers, multiples often account for a high share of the manufacturer s total production. While large manufacturers certainly continue to possess a strong bargaining position when it comes to some must-stock brands, this strength does not necessarily carry over to other goods, since negotiations mostly take place on a product-by-product basis. 5 Interestingly, real-world evidence indicates that both the incidence and the magnitude of slotting allowances are associated with the exercise of retail bargaining power. 6 To capture this, arx & Shaffer (2004) consider a model of vertical negotiations where retailers have the initiative and the bargaining power and show in that context that strong retailers can use upfront payments to exclude other retailers. Their analysis relies on the use of three-part tariffs, which include upfront payments such as slotting allowances, paid by the manufacturer even if the retailer does not buy anything afterwards, and conditional fixed fees, paid by 1 See for example the 2001 FT staff report "Report of the Federal Trade ommission Workshop on Slotting Allowances and Other arketing Practices in the Grocery Industry" or the 2000 Office of Fair Trading "Supermarket Report". 2 Bloom et al. (2000), for example, argue that a large manufacturer can offer a large slotting allowance to the retailer, expecting to recover it later through the wholesale margin. Smaller manufacturers will be unable to match such offers if their pockets are not deep enough. This argument has been formalized by Shaffer (2004). 3 Shaffer (1991) shows even manufacturers that are perfectly competitive can dampen retail competition by offering wholesale prices above marginal cost, and compensate retailers by means of slotting allowances. 4 See Inderst & Wey (2004) for a more evidence on the retailers growing bargaining power in diferrent secotrs both in Europe and in the US. 5 See the OFT supermarket report. 6 See e.g. the 2001 FT staff report. 2

3 the retailer only if it actually buys from the manufacturer. Building on their analysis, we find that retailers may use slotting allowances and conditional fixed fees to achieve monopoly profits in a common agency situation, i.e. when distributing the good of a common supplier. ore precisely, we consider the role of conditional fixed fees and upfront payments in determining (i) whether exclusion is a profitable strategy for a retailer, and (ii) the levels of prices in a common agency situation. As in arx & Shaffer (2004), we suppose that two rival retailers offer public take-it-or-leave-it contracts to a single manufacturer; however, we allow contracts to be contingent on exclusive dealing. This assumption reflects the idea that firms would renegotiate (non-contingent) contracts if the market configuration did not turn out to be as expected. We find that each retailer s profit is bounded above by its contribution to industry profits, and that this leads the retailers to select the industry structure (exclusive dealing or common supplier) and the prices that maximize industry profits. Westressfurthermore thatstandardtwo-part tariffs, consisting of an upfront payment and a wholesale price, cannot yield monopoly common agency profits. First, maintaining monopoly retail prices requires wholesale prices above marginal costs, to compensate for the competitive pressure on retail margins. At these wholesale prices, however, each vertical pair has an incentive to free-ride on the rival retailer s revenue by reducing its own price. Second, since this free-riding reduces the profits that can be achieved in a common agency situation, common agency may fail to arise in equilibrium. onditioning fixed fees on actual trade protects retailers, however, and may reestablish the existence of common agency. And indeed, when combined with upfront payments by the manufacturer, conditional fixed fees always allow the retailers to preserve common agency and achieve the integrated monopoly profits: conditional payments equal to retailers anticipated (variable) profits serve as a commitment to monopoly prices, and upfront payments by the manufacturer can then be used to give ex ante each retailer its full contribution to the industry profits. Thus, when combined with conditional fixed fees, upfront payment do not lead to exclusion. Yet, they are still potentially detrimental for welfare, since they eliminate all retail competition. Incidentally, our analysis confirms the observation that slotting allowances are associated with retail bargaining power. While in our model retailers obviously want to use three-part tariffs whenever permitted, the integrated monopoly outcome could be achieved without slotting allowances were bargaining power upstream; standard two-part tariffs would suffice. Once retailers have the bargaining power, however, up- 3

4 front payments are necessary to maintain monopoly prices. Our paper is also related to the literature on exclusive versus common dealing. ost of this literature assumes upstream bargaining power and examines whether a manufacturer can profitably exclude a rival from distribution. Bernheim & Whinston (1998) stress that, because of the compensation required by a monopoly retailer, exclusion cannot occur in the absence of any contracting externalities, unless even an integrated monopolist would only distribute one product; thus, common agency arises as long as it is efficient, and standard (non-contingent) two-part tariffs suffice to achieve it. ontracting externalities can arise, for example, from a restriction on the contracts allowed, 7 or can affect third parties not present at the contracting stage. 8 The remainder of this paper is organized as follows. Section 2 outlines the general framework. Section 3 derives upper bounds on retailers rents, which will serve as benchmarks in the following analysis. Sections 4to6considerdifferent classes of contracts: classic two-part tariffs with an upfront fixed fee, two-part tariffs with a conditional fixed fee, and finally three-part tariffs combining upfront and a conditional fixed payments. Section 7 discusses the policy implications of our findings. The final section concludes. 2 Framework Two differentiated retailers, R 1 and R 2, distribute the product of a manufacturer. The manufacturer produces at constant marginal cost c, while retailers incur no additional distribution costs. Retailers have all the bargaining power in their bilateral relations with the manufacturer; their interaction is therefore modelled as a three-stage game, where at stage 1, R 1 and R 2 simultaneously make take-it-or-leave-it offers to. Offers can be contingent on the exclusivity of. At stage 2, decides whether to accept both, only one, or none of the offers; all offers and acceptance decisions are public. At stage 3, the retailer(s) with accepted contracts decide how much to purchase, pay the manufacturer accordingtothecontractssigned,andfinally compete with each other. R i s revenue, as a function of the quantities bought, is given by R i (q i,q i ), 9 which we assume to be twice differentiable. 7 athewson & Winter (1987) consider a restriction to linear prices. 8 For example, an incumbent manufacturer can sometimes profitably prevent efficient entry; see Aghion and Bolton (1987), Rasmusen et al.(1991) and Segal & Whinston (2000). 9 Throughout the paper, we will use the notation i to refer to the rival retailer. Note also that the general formulation of the revenue function used here allows for the possibility that a retailer does not resell all units. Essentially, retailers order quantities, which determine their capacities, before competing for consumers 4

5 Total industry profits are thus Π(q 1,q 2 ) X i=1,2 R i (q i,q i ) cq i. A fully integrated firm would optimally produce and sell (q 1,q 2 ) arg max (q 1,q 2 ) 0 Π(q 1,q 2 ), which we assume to be unique and strictly positive. The corresponding industry profits are denoted by Π. Were only product i available, a vertically integrated firm would choose q m i arg max q i 0 R i(q i, 0) cq i, earning total profits of Π m i. We make the following assumptions about revenues and profits. First, the two retailers are imperfect substitutes for consumers: that is, R i q i (q i,q i ) < 0 when q i > 0 and Π m 1 + Π m 2 > Π > Π m 1. Second, without loss of generality, R 1 on its own is at least as profitable as R 2 : Π m 1 Π m 2. At this point, let us discuss the main assumptions underlying our model. First, we have assumed that contract offers are public; however, this is not crucial. In fact, it is sufficient that acceptance decisions are ex post observable before the retailers compete at stage 3. Since the monopoly manufacturer observes both offers at stage 1, no problem of opportunism arises even when the retailers cannot observe contracts at this stage. Second, as will become clear later on, it is also not crucial that retail competition takes place in quantities. A key assumption, on the other hand, is that retailers are allowed to condition their contract terms upon the market configuration (i.e., common sales agency versus exclusivity). We believe that this is a reasonable "short-cut" for describing a more realistic dynamic negotiation framework, where refusal to deal would trigger renegotiation. A manufacturer s decision to reject one retailer is an important and observable change in market environment. oreover, the appropriate contract terms are clearly very different in a different market structure. It therefore seems reasonable to expect a renegotiation of contract terms in response to the rejection of one retailer, and each retailer should take into account this outside option for the manufacturer when making a 5

6 (common) offer. Letting each retailer announce contract terms for every possible market configuration at stage 1 is a simple way to represent this process of "reactive renegotiation" ommon agency profits Before turning to specific contractual relationships, it is useful to derive bounds on the equilibrium payoffs for common agency situations. We will only assume here that each pair R i canachieveandshare the bilateral monopoly profit Π m i as desired. 11 We denote by Π the equilibrium industry profits under common agency, and by r1, r2 and r, respectively, the retailers and the manufacturer s equilibrium profits: By definition, Π cannot exceed the integrated monopoly profits Π ; it may, however, be lower if contracting externalities prevent the maximization of joint profits in equilibrium. First note that, in any common agency equilibrium, the joint profit of the vertical pair R i must exceed the bilateral profit itcould achieve by excluding R i ; indeed, if ri + r < Π m i, then R i could profitably deviate by offering an exclusive contract generating the bilateral monopoly profit and leaving a slightly higher payoff to. 12 Since ri + r = Π r i, there is no deviation to exclusivity if, for i =1, 2: Π r i Π m i, (1) ondition (1) implies in turn that R i s equilibrium profit cannotexceed its contribution to total profits: for i =1, 2, r i Π Π m i. (2) Since these upper bounds increase with Π, common agency is potentially most attractive for the retailers when equilibrium industry profits are large. These upper bounds moreover imply that the manufacturer s equilibrium payoff r is always positive: r = Π r1 r2 Π Π Π m 2 Π Π m 1 = Π m 1 + Π m 2 Π Π m 1 + Π m 2 Π > A similar justification for contingent contracts is provided in Bernheim & Whinston (1985). 11 Standard two-part tariffs, for example, are sufficient to achieve this. 12 For example, a two-part tariff F i + cq i,withf i just above r,woulddo. 6

7 s individual rationality constraint is thus strictly satisfied in any common agency equilibrium; since individual rationality also requires r i 0 for all i, condition(2) implies that a common agency equilibrium can exist only if Π Π m 1. (3) 4 Two-part tariffs We suppose in this section that retailers offer two-part tariffs, of the form t i (q) =U i + w i q for q 0. Bernheim and Whinston (1998) have shown that, when rival manufacturers deal with a common retailer, two-part tariffs suffice to achieve the integrated industry monopoly profits. 13 As we will see, this is no longer the case when rival retailers distribute a common manufacturer s product and have substantial bargaining power in their relations with the manufacturer. In addition, in the context studied by Bernheim & Whinston (1998), or when a single manufacturer offers (public) contracts to competing retailers, two-part tariffs do not need to be contingent on common agency to sustain the common agency equilibrium. It is an equilibrium for the manufacturer to offer (non-contingent) contracts with wholesale prices at marginal cost and fixed fees up to their contribution to industry profits, and this equilibrium yields the desired common agency outcome. In the setup we consider, arx & Shaffer (2004) illustrate that, with non-contingent two-part tariffs, the bilateral common agency profits of any vertical pair always lie strictly below this pair s bilateral monopoly profits. A profitable deviation to an exclusive offer that generates monopoly profits therefore always exists. As shown by arx & Shaffer, a profitable deviation to exclusivity is possible by means of a non-contingent three-part tariff that contains both an upfront fixed fee and a conditional fixed fee. 14 In the following, we therefore consider contingent two-part tariffsoftheform ª Ui,wi, U E i,wi E, and establish 13 Bernheim and Whinston (1998) focussed on the case where manufacturers have the bargaining power in their bilateral relations with the common retailer. The conclusion remains however valid when the retailer has all the bargaining power: in both instances, the retailer plays the role of a unique gatekeeper for access to consumers and fully internalizes through marginal cost pricing any contracting externalities. This moreover remains the case when contracts are not publicly observable contract observability is irrelevant when the manufacturers are the ones that make the offers; if instead the retailer makes take-it-or-leave-it offers, it would require the manufacturers to supply at cost and have no incentive to behave opportunistically (altering one contract cannot hurt the other manufacturer). 14 Under certain conditions on demand, a retailer could also profitably deviate to a (non-contingent) two-part tariff with a slightly higher wholesale price that induces de facto exclusivity. 7

8 the existence of a common agency equilibrium in this context. Exclusive dealing We firstnotethattherealways existanexclusive dealing equilibrium. learly, if R i insists on exclusivity (e.g., by offering only exclusivity, or by degrading its offer for common agency), R i cannot do better than insist on exclusivity as well. In addition, if sells at cost exclusively to R i (w i = c, w i =+, say),r i will maximize R i (q i, 0) cq i U i, and thus choose the quantity qj m that maximizes the joint profits with, generating a total profit ofπ m i. The fixed fee F i canthenbeused to share these profits as desired. As a result: Lemma 1 There always exists an exclusive dealing equilibrium. In addition: If Π m 1 > Π m 2, in any such equilibrium R 1 is the active retailer while R 2 gets zero profit; among these equilibria, the unique tremblinghand perfect equilibrium, which is also the most favorable to the retailers, yields Π m 1 Π m 2 for R 1 and Π m 2 for. If Π m 1 = Π m 2, there exist two exclusive dealing equilibria, where either retailer is active; in both cases, retailers get zero profit and gets Π m 2. Proof. If one retailer offers only an exclusive dealing contract, there is nogainfortheotherretailerfromoffering a common agency equilibrium. Hence, without loss of generality we can restrict attention to equilibria in which both retailers offer only exclusive dealing contracts. In any such equilibrium, the joint profits of the manufacturer and the active retailer, R i, must be maximized; otherwise R i could profitably deviate to a different exclusive contract. R i therefore sets the wholesale w i equal to the marginal cost c, and industry equilibrium profits are Π m i. For Π m 1 > Π m 2, R 2 cannot be an exclusive retailer, since R 1 could outbid any exclusive deal. In addition, R 1 s equilibrium fixed fee U1 E must be in the range [Π m 2, Π m 1 ]: ifu1 E < Π m 2,thenR 2 could and would outbid R 1 s offer; and if U1 E > Π m 1,thenR 1 would be better-off not offering any contract at all. onversely, any U1 E [Π m 2, Π m 1 ] can sustain an exclusive dealing equilibrium, in which both retailers offer (only) the same exclusive dealing contract t E i (q) =U1 E + cq. The best equilibrium for R 1 (and thus the Pareto-undominated equilibrium for both retailers) is such that U1 E = Π m 2,inwhichcaseR 1 s payoff is Π m 1 Π m 2. In addition, for U1 E > Π m 2, R 2 s equilibrium offer is unprofitable and would thus not 8

9 be made if it could be mistakenly accepted; therefore, such equilibrium is not trembling-hand perfect. 15 For Π m 1 = Π m 2 = Π m, the same reasoning implies that exclusive dealing offersmustbeefficient (w 1 = w 2 = c) and yield exactly Π m to : it would be unprofitable for the active retailer to offer a higher fixed fee, and its rival could outbid any lower fixed fee; conversely, it is an equilibrium for both retailers to offer (only) the exclusive dealing contract t E (q) =Π m + cq. Thus, there always exists an exclusive dealing equilibrium where the more efficient retailer, R 1, outbids its rival and generates the maximal bilateral profits, Π m 1. When both retailers are equally efficient, standard competition à la Bertrand leaves all the profit to; otherwise, R 1 can earn up to its contribution to bilateral profits, Π m 1 Π m 2. ommon agency We first stress that, unlike under exclusivity, marginal cost pricing cannot implement the monopoly outcome in a common agency situation. Indeed, if wholesale marginal prices reflect the production cost c, each retailer earns the full margin on each unit sold. But then, since retailers compete for consumers, when maximizing profits, each retailer ignores the impact of its own actions on the competitor s sales and thus profits. This leads to a competitive outcome, with final prices below those of an integrated monopoly. For the sake of exposition, we will assume from now on that, for any (w 1,w 2 ): each retailer has a unique best response function for i =1, 2:BR i (q i ; w i ) arg max R i(q i,q i ) w i q i ; q i 0 there is a unique retail equilibrium q1,q2, characterized by: for i 6= i {1, 2} : q i (w i,w i )=BR i q i (w i,w i );w i, which varies continuously with wholesale prices. A simple revealed preference argument confirms that marginal cost pricing induces retailers to compete more aggressively than required for joint profit maximization. Letting ˆq i BR i q i,c denote for simplicity R i s best response to its rival s monopoly quantity, we have: R i ˆqi,q i cˆqi R i q i,q i cq i, R i q i,q i + R i q i,qi cq i R i ˆqi,q i + R i q i, ˆq i cˆqi. 15 The situation is formally the same as Bertrand competition between asymmetric firms, where one firm has a lower cost or offers a higher quality. 9

10 In addition, the assumption R i / q i < 0 for q i > 0 implies that the first inequality is strict. 16 Therefore, summing up: R i q i,q i >R i q i, ˆq i, which in turn implies ˆq i >qi. 17 Wholesale prices above cost can, however, be used to offset the impact of retail competition and sustain the monopoly outcome. Indeed, if the best responses decrease continuously as wholesale prices increase, there exist wholesale prices w1,w2 sustaining the monopoly outcome; it suffices to choose, for each R i, wi >csuch that BR i (q i; wi )=qi. For i =1, 2 and a given pair of wholesale prices (w i,w i ),itwillbe convenient to denote (with a slight abuse of notation) the continuation equilibrium profits for R i,, and the entire industry, respectively, by Π i (w i,w i )=R i q i (w i,w i ),q i (w i,w i ) w i qi (w i,w i ), Π (w i,w i )=(w i c) qi (w i,w i )+(w i c) q i (w i,w i ), Π (w i,w i )=Π (w i,w i )+ X Π j (w j,w j ). j=1,2 By construction, the wholesale prices (w1,w2 ) maximize industry profits: Π w1,w2 = Π.Thus,if could make take-it-or-leave-it offers to the retailers, it would indeed choose these wholesale prices and set fixed fees so as to recover retail margins: in this way, would generate and appropriate the monopoly profits Π. 18 If retailers have the bargaining power, however, the integrated monopoly outcome cannot be an equilibrium. This is because while each retailer can internalize s upstream margin on all sales by adjusting the fixed fee appropriately, 16 Π > Π m i implies q i > 0 and thus, by assumption, R i q i,qi Therefore, the first-order condition characterizing qi implies / q i < 0. R i q i q i,q i R i c = q q i,qi i > 0. Thus, starting from q i = qi,asmallincreaseinq i increases R i s profit; the uniqueness of the best-reply BR i q i,c in turn implies ˆq i 6= qi,andthefirst inequality is thus strict. 17 Both quantities will exceed monopoly levels if the retail equilibrium is wellbehaved, e.g. if, as in standard ournot models, retail best responses are decreasing and generate a stable equilibrium: 1 < BR i / q i < This is indeed an equilibrium when contract offers are public. Private offers give the opportunity to behave opportunistically, which in turn is likely to prevent from sustaining the monopoly outcome. See Hart-Tirole (1990) and cafee-schwartz (1994) for the case of ournot downstream competition and O Brien-Shaffer (1992) and Rey-Verge (2004) for the case of Bertrand competition. Rey-Tirole (2004) offers an overview of this literature. 10

11 it still has an incentive to free-ride on its rival s downstream margin. Suppose that R i chooses w i; setting w i = wi would then maximize industry profits Π w i,w i, but not the bilateral joint profits of Ri and, givenby: Π i wi,w i + Π wi,w i + U i = Π w i,w i Π i w i,w i + U i. Hence, whenever the wholesale price w i affects the rival retailer s profit, the equilibrium cannot yield the integrated monopoly outcome. To fix ideas, we will suppose that a retailer always benefits from any increase in its rival s wholesale price: for i =1, 2, Π i > 0. w i A simple revealed preference argument then shows that R i has an incentive to respond to w i by offering a wholesale price below wi,and adjusting the fixed fee F i so as to absorb any increase in s profit. ore generally, this reasoning implies that, in any common agency equilibrium, the wholesale price w i must maximize the bilateral profits that R i can achieve with, givenw i. That is, equilibrium wholesale must satisfy, for i =1, 2: prices w 1,w 2 w i = W BR i (w i) arg max w i Π i wi,w i + Π wi,w i. (4) The system (4) has a unique solution in standard cases (e.g., when demand is linear). For the sake of exposition, we will suppose that there exists indeed at least one solution, 19 denote by ( ew 1, ew 2 ) the solution for which the industry profits are the largest, and by eπ Π( ew 1, ew 2 ) these profits. Since Wi BR (w i) <wi, ( ew 1, ew 2 ) 6= (w1,w2 ) and thus eπ < Π. Two-part tariffs thus cannot implement the integrated monopoly outcome: even if common agency arises, contracting externalities prevent the retailers from using the manufacturer as a perfect coordination device. This lack of coordination may in turn prevent common agency from arising in equilibrium. Indeed, we have seen in the previous section that common agency can prevail only if it generates more profits than exclusive dealing, that is if: eπ Π m 1. (5) Since e Π < Π, condition (5) may be violated; in that case, common agency cannot arise in equilibrium, even though an integrated structure would always opt for it. 19 If this is not the case, there is no common agency equilibrium. 11

12 We now show that eπ Π m 1 is not only a necessary but also a sufficient condition for the existence of a common agency equilibrium with contingent two-part tariffs. As before, let r1, r2 and r denote the two retailers and the manufacturer s equilibrium profits. Wehavealready seen that, in any common agency equilibrium, R i cannot earn more than its contribution to the equilibrium profits, which is Π e Π m i here. onversely, it is straightforward to check that there exists an equilibrium where both retailers indeed earn these maximal profits. To see this, suppose that each R i offers wi = ew i, so that industry profits are equal to eπ, h i Ui = Π i ( ew i, ew i ) eπ Π m i so that R i gets exactly ri Π m i 0 and gets r = Π m 1 + Π m 2 eπ > 0, = e Π w E i = c, so that industry profits would be equal to Π m i if this exclusive offer were accepted, U E i = r. By construction, earns positive profits and is indifferent between accepting one or both offers. 20 In addition, wholesale prices are, by definition, such that no retailer can benefit from deviating to another common agency outcome. It thus only remains to check that no retailer R i can benefit from deviating to an exclusive dealing arrangement. This is straightforward: since can always secure r by accepting R i s exclusive contract, a deviation to exclusivity cannot yields more to R i than ³ Π m i r = Π m i Π m 1 + Π m 2 eπ = eπ Π m i = ri. Note that when this common agency equilibrium exists (that is, when eπ Π m 1 ), it is preferred by the retailers to any exclusive dealing equilibrium; finally, in the limit case where eπ = Π m 1, it is by construction the only possible equilibrium with common agency. The following proposition summarizes this discussion: Proposition 1 When contract offers are restricted to two-part tariffs, common agency equilibria exist if and only if e Π Π m 1,inwhichcase: 20 Whenever contracts allow the partners to share their bilateral profits as desired (as here through the fixed fee), in any common agency equilibrium must be indifferent between dealing with both retailers or with either retailer on an exclusive basis: if strictly preferred common agency to dealing exclusively with R i,say,then R i could profitably deviate by both decreasing F i and withdrawing or degrading its own exclusivity offer. 12

13 industry profits are eπ < Π ; if e Π > Π m 1, both retailers prefer the common agency equilibrium in which each retailer R i earns its marginal contribution to total profits, eπ Π m i, while the manufacturer earns Π m 1 + Π m 2 eπ, to all other equilibria, common or exclusive. For eπ = Π m 1,theunique common agency equilibrium is payoff equivalent to the retailers preferred exclusive equilibrium. omparison with Bernheim-Whinston (1998) At this point, it is useful to compare our analysis with Bernheim & Whinston s (1998) seminal exclusive dealing paper. In their model, two manufacturers of imperfect substitutes offer contingent supply contracts to a monopolistic retailer. Focussing on equilibria that are Pareto-undominated for the manufacturers, on the grounds that these are first-movers, they find that the equilibrium market structure maximizes industry profits, given the profits that each structure can generate, and in particular given the contracting externalities that may prevent the generation of monopoly profits under common dealing. The same result prevails here: given the wholesale prices that can arise in a common agency equilibrium, and the resulting industry profits, common agency can arise in equilibrium (and is then Pareto-undominated for the retailers) if and only if comon agency profits exceed the bilateral monopoly profits. In Bernheim & Whinston s setup, two-part tariffs with marginal cost pricing moreover implement the integrated monopoly profits under common agency: when wholesale prices reflect the marginal costs of production, the monopoly retailer is the residual claimant on all sales and sets quantities so as to maximize joint industry profits; in addition, these wholesale prices form an equilibrium. First, through its fixed fee each manufacturer internalizes any impact of its own wholesale price on the retailer s revenue. Therefore, just as in our model, each vertical pair maximizes its joint profits. Second, the retailer being the residual claimant on all sales of the rival product, the joint profits of a vertical pair coincide, up to a constant (the rival s fixedfee),withtheindustryprofits. Hence, if the other manufacturer prices at marginal cost, each vertical contracting pair sets its own wholesale price so as to maximize industry profits, that is at marginal cost. With two-part tariffs, the retailers preferred equilibrium therefore involves common agency. The crucial difference in our framework is the role of retail competition. aximizing industry profit requires wholesale prices above marginal costs, to compensate for the competitive pressure on retail margins. However, for these wholesale prices, none of the vertical pairs unilaterally maximizes its joint profits: each pair has an incentive to free-ride 13

14 on the rival retailer s revenue. Thus, with two-part tariffs the integrated monopoly solution cannot be sustained in a common agency equilibrium. ommon agency is therefore less profitable and, as a result, may not even be sustainable in equilibrium. 5 onditional fixed payments Standard two-part tariffs thusfailtosustainthemonopolyoutcome when retailers have the bargaining power but compete against each other. We now show that fixed payments that are conditional on the quantity bought being strictly positive, can help eliminate contracting externalities and allow the parties to sustain the monopoly outcome. The basic intuition is that retailers can commit to higher profits by proposing high conditional fixed fees. We now consider contingent contracts Fi,wi tariffs oroftheform, F E i,w E i ª,where t k i (q) =F k i + w k i q for q>0, andt k i (0) = 0 (i =1, 2, k =, E). The marginal price is thus constant except at q =0. A retailer with a signed contract faces the following profit maximization program at the retail competition stage: max 0, max q i 0 Ri (q i,q i ) w k i q i F i ª. 21 The best response functions are therefore truncated. In the case where both contracts are accepted, ½ dbr i q i ; wi,fi BRi q i ; w = i if Π i q i ; wi F i, 0 otherwise. Note that retailers individual rationality constraints are trivially satisfied here, since retailers can avoid any loss by choosing not to buy in the last stage. Exclusive equilibria With standard two-part tariffs, the unique tremblinghand perfect exclusive equilibrium, which coincides with the Paretoundominated exclusive equilibrium, is such that only the more efficient retailer R 1 is active and earns its contribution to industry profits, Π m 1 Π m 2. When fixed fees are conditional, this is also the unique exclusive equilibrium. R 2 can now secure non-negative profits by not buying in 21 If the accepted contract is exclusive, then obviously q i =0and wi k = wi E in this problem. 14

15 the last stage, and would do so if its contract specified a fixed fee exceeding Π m 2. Hence, cannot earn more than Π m 2 by accepting R 2 s exclusive offer, and R 1 thus never needs to offer a fixed fee above Π m 2. Remark: There can exist pseudo common equilibria where accepts both offers, but eventually only one retailer is active (i.e., buys a positive quantity). However, it is straightforward to check that any such common equilibrium is outcome equivalent to the unique exclusive equilibrium just described. In what follows, we therefore focus on proper common equilibria where both retailers eventually buy positive quantities. ommon equilibria Since we consider common agency equilibria where both retailers buy positive quantities, we must have Π i w i,w i F i. (6) If the inequality (6) is strict for R i, then it still holds for small variations of the rival s wholesale price. Hence, R i could slightly modify w i in any direction and maintain a common agency outcome, by adjusting F i so as to appropriate any resulting modification in s profit. To rule out such deviations, 22 w i must maximize (at least locally) the joint profits of and R i among (proper) common agency situations, that is, R i must be on its above-described best reply: w i = W i BR (wi ). If the inequality (6) is strict for i =1, 2, both retailers must therefore be on their best replies; industry profits are then bounded above by eπ, andr i cannot hope to earn more than eπ Π m i. onversely, it is straightforward to check that, whenever eπ Π m 1, the previously described equilibrium, where each R i gets eπ Π m i and gets Π m 1 +Π m 2 eπ, remains an equilibrium Proper common agency equilibria may co-exist, for given contract offers, with de facto exclusive equilibria. Since R i / q i < 0 and quantities are likely to be strategic substitutes, increasing R i s quantity may induce R i to exit, which indeed encourages R i to expand. We assume in this section that the proper common agency equilibrium is played whenever it exists (that is, when Π i w i,w i F i for i =1, 2). This assumption, which is also made for example in arx & Shaffer (2004), can be justified by the fact that buying a positive quantity is a dominant strategy for each retailer. Still, this assumption possibly restrict the analysis; a common agency equilibrium might for example be sustained by switching to de facto exclusivity in case of a deviation. We show however in the next section that conditional upfront payments suffice to sustain common agency and the integrated monopoly outcome when combined with classic two-part tariffs. 23 It suffices to check additionally that a retailer R i cannot generate higher bilateral profits by deviating to a pseudo common agency situation. Such a deviation cannot generate joint profits higher ³ than Π m i ³, which is precisely what and R i get in equilibrium: ri + r = eπ Π m i + Π m 1 + Π m 2 Π e = Π m i. 15

16 We now look for equilibria where (6) is binding for at least one retailer. For expositional purposes, we consider here the case where R 1 is strictly more profitable: Π m 1 > Π m 2 ;webriefly discuss the case Π m 1 = Π m 2 at the end of the section. We first show that (6) cannot be binding for R 1. Indeed, in a common agency equilibrium must be indifferent between dealing with both retailers or only with R 2, otherwise, R 1 could profitably deviate by slightly lowering its fixed fee F1 (and degrading its exclusive dealing offer): would still accept both contracts rather than dealing only with R 2,andR 1 would increase its profit. But R 2 s exclusive dealing contract cannot offer more than Π m 2, since otherwise R 2 would rather not buy at the last stage. Therefore, in equilibrium, cannot earn more than Π m 2 : 24 r Π m 2. (7) In addition, it is still the case that no retailer can earn more than its contribution to the industry profits, Π. Hence: Summing up (7) and (8) yields: r 2 Π Π m 1. (8) Π Π m 1 + Π m 2 r + r 2 = Π r 1, and thus r1 Π m 1 Π m 2 > 0, which implies Π 1 w 1,w2 >F 1. Given the above discussion, we must therefore have: w 2 = W BR 2 (w 1 ). As a result, R 1 cannot hope to earn more than bπ 1 Π m 2,where ³ bπ 1 max Π(w 1,W2 BR (w 1 )) Π, e Π. w 1 As before, this common agency situation cannot be an equilibrium if it is less profitable than exclusivity (that is, bπ 1 < Π m 1 ). onversely, we show below that, whenever Π b 1 Π m 1, there exists an equilibrium where (6) is binding for R 2 (and thus R 2 get zero profit) and R 1 gets bπ 1 Π m This condition is indeed satisfied in the common agency equilibrium just described, since then gets Π m 1 + Π m 2 Π e ³ = Π m 2 eπ Π m 1 Π m 2. 16

17 Proposition 2 When contract offers are restricted to two-part tariffs with conditional payments, common agency equilibria exist if and only if bπ 1 Π m 1.oreover,ifΠ m 1 > Π m 2,then: if bπ 1 Π m 1 > eπ, in any (common agency or exclusive dealing) equilibrium R 2 gets zero profit and gets Π m 2.Thebestequilibrium for R 1 (and thus the unique Pareto-undominated equilibrium) involves common agency and gives a profit Π b 1 Π m 2 to R 1. if Π e Π m 1, there are two Pareto-undominated equilibria for the retailers, which both involve common agency: the equilibrium just described, which yields bπ 1 Π m 2 to R 1 and 0 to R 2, and the equilibrium described in the previous section, which yields a lower profit eπ Π m 2 to R 1 but a positive profit Π e Π m 1 to R 2. Proof. As already noted, the common agency equilibrium studied in the previous section remains an equilibrium when eπ Π m 1. Suppose now bπ 1 Π m 1 and consider the following candidate equilibrium: w1 = ŵ 1 arg max w1 Π(w 1,W2 BR (w 1 )) and w2 = W2 BR (ŵ 1 ),so that industry profits are equal to Π b 1, F1 such that R 1 gets exactly r1 = bπ 1 Π m 2 0 and F2 = Π 2 w 2,w1,sothatR2 gets r2 =0and gets r = Πm 2 > 0, for i =1, 2, w E i = c and F E i = r = Π m 2. By construction, earns Π m 2, which it can also secure by opting for either retailer s exclusive offer. Hence a deviation by any retailer R i must increase the joint profits of and R i to be profitable. This cannotbethecaseforr 2, since it cannot offer more than Π m 2 = r +r2 through exclusivity (or pseudo-common agency) and, given w1,already maximizes the joint bilateral profit among common agency situations. 25 Similarly, R 1 cannot increase its joint profit with by deviating to exclusivity or pseudo common agency, since this would generate at most Π m 1 Π b 1 = r + r1. And R 1 cannot profitably deviate to another proper common agency outcome either, since w1 maximizes the joint profits with, under the constraint that R 2 remains active. Thus the above contracts constitute an equilibrium. 25 ore precisely, w2 maximizes the joint profit of and R 2 among those situations, even when ignoring the constraint that R 1 must remain active, and this constraint is indeed satisfied for w2 ; w 2 therefore also maximizes these profits when taking the constraint into account. 17

18 When bπ 1 Π m 1 > eπ, there exist no common agency equilibrium where conditions (6) are strictly satisfied for both retailers, since in any such candidate equilibrium industry profits are bounded above by eπ and would therefore not survive deviations to exclusive dealing. The only common agency equilibria are thus such that R 2 get 0, andr 1 gets at most Π b 1 Π m 2. All other equilibria are such that R 2 is inactive andthusgetsagain0, while gets Π m 2 and R 1 gets Π m 1 Π m 2. Hence the common agency equilibrium where R 1 gets Π b 1 Π m 2 is the unique Pareto-undominated equilibrium. When eπ Π m 1, in addition to the equilibria just mentioned there also exists common agency equilibria where conditions (6) are strictly satisfied for both retailers, and in the best of these equilibria for the retailers each R i gets eπ Π m i. The conclusion follows. onditional payments thus increase the scope for common agency equilibria: with unconditional fixed fees they exist only when eπ Π m 1, while with conditional payments they exist whenever bπ 1 Π m 1,whereby construction bπ 1 > eπ. In the additional common agency equilibria, however, the less profitable retailer gets zero profit; hence when eπ Π m 1,the retailers may disagree over the equilibrium selection: the more profitable retailer would rather opt for the new asymmetric equilibrium, while the other retailer would favor the previous, more balanced equilibrium. Finally, it is straightforward to check that, when the two retailers are equally profitable (Π m 1 = Π m 2 = Π m ), there exists two types of asymmetric equilibria, in which either retailer R i gets up to bπ i Π m i, where bπ i max wi Π(w i,w i BR (w i )), while the other retailer gets zero profit. Remark : As long as contracts are ex post verifiable, conditional payments solve the problem of opportunism in the Hart & Tirole (1990) framework, where the manufacturer makes unobservable offers to the retailers. Since conditional fixed fees give retailers the opportunity to "exit" later on, they are willing to accept high fixed fees at stage 1 even without observing the offer the manufacturer makes to the rival retailer. 6 Three-part tariffs We now consider so-called three-part tariffs that combine classic twopart tariffs with conditional fixed payments. ontingent contracts are of the form (Ui,Fi,wi ), (Ui E,Fi E,wi E ) ª, where tariffs are: ½ U t k k i (q i )= i if q i =0 Ui k + Fi k + wi k (i =1, 2; k =, E). q i if q i > 0 We now show that these tariffs can implement the integrated monopoly profits Π, and indeed allow each retailer R i to earn its contribution Π Π m i. To see this, consider the following contracts: for i =1, 2, 18

19 U i = U E i = Π Π m i, so that retailers get their contributions to common agency industry profits through the upfront payments, w i = w i, so that wholesale prices sustain the monopoly prices and quantities, F i = Π i (w i,w i), sothat recovers ex post all retail margins if both contracts are accepted, w E i = c and F E i = Π m i. is willing to accept both contracts, since it earns the same positive profit by accepting either one or both offers: r = r E = Π m 1 + Π m 2 Π. Double acceptance in turn induces the retailers to implement the monopoly outcome: since conditional payments are just equal to each retailer s variable profits when both retailers are active, each retailer is willing to buy a positive quantity, in which case wholesale prices lead to the monopoly outcome. 26 Finally, the slotting allowances are designed so as to give each retailer its contribution to profits. Therefore, if both contracts are proposed, they are accepted by and yield the desired monopoly outcome. We now check that no retailer has an incentive to offer any alternative contract (even outside the particular class of three-part tariffs). By construction, can get its equilibrium profit r by opting as well for either retailer s exclusive offer; therefore, in order to benefitfrom adeviation,r i must increase its joint profits with. Since these are equal to Π m i in equilibrium, R i cannot lure into a more profitable exclusive dealing arrangement. And given the contract offered by R i, bilateral profits cannot be higher than Π m i in any (pseudo or proper) common agency situation either. Total industry profits cannot exceed Π.oreover,sinceR i can always choose not to buy in the last stage, R i s overall profit is at least equal to its slotting allowance Π Π m i ; hence, the joint profits of and R i cannot exceed Π Π Π m i = Π m i. The above contracts thus constitute a common agency equilibrium where each retailer R i earns the maximal achievable profit, Π Π m i. Both retailers prefer this equilibrium to any other exclusive or common agency equilibrium. The following proposition summarizes this discussion: 26 Note that while retailers are ex post indifferent between buying or not (given the other retailer buys), buying constitutes a weakly dominant strategy. 19

20 Proposition 3 When retailers can offer three-part tariffs (or more general contracts), common equilibria in which total industry profits are Π exist. Theretailers preferredequilibrium(outofallexclusivedealingand common agency equilibria) is the common agency equilibrium in which industry profits are Π, pays an initial slotting allowance of Π Π m i to each R i, and then receives R i s variable profits Π i (wi,w i) as a conditional fixed fee. onditional payments can hence be used as a commitment to maintain high prices; indeed, if a retailer tries to undercut its rival, this will induce the rival to exit and waive the conditional payment to the manufacturer. This generates a loss for that needs to be compensated, whichinturnreducestheprofitability of any such deviation. In the limit, conditional payments equal to the profits that retailers expect to achieve ex post can sustain the desired outcome. Upfront payments by the manufacturer can then be used to share the profits with the retailers. There exist other common agency equilibria where three-part tariffs still sustain monopoly prices, but which are more favorable to the manufacturer who can in fact get up to Π. 27 onditional payments are, however, always required to sustain the monopoly outcome; they must moreover be equal to the retailers ex post variable profits, implying that common agency upfront payments are always negative (as is the case for slotting allowances). 7 Policy Implications The welfare implications of banning slotting allowances are a priori ambiguous. On the one hand, slotting allowances in combination with conditional fixed fees may in some situations lead to common agency where classictwo-parttariffs would be exclusionary. In that sense, three-part tariffs can be competition enhancing. On the other hand, given common agency, three-part tariffs lead to the complete elimination of downstream competition, which clearly harms consumer and total welfare. It is thus not clear whether a ban on slotting allowances would be a sensible policy recommendation. We have identified two factors that influence whether classic two-part tariffs will lead to exclusion or not. First, the degree of substitutability between retailers: as retailers become closer substitutes, it becomes more likely that Π e < Π m 1, so that retailer 2 will be excluded. To see this, note that Π > Π m 1 whenever retailers are imperfect substitutes, 27 The equilibria most favorable to require non-profitable exclusive offers, and are thus not trembling-hand perfect. 20

21 but Π = Π m 1 when retailers are perfect substitutes. ommon agency equilibrium profits with two-part tariffs, eπ, on the other hand are equal to Π if and only if retailers are not substitutable, otherwise Π e < Π. Hence, it is obvious that in the limit when retailers are perfect substitutes, eπ < Π m 1, while for unrelated retailers eπ > Π m 1. In fact, there will be some threshold on the degree of substitutability such that, with classic two-part tariffs, common agency will only arise below the threshold. 28 Intuitively, better substitutability increases the incentives of each vertical pair to free-ride on the margin of the other retailer, as business stealing becomes easier. A second relevant factor is the degree of asymmetry between retailers. Not surprisingly, asymmetry increases bilateral monopoly profits relative to eπ: while the bilateral monopoly only involves the more profitable retailer, a common structure by definition also includes the less profitable retailer. eteris paribus, asymmetry therefore favours exclusion. When retail competition is very strong in the sense of a high degree of substitutability between retailers, three-part tariffs are thus likely to increase welfare by inducing common agency. When retail competition is not that strong, however, and retailers are rather symmetric, slotting allowances, or more precisely three-part tariffs, should be banned, since they merely serve retailers as a way to eliminate competition. 8 onclusion Our analysis confirms the hicago critique, as formalized by Bernheim & Whinston (1998), in a model where competing retailers have all the bargaining power when negotiating with an upstream monopolist. Given whichever contracting restrictions may prevail, the equilibrium market structure is chosen so as to maximize total industry profits. Thus, an exclusionary strategy cannot be profitable as long as common agency profits exceed exclusive profits. The main contribution of our paper is then to examine the role that upfront payments and conditional fixed fees play in determining the market structure and retail prices. We first show that with classic twopart tariffsthatcontainanupfrontfixedfee,acommonagencystructure cannot sustain the industry monopoly outcome. This implies that all equilibria may be such that the less efficient retailer is excluded. We, however, also show that conditional fixed fees permits to maintain higher common agency profits, by serving as a commitment to stay out of the 28 In a simple symmetric model, where (inverse) demand functions are P i (q i,q i )= 1 q i αq i for i 6= i {1, 2}, the relevant threshold on the subsitutability parameter α is bα 0.65: common agency equilibria exist with classic two-part tariffs if and only if α bα. 21