Discounts as a Barrier to Entry

Transcription

1 Discounts as a Barrier to Entry Enrique Ide, Juan-Pablo Montero and Nicolás Figueroa April 30, 2015 Abstract To what extent an incumbent manufacturer can sign discount contracts (e.g., rebates) with one or more retail buyers to effectively deter the entry of a more efficient supplier? We study the potential exclusionary effects of such contracts in a variety of market settings and show that off-list-price rebates without upfront payments like the ones in Michelin II v. Commission, for instance cannot be anticompetitive. This is true even in the presence of cost uncertainty, scale economies, or intense downstream competition; all three settings where exclusion has been shown to emerge with exclusive dealing contracts. The difference is explained by the easy terminability of rebates, the fact that buyers are not prevented ex-ante from dealing with rival suppliers. (JEL L42, K21, L12, D86) 1 Introduction Suppose we observe a dominant manufacturer offering the following rebate contract to a retail buyer who is currently considering buying a few units from an alternative (small) supplier: As long as you buy exclusively from me you get a 10% off the list price on all the units you purchase, otherwise you pay the full list price for as many units as you want.... How can the antitrust authority be sure that such contract is not offered to monopolize the market? Despite Ide: Stanford GSB and PUC-Chile Economics (eide@stanford.edu); Montero: PUC-Chile Economics (jmontero@uc.cl); Figueroa: PUC-Chile Economics (nfigueroa@uc.cl). We thank two referees, Larry Samuelson (the Editor), Matias Covarrubias, Liliane Giardino-Karlinger, Laurent Linnemer, Cristóbal Otero, Joaquín Poblete, Patrick Rey, Dick Schmalensee, Ilya Segal, Andy Skrzypacz and audiences at CRESSE 2013, CREST-Paris, IIOC 2013, LAMES 2013, MIT, Paris School of Economics, PUC-Rio, TOI-Chile 2013, IO Workshop in University of Salento, University of Miami and University of Torcuato di Tella for very good comments and discussions. The three authors thank the ICSI Institute (Milenio P05-004F and Basal FBO-16) for financial support and Montero also thanks the Tinker Foundation for support during his visit to Stanford CLAS and Economics. 1

2 the close proximity to an exclusive dealing arrangement, which has been shown to effectively foreclose the entry or expansion of a more efficient rival in a variety of market settings, one of the main objectives of this paper is to explain why in those same settings the rebate contract above cannot be anticompetitive. One of the most controversial issues in antitrust and competition policy is indeed the potential exclusionary effects of exclusive dealing arrangements, discount contracts (e.g., rebates), and related vertical practices. This controversy dates back at least to United States v. United Shoe Machinery (1922) and Standard Fashion v. Magrane Houston (1922) and has remained very much alive since then, as illustrated by recent rulings on both sides of the Atlantic; for example, EU Commission v. Michelin II (2003), EU Commission v. British Airways (2003), AMD v. Intel (2005), Allied Orthopedic v. Tyco Healthcare Group LP (2010), and ZF Meritor v. Eaton (2012). What makes these rulings controversial is that these practices can arise without an exclusionary motive and, more importantly, be efficient. Exclusivity, either de jure through explicit provisions or de facto through rebate schemes, may foster relationship-specific investments between manufacturers and retailers by solving hold-up and free-riding problems (Marvel 1982; Spiegel 1994; Segal and Whinston 2000a). Rebates may also be used in a bilateral monopoly setting to avoid double marginalization when demand is known to both sides, and as a screening device when demand is only known to downstream retailers (Kolay, Ordover and Shaffer 2004), or simply to stimulate retailers sale efforts (Conlon and Mortimer 2014). 1 According to the so-called Chicago critique (Posner 1976; Bork 1978), these efficiency gains is all that matters when evaluating these contracts because a downstream retailer would never sign an exclusive that reduces competition unless it is fully compensated for it, which the incumbent manufacturer cannot afford when the entrant is more efficient. We know now, however, that the Chicago critique fails to hold in a variety of settings, namely, when the entrant s cost is unknown to both the incumbent and the buyer (Aghion and Bolton 1987; Spier and Whinston 1995; and Choné and Linnemer 2015), when scale economies require the entrant to supply to more than one buyer (Rasmusen et al. 1991; Segal and Whinston 2000b; and Spector 2011); and when buyers are not local monopolies (e.g., retailers that sell in completely separate markets) but downstream competitors (Simpson and Wickelgren 2007; Abito and Wright 2009; and Asker 1 Exclusives can also be the result of fierce competition among two or more incumbent suppliers when they need to screen consumers (Calzolari and Denicolo, 2013). 2

3 and Bar-Isaac 2014). Although the focus of these post-chicago models has been on the exclusionary potential of exclusive contracts, 2 there is a growing consensus that discount contracts like in our opening example can also be used for exclusionary purposes (e.g., Rey et al. 2005; Spector 2005). All-unit rebates, where the per-unit price falls discontinuously for all units purchased after a pre-specified sales threshold or some exclusivity condition is met, have been particularly controversial. They are believed to be an even cheaper and more effective way of exclusion, by apparently combining features of the leverage theory of tying (e.g., Whinston 1990) with those of the anticompetitive theory of exclusive dealing. This is well captured in a recent statement of the EU Commission (2009, parr. 39): a rebate may enable a dominant supplier to use the non contestable portion of the demand of each buyer (that is to say, the amount that would be purchased by the buyer from the dominant supplier in any event) as leverage to decrease the price to be paid for the contestable portion of the demand (that is to say, the amount for which the buyer may prefer and be able to find substitutes). This tying or leverage theory has played a central role in virtually all rulings, so a simple example illustrating how it works may help. Consider a dominant supplier that can produce units at $5 each and a retail buyer that needs to buy a total of 100 units. The buyer s reservation value is $10 per unit (above that she develops her own private label). If the dominant supplier is the only one around, he would charge $10 for each unit and make a total profit of $500. Suppose now the buyer is willing to look for an alternative supplier for 10 units, not more (in the language of the Commission, the contestable share of the demand is 10%). There is a potential entrant that can produce each unit at zero cost but after sinking a fixed cost of 1 cent. It is clearly efficient to let the rival enter and supply the buyer with 10 units. In fact, this is what would happen in equilibrium if suppliers were to serve the buyer in the spot market, for example, by simultaneously setting (non-linear) prices. The entrant would price each unit slightly below $5 and make a total profit of $50, while the incumbent would price according to a non-linear schedule, e.g., a two-part tariff with a unit price of $5 and a fixed fee of $450. The incumbent would then sell 90 units resulting in a payoff of $450. The buyer s payoff, on the other hand, would be $50, which comes from the last 10 units bought to the entrant. 2 The exclusionary potential of exclusives is greatly diminished or eliminated altogether if (independent) buyers are strategic and cannot be price discriminated (Innes and Sexton 1994) or if they are allowed to breach by paying expectation damages (Masten and Snyder 1989; Simpson and Wicklegren 2007). We connect this literature to our results below. 3

4 Suppose now the incumbent offers the buyer a rebate contract consisting of a list price of $10 and a discount off the list price of 10% or $1 per unit to be applied retroactively over all units provided the buyer has purchased everything from him. If the buyer agrees and buys exclusively from the incumbent, her payoff would jump to $100, twice as much as if she rejects the rebate and goes to the spot. Therefore, for the entrant s offer to be attractive, he would need to charge $0 for each of those units (since the buyer would be buying the remaining 90 units at $10 according to what is specified in the contract), which makes entry unprofitable. The reason for the entry foreclosure is that the effective price faced by the entrant is not the actual price paid by the buyer when she buys exclusively from the incumbent (the list price minus the discount or $10 $1 = $9) but the price the entrant must offer the buyer to switch supplier (the list price minus the discount augmented by the forgone rebate in all remaining units or $10 $1/0.1 = $0). What explains this gap is precisely the workings of the Commission s leverage theory, the fact that the incumbent can take advantage of the contestable share of the demand being strictly less than 100%. There is a fundamental problem with this leverage theory, however, which forms the core of all our results in the paper. Notice that the incumbent s profit under the rebate contract, $400, is strictly less than in the absence of the contract, $450. This puzzling result raises two issues. First, what does explain that the leverage theory does not work for rebates as it does for tying? 3 The key observation is that rebates do not ex-ante prevent buyers from dealing with rival suppliers, so exclusivity must be optimally induced ex-post, that is, through a price schedule consisting of a list price and a reward if the exclusivity is met. But granting these rewards is costly for the incumbent because he must leave rents with buyers. In our simple example, for instance, the facto exclusivity is achieved by giving the buyer an extra of $50 above that without the contract, which obviously comes from the incumbent s pocket. We call this the easy terminability of rebate contracts. This easy terminability marks a clear departure from leverage theories of foreclosure, where the incumbent physically ties goods exante to become more aggressive ex-post; and from models of anticompetitive exclusive dealing arrangements, where exclusivity is contractually committed ex-ante. It is important to notice 3 The way the incumbent in our example could hypothetically implement Whinston s (1990) foreclosure strategy is by physically tying the sale of the first 90 units to the sale of the last 10 units. By committing ex-ante to sell either 100 units or nothing in the spot, the incumbent can credibly communicate that in the case of entry he will price his 100 units slightly below $9, forcing the entrant to price his 10 units below $0. In the absence of entry, the incumbent can then sell the 100 units at $10 each. 4

5 that this easy terminability of rebates does not imply that there are no consequences for the buyer if she fails to meet the exclusivity requirement, 4 but rather that it is costly for the incumbent to implement this requirement ex-post. The second issue is that our simple example is not immune to the Chicago critique given the absence of contractual externalities, namely, cost uncertainty, scale economies, or downstream competition. Indeed, if the incumbent tries to foreclose the entrant by offering the buyer an exclusive contract with arbitrarily large liquidated damages, he would need to agree to a perunit wholesale price of $9.5 in order to compensate the buyer for the $50 payoff she would otherwise get by rejecting the contract. This clearly does not improve upon the $450 payoff the incumbent gets anyway by going directly to the spot. So the remaining question is, will the conclusions derived from the easy terminability of rebates change in the post-chicago settings where contractual externalities are present? We show that they do not, that the easy terminability implies that rebates like the one in our example consisting of a list price, a discount off the list price and a sales threshold (that can be either set in terms of volume or market share) are never anticompetitive, regardless of whether the entrant s cost is unknown (Sections 3 and 4), there are externalities across buyers (Section 4), or buyers are downstream competitors (Section 5); all three settings where exclusion has been shown to emerge under exclusive contracts. This is important because many of the rebate contracts we observe in practice, 5 and in particular those examined in antitrust cases (e.g., Commission v. Michelin II, Commission v. British Airways, and Allied Orthopedic v. Tyco), share these characteristics. There is nevertheless a way in which the incumbent can alleviate the easy terminability and restore the anticompetitive potential of rebates, at least in the three settings previously discussed. Despite it is neither mentioned nor identified in any of the antitrust cases listed above, up-front transfers from retailers to manufacturers can help. Indeed, by demanding an unconditional fee at the time the contract is signed, the incumbent can now persuade the buyer to conform to the exclusivity by offering large rewards ex-post, without sacrificing surplus. 6 4 In principle, rewards for, and therefore penalties for not reaching the target can be made arbitrarily large. 5 For example, the rebates used by the chocolate and candy manufacturer Mars with retail vending operators, as documented by Conlon and Mortimer (2014). 6 Some of the cases listed do show, however, upfront payments going from the incumbent to the buyers. These are usually innocuous in our model, except when buyers are downstream competitors. Using lump-sum rebates as opposed to off-the-list-price rebates allows the incumbent to bribe buyers not to deal with alternative suppliers without affecting retailers pricing decisions at the margin. See Section 5, which builds upon Asker and Bar-Isaac 5

6 As we show in the paper, this opens up an opportunity for the incumbent to profitably offer anticompetitive rebates in some circumstances. This latter possibility, however, raises yet another question: if rebates without up-front payments cannot be used to block (efficient) rivals, why do we see them so often in the first place? Like the exclusives in Innes and Sexton (1994), we briefly discuss (in Section 2) that in our model such rebates can still be optimally used to deter inefficient entry. Nevertheless, it is important to emphasize that we are primarily interested in understanding how rebate contracts perform from an anticompetitive perspective, so we abstract ourselves from any efficiency-based rationale for rebates, such as relationship-specific investments, screening, moral hazard, to name a few; and concentrate on a model where the only reason for eventually signing these contracts is to exclude efficient rivals. Our aim then, is to provide antitrust authorities with some logical consistency checks that may help better assess monopolization claims involving rebates. In that regard, our analysis suggests that authorities should not only look at market conditions when evaluating the (allegedly) anticompetitive potential of a rebate contract, but also at the specific features of the contract in question, given that our results indicate quite clearly which of them are essential for exclusion. The rest of the paper is organized as follows. In Section 2 we present the basic ingredients of our model that form the basis of the of rent-shifting model of Aghion and Bolton (1987), the naked-exclusion models of Rasmusen et al. (1991) and Segal and Whinston (2000b), and the downstream-competition model of Asker and Bar-Isaac (2014); henceforth AB, RRW, SW and ABI, respectively. Sections 3, 4 and 5 take the model to the setups of AB, RRW-SW and ABI, respectively. We conclude in Section 6 with a closer look at some of the antitrust cases listed above and a brief discussion regarding why up-front payments are so relevant for exclusion. 2 The model 2.1 Notation Consider a unit mass of final consumers with reservation value v for a good that can be supplied by two (risk-neutral) manufacturers. Manufacturer I is an incumbent supplier that can produce the good at a constant marginal cost c I < v. Manufacturer E, on the other hand, is a potential entrant that can produce the good at constant marginal cost c E < v but only after sinking a (2013). 6

7 fixed entry cost F. Our only departure from the basic structure of existing models (e.g., AB, RRW, SW and ABI) is that only a fraction λ < 1 of final consumers see no difference between I s and E s products; the remaining fraction buy either I s products or nothing at all. In the language of the EU Commission (2009), λ is the contestable demand, which in most antitrust cases is thought to be rather small. In addition, and given our focus on the possibility of I writing anticompetitive rebates, we assume entry is efficient, that is c E + F/λ < c I, unless otherwise indicated. Manufactures do not supply directly to final consumers but indirectly through (risk-neutral) retail buyers, who, for simplicity, have no costs other than the costs of purchasing the good from one or both manufacturers. We will consider settings of one retail buyer (as in AB), two independent retail buyers each monopolistically serving half of the market (as in RRW and SW), and two retail buyers competing intensely for final consumers (as in ABI). We denote these buyers by B, or B1 and B2 if there is more than one, and use feminine pronouns to refer to them. The timing of the game in any of these settings is as follows. At date 1, I can make a takeit-or-leave-it contract offer to B (or to B1 and B2). The form of the contract offer is specified below as we will consider both rebate and exclusive contracts. At date 2, is E s turn to make a take-it-or-leave-it price offer to B for his λ units. 7 Then, at date 3, E decides whether to enter or not. If he does not, his offer is automatically canceled, and if he does, he pays the entry cost F. Finally, at date 4, B decides how much to buy from each supplier according to the conditions established in I s contract and E s offer provided this latter has entered. Otherwise, B is served through the spot (wholesale) market where I and E compete in (non-linear) prices On the exclusionary potential of rebates To better understand the controversy surrounding rebate contracts, consider the simplest possible case where I and E must deal with a single monopoly retailer who afterwards charges v to final consumers. 7 Since E may be relatively small, it is important to point out that our main results do not change if the bargaining power between I and E is more evenly split. 8 Note that non-linear pricing leads to efficient spot competition, as in existing models of linear pricing with λ = 1 (e.g., AB, RRW, SW). In an earlier version we introduced spot inefficiencies by restricting firms to set linear prices and show that none of our results change. This variation of the spot equilibrium is in the Online Appendix. 7

8 Consider then a rebate contract (r, R) offered by I to B, where r v is the list price and R is a off-list-price discount applied to all units provided B buys exclusively from I. In this scenario and under this contractual arrangement, B faces a unit price of r when purchasing q < 1 units from I and r R when purchasing q = 1. In this unit-demand and linear-cost case, it is easy to see that it is optimal for I to require full exclusivity, if anything. 9 If B signs the contract (r, R), E can still induce B to buy λ units from him if she is compensated for the forgone rebate. For that to be the case, E s wholesale price offer w E must satisfy v (1 λ)r λw E v r + R or w E r R/λ. Therefore, to block E s entry, I must set the effective price x r R λ slightly below E s break-even price, that is, c E + F/λ. There are two observations to make. The first is that focusing on contracts with r v is without loss of generality because they are strictly superior to contracts with r > v. In fact, if r is increased above v and R is increased accordingly to keep r R unchanged, I s profit under exclusivity is the same, r R c I, while the effective price associated to this new contract is strictly higher x = r R λ + 1 λ (r v) λ reducing its foreclosure potential, unless I further increases R and gives up some profit. This is not surprising because B will not be buying units from I if she decides to buy some from E. A more fundamental observation is that the effective price x = r R/λ differs from r R precisely because λ < 1, which is what allows I to leverage his position. It is for this reason that it appears relatively easy to conceive a profitable (actual price above cost), yet anticompetitive (effective price below cost), rebate scheme when λ is particularly small r R λ < c I < r R (1) It is not surprising then the great deal of attention and controversy around the estimation of the contestable demand that we have seen in some recent cases; notably, EU Commission v. 9 If I sets the rebate threshold below a 100% he would need to increase R to produce the same exclusionary effect. Notice moreover that this exclusivity condition could be always replicated, at least in this simple setting, using a quantity threshold q = 1 instead. 8

9 Intel (in the concluding section we come back to this case). Our point of departure in this paper is that this leverage theory does not work for rebates because the exclusivity must be implemented ex-post, not ex-ante. As we will see next, this difference in implementation matters a great deal, so much that regardless of how small λ may be, a rebate contract (r, R) cannot be used to exclude efficient rivals in settings where exclusives can. But before doing that, it is worth explaining that rebates (r, R) can still be used to block inefficient entry, very much like the exclusives in Innes and Sexton (1994). Take for example a potential entrant E with costs such that c I < c E + F/λ < v. We know that if I and B fail to sign a rebate contract at date 1 and E does not enter at date 3, then, B ends up buying everything in the spot from I at price v. Therefore, in the absence of a rebate contract, E and B can agree on a contract where the latter commits to buy λ units from the former at a unit price w E (c E + F/λ, v), even if c E + F/λ > c I. The exact value of w E will split the surplus λ(v c E ) F between B and E according to their bargaining powers. This is equivalent to B subsidizing E for (a fraction of) the sunk cost F, so as to increase competition in the spot market. Notice however, that regardless of how B and E split the surplus, I can always offer a rebate contract to block E s entry since he has more surplus to offer. 10 Interestingly, this form of using rebates to deter (inefficient) entry/expansion conforms well to the developments in Barry Wright v. ITT Grinnell (1983) The AB setup: Contracting with unknown costs In an AB setup there is a single buyer, B, that like I, does not know c E at the time of contracting; they only know that c E distributes according to the cdf G( ) over the support [0, c I F/λ], which ensures that entry is socially efficient for any possible realization of c E. As usual, G/g is non-decreasing and (1 G)/g is non-increasing. The AB set up also assumes that E s offer at date 2, if any, does not lead I and B to renegotiate a contract signed at date 1, which would be 10 The effective price x = v R/λ must be such that λ(v x) λ(v c E) F, that is, it must be low enough to prevent E to come up with an offer that B might accept. 11 As documented by Kobayashi (2005), ITT Grinnell, a manufacturer of pipe systems for nuclear power plants, agreed to contribute to Barry Wright s cost to develop a full line of mechanical snubbers, essential component in pipe systems, presumably to improve its negotiation power with Pacific, the existing dominant supplier of mechanical snubbers. Pacific reacted to Grinnell s deal with Barry Wright with a rebate contract offer that Grinnell could not resist; it included discounts of 30-25% off list price if Grinnell would agree to purchase virtually everything from Pacific. 9

10 the case if B is the only one informed about E s price offer (and c E is still unknown to I and possibly, but not necessarily, to B). 12 In any case, the value of c E becomes publicly known at the opening of the spot at date 4. Finally note that there is no loss of generality in this setup in letting F No-contract benchmark Suppose the only way for I and E to serve the buyer is through the spot market. Since entry is efficient, the equilibrium in non-linear prices involves E entering and offering his units at a price slightly below c I, while I offering a two-part tariff with marginal cost c I and a fixed fee of (1 λ)(v c I ). π NC I = (1 λ)(v c I ), π NC E Therefore, payoffs in this no-contract benchmark are, respectively, = λ(c I c E ) and π NC B = λ(v c I). Note that it makes no difference to these outside payoffs if in the absence of a contract between I and B, E makes a price offer to B at date 2. The maximum surplus the buyer-entrant coalition can achieve with these offers is λ(v c E ) F, 13 which is exactly equal to π NC E + πnc B. 3.2 The AB exclusive To better appreciate how rebates work in the AB world it helps to see first how exclusives do. An AB exclusive includes a wholesale price w and a penalty D (liquidated damages) in case B decides to buy from E. Since the effective price E must charge to make a sale is w D/λ (just like in the rebate contract of Section 2) and B pays w for each unit regardless of entry, the AB program that I solves is (recall that F 0) max w,l Eπ I(w, D) = [(1 λ)(w c I ) + D] G(w D/λ) + (w c I ) [1 G(w D/λ)] (2) subject to B s participation, that is, v w πb NC. In the case of entry, which happens with probability G(w D/λ), I sells 1 λ units at price w and gets compensated in D for the λ units B buys elsewhere; otherwise he is the only one selling at price w. Solving (2) leads to the well known AB exclusionary outcome w D λ = c E c I G( c E) g( c E ) 12 Dewatripont (1988) was the first to show that contracts as commitment devices are renegotiation-proof if one introduces asymmetric information at the renegotiation stage. 13 If E and B can themselves sign exclusive contracts with arbitrarily high liquidated damages (i.e., above expected damages), they can potentially leave I with no surplus, which seems very unlikely in any of the cases we have discussed of relatively small entrants. (3) 10

11 and w = v π NC B. If we plug this latter and D = λ(w c E ) into (2), we obtain Eπ I (w, D ) = (1 λ)(v c I ) + λ(c I c E )G( c E ), which is greater than π NC I since c E < c I. As first shown by AB for λ = 1, these contracts are not only profitable for both I and B to sign, but they have anticompetitive implications in that they block the entry of some efficient rivals, those with costs c E [ c E, c I ]. As discussed by Masten and Snyder (1989), and more recently by Simpson and Wickelgren (2007), the exclusionary potential of these exclusives is subject to the possibility of using penalties that can be enforced in court. If, as the legal practice in common law countries seem to suggest, an exclusive contract cannot rely on penalties above the expected damages that I will experience in the event B breaches the contract, i.e., D λ(w c I ), then, the exclusive losses its exclusionary grip altogether, i.e., w D/λ c I. Given this legal constraint, it is natural that the attention has shifted towards alternative vertical practices with apparently similar exclusionary potential such as rebates. We turn to this now. 3.3 Rebate contracts Consider the rebate contract (r v, R) introduced in Section 2. Since E will enter only if his cost c E is below the effective price r R/λ, I s expected payoff in case B accepts the contract is equal to Eπ I (r, R) = (1 λ)(r c I )G(r R/λ) + (r R c I ) [1 G(r R/λ)] (4) where the first term is the profit from selling 1 λ units at price r, which happens when there is entry and the rebate R is not granted, and the second term is the profit from selling all the units at price r R, which happens with probability 1 G(r R/λ). There is an apparent similarity to the exclusive above that is hard to overlook. In fact, one can arrive at (4) from (2) by simply relabeling w as r R and D as (1 λ)r. This apparent similarity show that the exclusivity clause could be made equally costly to break under either contract, in one case by paying the penalty D while in the other by giving up an equivalent amount (1 λ)r for the forgone rebate on the 1 λ remaining units. This is important because it shows that the easy terminability of rebates we refer to does not lie on the idea that the exclusivity is necessarily cheaper to break under rebates. It lies on whether the exclusivity is implemented ex-ante or ex-post, so much that 11

12 Proposition 1. Even when the costs of an efficient rival E are unknown, it is not profitable for I to offer an anticompetitive (r, R) rebate. Proof. Suppose the contrary, that it is profitable to set x r R/λ < c I. If so, it must be true then that Eπ I (r, R) πi NC. Using x = r R/λ to replace R = λ(r x) in the expected payoff Eπ I (r, R) in (4), we obtain that condition Eπ I (r, R) π NC I But since π NC I 0 is equivalent to [(r c I )(1 λ) π NC I ] + λ(x c I )[1 G(x)] 0 (5) = (1 λ)(v c I ) and r v, the first term in (5) is non-positive, which requires the second term to be non-negative. But since G(x) < 1 because x < c I, we must have x c I, a contradiction. The proof and the intuition of the proposition follows what we already discussed for the simple example in the introduction. B is the one that benefits when I, and eventually E, sets (effective) prices below c I for the last λ units. And since it is ex-post unfeasible for I to require B to transfer part of those benefits back to him, at least enough to cover his outside payoff, he will never agree on an anticompetitive rebate. This ex-post implementation problem gives rise to what we call the easy terminability of rebates. The exclusive contract (w, D ) does not face this ex-post implementation problem because D is contractually committed ex-ante, so B does not capture any additional benefits ex-post from the low effective prices induced by the penalty D; she only serves as a vehicle to transfer the penalty D from E to I, in case there is entry. In light of the legal restrictions affecting exclusives and the implementation problems affecting the rebates of Proposition 1, one wonders if more complex rebate contracts can be of any help. Despite it is neither mentioned nor identified in any of the antitrust cases listed earlier, including an up-front payment Z from B is the only way for I to restore the exclusionary potential of rebates. 14 Proposition 2. There are many ways for I to design a rebate contract (r, R, Z) that replicates the AB exclusionary outcome (3), from the one with the lowest up-front payment, (r = v, R = λ(r c E ), Z = λ(v c E ) πb NC), to the one with the highest, (r = c E, R = 0, Z = v c E πb NC). Proof. Immediate as r R/λ = c E and Eπ B (r, R, Z) = π NC B under either contract. 14 As we showed in an earlier version of the paper, the two-step schedule (r, R) is the best (ex-post) schedule I can offer. 12

13 By demanding an unconditional fee at the time the contract is signed, I can now persuade B to sign an exclusionary rebate with large rewards ex-post (i.e., r R/λ < c I ) but without sacrificing any profits (i.e., Eπ I (r, R, Z) π NC I ). In other words, I can now trade ex-post rewards for ex-ante transfers, allowing him to extract rents not only from B but also from those entrants that decide to enter. And as long as I and B have some uncertainty about c E, so that g(c E ) has full support over the [0, c I ] interval, extracting rents from E will not be perfect and some exclusion will necessarily occur. Only when c E is known (or the support sufficiently away from from c I ) these rebates achieve perfect rent extraction and with that no exclusion of efficient entrants whatsoever The RRW-SW setup: Contracting with buyer externalities In the previous section we showed that rebates (r, R) were never anticompetitive when only one retailer was involved. Intuitively, the easy terminability of rebates made exclusion unprofitable as the incumbent had no means to recoup the large ex-post rewards needed to sustain the exclusionary outcome; unless, of course, if he could pay for any ex-post reward with an equivalent ex-ante unconditional payment from the same buyer. Whether this intuition can be extended to other settings is not immediately obvious. Consider for example the situation of multiple buyers and scale economies of RRW and SW, where I needs only to lock-up a subset of buyers to deny E from the minimum viable scale of operation. In this situation, offering rebate contracts to a subset of lucky buyers reduces the likelihood of entry, making it easier to fully exploit the remaining buyers. It appears then that I has found a new source of funding to pay for ex-post rewards with, presumably, no need for up-front payments: the unlucky buyers. We will show however that the ex-post implementation problem of rebates still extends to this multiple-buyer setting. The reason is that in the end both suppliers, I and E, compete for the lucky buyers, as the others get to be fully exploited by both of them. So, as in AB, exclusion is possible only when up-front payments are contractually available. To convey our ideas, we will consider the simplest possible case that allows us to extend our model into the world of RRW-SW. Consider then two retail buyers, B1 and B2, each serving 15 Exclusion may also be unlikely when Z s are somehow restricted, whether for limited liability and/or asymmetric information reasons; see Ide et. al. (2015). Since I has some flexibility to design these rebates, as Proposition 2 indicates, a complete treatment of the issue can be found in the Online Appendix. 13

14 half of the final consumers in completely separate markets, and assume that E s fixed entry cost F is such that λ(v c E )/2 < F λ(c I c E ) (6) Where we are using the fact that the price downstream is equal to v in both market segments, as retailers are local monopolies. The first inequality indicates that E must necessarily deal with both buyers to make enough profit to cover his fixed cost while the second inequality is the efficient entry condition. These inequalities restrict the value of the parameters to v 2c I +c E In contrast to AB, the simplest RRW-SW environment involves no uncertainty over c E, though results do not changed if we keep c E unknown as in the previous section (see the Online Appendix for a formal treatment of this case). In this kind of settings there is always a myriad of equilibria, as a buyer s best response is to accept any exclusionary offer if she conjectures that the other buyer will also accept. To avoid such coordination failures, we will follow the literature and assume that buyers can communicate with each other but cannot sign binding agreements. Therefore, the equilibrium concept we adopt is perfect coalition-proof Nash equilibrium, as defined in Bernheim et al. (1987). Even though it may appear that buyers communication makes exclusion harder, I can circumvent it by using a divide-and-conquer strategy that discriminates among buyers. first noted by Innes and Sexton (1994), I may find it worthwhile to induce one of the buyers (the lucky one) to sign an exclusionary contract because by doing so he can fully monopolize the other buyer (the unlucky one) without paying her anything. As later pointed out by SW, the cost of implementing this divide-and-conquer strategy depends on whether at date 1 the incumbent approaches the two buyers simultaneously or sequentially. We will assume the former since it is the standard in the literature, though our results do not depend on it. 17 Before going through the exclusionary results of RRW and SW and explaining why rebates fail to replicate them, we present the equilibrium outcome when I does not offer any contract or when both buyers reject I s offers. Lemma 1. If I does not contract with B1 and B2 at date 1, then E is indifferent between making offers to any of the buyers or going directly to the spot at date 4. In either case, the 16 This may look restrictive, though it is an artifact of our two buyer assumption. 17 Essentially, what sequential offering does is to allow I in some circumstances to extract more rents from buyers and entrants, though the qualitative nature of equilibria stays the same. As 14

15 no-contract payoffs are πi NC = (1 λ)(v c I ), πe NC = λ(c I c E ) F and πbi NC = λ(v c I )/2 for i = 1, 2. Proof. See Appendix A. 4.1 Exclusive contracts We will now show that the exclusionary results of RRW and SW still apply in our slightly different structure, 18 but we will be brief because these results are well known. Following RRW- SW, suppose that at date 1 I offers buyers exclusive contracts, and buyers decide whether to accept or reject them. An RRW-SW exclusive is a transfer t i at date 1 from I to Bi in exchange for the buyer s promise not to buy from E ever (breaching the contract entails penalties infinitely large). As standard in the literature of exclusives (e.g., RRW, SW and ABI), we assume that the terms of the contract, other than the compensation t i, are specified at date 4. Proposition 3. (after RRW and SW) It is profitable for I to deter E s entry with a pair of exclusive contracts with compensations t 1 = π NC B1 + ɛ and t 2 = ɛ with ɛ 0, or vice versa. Proof. It is clearly an equilibrium for both B1 and B2 to accept these exclusives. B1 gets nothing if she rejects her offer and B2 does not because in that case E does not enter and I charges v in the spot. Similarly, B2 gets zero if she rejects her offer and B1 does not because again E does not enter. Note also that despite B2 and B1 would be, on aggregate, better off if they both reject their offers (and obtain a total of π NC B1 + πnc B2 ), the absence of binding agreements rules out such coordination, i.e., B2 cannot credibly commit to any compensation that would induce B1 to reject her offer in the first place. Finally, it is easy to see that foreclosure is a profitable strategy for I in that π I = v c I t 1 t 2 = (1 λ/2)(v c I ) > (1 λ)(v c I ) = πi NC. The proposition shows that it pays I to induce one of the buyers to sign an exclusive for slightly more than her outside option πb1 NC, because by doing so he can fully exploit the other buyer. 19 Because this divide-and-conquer strategy relies on infinitely large breaching penalties, 18 The models of RRW and SW assume a downward sloping demand, which creates an additional efficiency loss from linear monopoly pricing. As first noticed by Innes and Sexton (1994), this loss is not needed for (naked) exclusion to exist and is most reasonable to assume it away for wholesale markets as firms can always use non-linear prices. Our inelastic demand model intends to capture this in the simplest possible way. 19 This result is robust to different buyers outside options. Suppose each buyer s outside option is half the social surplus E brings to market, λ(v c E) F. It still pays I to compensate the lucky buyer provided v is not too close to c I. 15

16 it remains to see how that may change when arbitrarily large penalties cannot be enforced in court. We know from the single-buyer setting of AB that exclusion is unfeasible if liquidated damages are subject to a cap equal to expected damages, i.e., I s expected losses in case of breach. Simpson and Wickelgren (2007) show that same result extends to the RRW-SW setting, which eliminates the exclusionary potential of exclusives. 4.2 Rebate contracts Proposition 3 opens up the possibility that I could go around the easy terminability of rebates identified in Section 3 by discriminating among buyers, that is, by offering a very attractive (r, R) contract to one of the buyers to be paid by fully exploiting the other one. This is especially relevant considering that rebates, as opposed to exclusives, do not suffer from any efficient-breach considerations since R is not exogenously constrained. The main proposition of this section, however, establishes: Proposition 4. Even in the presence of externalities across buyers, it is not profitable for I to use rebates (r, R) to deter E s entry. Proof. Begin by relabeling (r, R) as (r, x), where x r R/λ. To foreclose E s entry, I must offer at least to one of the retailers, say B1, a rebate contract (r 1, x 1 ) that is ex-post superior to the best offer E could come up with. Since B2 gets zero if B1 gets locked-in, E would offer virtually nothing to B2 and as much as needed to B1 to induce her to switch. Hence, I s rebate offer to B1 must satisfy the ex-post implementation constraint (v (1 λ)r 1 λx 1 )/2 > λ(v c E ) F + (1 λ)(v r 1 )/2 (7) or equivalently λ(v x 1 )/2 > λ(v c E ) F. The left-hand-side of (7) is B1 s payoff if she sticks to the rebate contract and the right-hand-side is her payoff if she switches, which includes the most E can possibly offer her for agreeing to sell λ/2 units of his product, λ(v c E ) F, plus the gain from selling (1 λ)/2 units of I s product. Notice that the way for E to offer B1 the entire entry surplus is with a pair of offers at date 2 under which both buyers agree to buy from him λ/2 units, B2 at price w E2 = v ɛ and B1 at price w E1 = 2F/λ + 2c E v, where this latter is obtained from E s break-even condition λ(w E1 c E )/2 + λ(w E2 c E )/2 F = 0 16

17 On the other hand, I s payoff is v c I λ(v x 1 )/2 when exclusion goes through and (1 λ)(v c I ) = π NC I when it does not. Therefore, I will find it profitable to exclude whenever λ(v c I ) λ(v x 1 )/2 (8) Making λ(v c I ) = λ(v x 1 )/2 and replacing the resulting x 1 into (7) implies that exclusion is possible only if λ(v c I ) > λ(v c E ) F = λ(c I c E ) F < 0, that is, only if E is inefficient, a contradiction. The intuition for this result follows that of Proposition 1. To block E s entry, I must offer such an attractive reward to one of the buyers that he has no means to make up for it ex-post, even if he can fully exploit the other buyer. One may say that the easy terminability of rebates (or ex-post implementation problem) extends so naturally from the single-buyer setting to this multiple-buyer setting because in the end both suppliers compete for the attention of just one buyer, B1, as B2 gets to be fully exploited by both of them. The fact that I tries to exploit the unlucky buyer B2 in the first place is what allows E to do likewise, so the same (ex-post) rents coming from B2 that I is using to pay for the rebate to B1 are also used by E to induce B1 to switch. This ex-post implementation prevents I from taking advantage of any externality across buyers, which does not happen with the exclusives of Proposition 3 because the exclusivity is contracted ex-ante. 20 As already seen for the single-buyer case, there is a way for I to go around the easy terminability problem and deter E s entry: to demand an up-front payment at date 1. In fact, if the up-front payment can be made large enough, I can fully replicate the exclusionary outcome of Proposition 3 with the rebate offer (r 1 v, x 1, Z 1 ) that satisfies (v (1 λ)r 1 λx 1 )/2 Z 1 = π NC B1 while still complying with condition (7). This allows I to foreclose E s entry at the minimum possible cost, πb1 NC, while fully exploiting the remaining buyer. If up-front payments are available, one can go further and ask if I can do better than just deterring E s entry. In Appendix B we establish the form of the most profitable rebate contracts I can offer when up-front payments have no restrictions. Consistent with the exclusives in Innes and Sexton (1994) and in Spector (2011, section 4) that include breach penalties as vehicles to 20 While formally shown in the Online Appendix, it should be clear that the exclusionary result of Proposition 5 extends to the case in which c E is unknown at date 1, simply because exclusion is not profitably for any possible realization of c E. 17

18 transfer rents, the rebates in Appendix B lead to no inefficiencies with I pocketing the entire social surplus but π NC B1 + ɛ. By locking up just one of the retailers, B1, I can fully exploit B2 while simultaneously extract the entirety of E s efficiency rents. This no distortion result however, is clearly not robust. For instance, rent extraction would be incomplete when c E is unknown, in which case again, there will be exclusion of some efficient entrants even when (r, R, Z) contracts are at hand The ABI setup: Contracting with downstream competition Up to now, we have restricted our attention to settings where retailers were assumed to be local monopolies. However, this assumption does not fit well in a number of relevant antitrust cases. In AMD v. Intel for instance, the market structure consisted of a dominant incumbent manufacturer, Intel, and a small alternative supplier, AMD, selling microprocessors to Original Equipment Manufacturers (or OEM s) such as IBM, Dell and Lenovo, which in turn competed intensely for final consumers like all of us. In this section we analyze the implications of the easy terminability of rebates in such a setting, by assuming that B1 and B2 are not local monopolies, but rather undifferentiated Bertrand competitors, just like in ABI. The effects of downstream competition on upstream exclusion are not obvious. The initial observation, first raised by Fumagalli and Motta (2006), is that if retailers are downstream Bertrand competitors, then scale economies become irrelevant and with that any possible externality across buyers, since access to one retailer is all the entrant needs to reach the entire final market. This does not imply, however, that upstream exclusion is impossible in such a setting; on the contrary, intense downstream competition may be the cause of exclusion in the first place. Indeed, as later pointed out by Simpson and Wickelgren (2007) and Abito and Wright (2008), when retailers are intense downstream competitors small compensations may be enough to induce them to sign exclusive contracts that prevent entry. More recently, ABI have explained that because entry is likely to intensify upstream competition and dissipate industry profits in the form of lower prices to final consumers, the incumbent can afford even larger compensations to retailers, which are paid with the rents the incumbent keeps as a result of less competition. In this section we go over some of these results as they are important to understand the work of rebates in a downstream competition set-up. But to do that we need to introduce some 21 The formal argument can be found in the Online Appendix. 18

19 additional notation and assumptions. First, to simplify notation we assume that if two retailers offer the same price to final consumers but one has a lower marginal cost than the other, then all final consumers buy from the retailer with the lower cost. 22 Second, we assume that retailers can price discriminate between consumers in the non-contestable portion of the demand (the 1 λ segment) and those that are in the contestable portion (the λ segment). We will denote by p i,1 λ the retail price that retailer i = 1, 2 charges for I s products to final consumers in the 1 λ segment and by p i,λ the price she charges for both I s and E s products to final consumers in the λ segment. While one reason for adopting this latter assumption is tractability, 23 it actually has practical appealing. Imagine one of the OEM s above buying chips from both Intel and AMD. It would be easy for this OEM to price discriminate among contestable and non-contestable consumers by for example placing the exact same Intel chip in machines that do not look alike (similar to a damaged good strategy). 5.1 No-contract benchmark and consumer welfare Consider first the situation when E does not enter the market. In this case, the set of prices I can charge in the spot market is vast: any pair of non-linear schedules that maximize industry profits while leaving retailers with zero surplus is optimal from I s perspective. One possibility is to charge both retailers wholesale prices w I1 = w I2 = v without any fixed fees, so that they share the final market equally. Another one is to price discriminate among them and offer the 2PT {w I1 < v, T I1 = (1 λ)(v w I1 )} to B1 and the linear price w I2 v to B2, which would channel all sales through B1. In either case, retail prices for the contestable and non-contestable fraction of the demand are p 1,1 λ = p 2,1 λ = p 1,λ = p 2,λ = v as in the single-buyer case, leaving final consumers with no surplus. The situation changes for final consumers when E enters because any upstream competition for the contestable λ units is passed through by the Bertrand retailers. Given that retailers can price discriminate between consumers that only buy from I and those that can buy from either 22 Assuming otherwise would imply that equilibrium prices are a penny lower. 23 In Appendix C we work with the alternative assumption that retailers can set different prices for I s and E s products, as opposed to different prices across different segments of demand. Despite the retailers pricing game is similar to one of linear prices with capacity constraints, there is nevertheless an equilibria in pure strategies, largely because suppliers are free to make distinct offers upstream. More importantly, none of the results that follow change. 19

20 supplier, suppliers are effectively competing upstream in two separate markets, the contestable and non-contestable markets. The way for I to set different prices in these two markets while simultaneously extracting all retail rents in the non-contestable market is by charging a 2PT to one of the retailers, say B1, and a linear price to B2, that is, w I2 w I1 and {w I1, T I1 = (1 λ)(w I2 w I1 ) 0}. Notice that w I1 is the price that I is actually using to compete with E for the contestable consumers. Since this price cannot be below cost, w I1 c I, E s optimal reaction to I s prices is any combination of linear or 2PTs to either one or both retailers that just undercut w I1 ; for example, w E1 = w E2 = w I1, or w E1 > v and {w E2 < w I1, T E2 = λ(w I1 w E2 ) 0}. It is easy to see that in equilibrium I will set w I1 = c I and w I2 = v, which implies that p 1,1 λ = p 2,1 λ = v and p 1,λ = p 2,λ = c I. In equilibrium only one retailer will carry I s products but either one or both will carry E s products. Compared to the no-contract benchmark of the monopoly-retailer case (Section 3), suppliers are exactly as before (i.e., π NC I retailers are strictly worse off (i.e., π NC B1 = (1 λ)(v c I ) and π NC E = πnc B2 = λ(c I c E ) F ), while = 0). Any retailer s surplus is now in the hands of final consumers in the form of lower retail prices for the λ contestable units. The reason for this surplus transfer is that here retailers only provide access to final consumers, and because of Bertrand competition, access can be achieved with just one retailer. From a consumer perspective, this no-contract benchmark is clearly better than the nocontract benchmarks in the AB and RRW-SW settings where all consumers always paid v. This adds a new dimension regarding the effect of contracts on industry outcome. Hence, in addition to their effect on exclusion, we now need to pay attention to their effect on final prices. In a way, this broaden the definition of what makes a contract to be anticompetitive. In the settings of AB and RRW-SW settings, it is simply if it deters efficient entry. Now, it is not only that but also if it leads to higher retail prices, whether along with exclusion or not. 5.2 Exclusives As already noted by Simpson and Wickelgren (2007) and Abito and Wright (2008), the introduction of downstream competition can also have a significant effect on I s ability to deter efficient entry with the use of exclusives. If before (i.e., in Proposition 3) exclusion required important scale economies and leaving the lucky buyer with enough surplus, now fixed costs are immaterial though locking-up buyers is virtually costless. Proposition 5. Consider the RRW-SW exclusives that consist of a compensation t i and a 20