On the competition enhancing effects of exclusive dealing contracts

International Journal of Industrial Organization 31 (2013) 429–437

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International Journal of Industrial Organization journal homepage: www.elsevier.com/locate/ijio

On the competition enhancing effects of exclusive dealing contracts☆ Linda Gratz a, Markus Reisinger b,⁎ a b

E.CA Economics, Schlossplatz 1, 10178 Berlin, Germany Economics Department, WHU - Otto Beisheim School of Management, Burgplatz 2, 56179 Vallendar, Germany

a r t i c l e

i n f o

Article history: Received 26 June 2012 Received in revised form 28 February 2013 Accepted 22 July 2013 Available online 27 July 2013 JEL classification: D43 K21 L12 L42

a b s t r a c t Antitrust scholars have argued that exclusive contracts have anticompetitive, or at best neutral effects, if no efficiencies are generated. In contrast, this paper shows that exclusive contracts can have procompetitive effects, provided buyers are imperfect downstream competitors and contract breach is feasible. In that case, an efficient entrant is not necessarily foreclosed through exclusive contracts but induces buyers to breach. Because breaching buyers have to pay expectation damages to the incumbent, the downstream profits they obtain when breaching must be large enough. Therefore, the entrant needs to set a lower wholesale price than absent exclusive contracts, leading to lower final consumer prices and higher welfare. © 2013 Elsevier B.V. All rights reserved.

Keywords: Exclusive contracts Contract breach Antitrust policy

1. Introduction In many recent antitrust cases incumbent upstream firms were alleged of having used exclusive contracts to foreclose potentially more efficient entrants, thereby harming consumers.1 In these cases courts need to balance anticompetitive effects caused by increased wholesale prices against potential efficiency gains created through exclusive contracts within the vertical production chain. Several authors (e.g., Aghion and Bolton, 1987, or Segal and Whinston, 2000) have demonstrated that exclusive contracts by an incumbent firm can make entry more difficult or deter it altogether. Exclusive contracts then lead to higher prices, and therefore have anticompetitive effects. On the other hand, efficiency gains may arise due to service or effort provisions by buyers (see e.g., Mathewson and Winter, 1984). Only if these efficiency gains are large, exclusive contracts may have procompetitive effects.

☆ A previous version of this paper was circulated under the title “Can Naked Exclusion be Procompetitive?”. We are very grateful to Bernard Caillaud (the editor), two anonymous referees, Chiara Fumagalli, Bernhard Ganglmair, Fabian Herweg, Klaus Schmidt, as well as to seminar participants at the University of Düsseldorf, at the University of Munich, at the EARIE conference 2011 in Stockholm, at the EDGE Jamboree 2011 at Bocconi University, and at the IMPRS-CI/ETH Workshop 2011 in Wildbad Kreuth for helpful comments and suggestions. ⁎ Corresponding author. Tel.: +49 261 6509 290; fax: +49 261 6509 289. E-mail addresses: [email protected] (L. Gratz), [email protected] (M. Reisinger). 1 Recent examples are United States vs. Transitions Optical, AMD vs. Intel, and Pernod Ricard and Campbell Distillers vs. Bacardi-Martini. 0167-7187/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijindorg.2013.07.008

In this paper we challenge this conclusion. In particular, we point out that exclusive dealing contracts can have procompetitive effects even if no efficiency gains are generated. In a nutshell, the economic mechanism for this result is as follows: If competition between buyers is relatively intense, each buyer has an incentive to sign an exclusive dealing contract with the incumbent because the upfront payment guarantees the buyer some profits. An entrant must then induce the buyers to breach the exclusive dealing contract in order to make profits. Since buyers have to pay damages to the incumbent when breaching a contract, the entrant has to offer them a low wholesale price to make breach of contract profitable. This low input price then leads to lower final consumer prices, thereby rendering exclusive dealing contracts procompetitive. Let us explain this intuition in more detail. First, we look at the counterfactual scenario, when exclusive contracts are not allowed. In this case the upstream entrant is not foreclosed and competes against the incumbent. Given that there is Bertrand competition between upstream firms, the more efficient entrant sets its wholesale price equal to the incumbent's production cost and serves the entire market. If downstream buyers produce differentiated goods, they obtain positive profits, which we denote by π. If exclusive contracts are allowed, the incumbent will make use of such exclusive contracts, provided it can profitably induce the downstream buyers to sign. For signing, it has to offer the downstream buyers a compensation that ensures them a profit of π. If downstream competition is relatively intense, the incumbent can indeed profitably use exclusive contracts, since π is then small. If downstream firms have signed

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the exclusive contracts, the incumbent will set its wholesale price at the monopoly level. Although downstream firms have signed the exclusive contracts, the entrant will enter if it can profitably induce the downstream firms to breach the exclusive contracts. When a downstream firm breaches, it must compensate the incumbent the foregone profit. Therefore, to render breach of contract profitable, the entrant has to set a sufficiently low wholesale price. If downstream competition becomes more intense, the profit the downstream firms can obtain when breaching decreases, implying that the entrant needs to set a lower wholesale price in order to render breach of contract profitable. In particular, when downstream competition is moderate, the wholesale price the entrant needs to set to induce both downstream firms to breach lies below the incumbent's production cost. It follows that for moderate degrees of downstream competition, the downstream firms will breach the exclusive contract and buy from the entrant at a lower wholesale price than absent exclusive contracts. Since the downstream firms receive the input good at a lower wholesale price, they set lower prices to final consumers which makes exclusive contracts procompetitive. We show that this mechanism occurs for a general class of demand functions. Our analysis uses the framework developed by Simpson and Wickelgren (2007), which considers exclusive dealing contracts and allows for the possibility of contract breach. This possibility is of high practical relevance since common law provides each party to a contract the opportunity to breach that contract by paying expectation damages to the injured party. While in some situations breach of contract may indeed be prohibitively costly due to reputational reasons or high litigation costs, it seems unreasonable to assume generally that contract breach is not feasible. In their model, Simpson and Wickelgren (2007) analyze the cases in which downstream firms are either final consumers or (almost) perfect Bertrand competitors. They find that in the first case the effect of exclusive contracts is neutral. If downstream firms do not compete, the incumbent's gain in profit through entry deterrence is lower than the downstream firms' loss in profit. Therefore, the incumbent is unable to compensate the downstream firms for signing exclusive contracts. If instead the downstream firms are (almost) perfect Bertrand competitors, the incumbent can induce the downstream firms to sign because their profits when rejecting the exclusive contract are very low. Even though downstream firms have signed the exclusive contract, entry is not deterred due to the possibility of contract breach. The entrant enters and optimally sets a wholesale price which induces only one downstream firm to breach. This is because with (almost) perfect Bertrand competition downstream firms could only make very low profits if both breached the contract. Since only the breaching downstream firm obtains the input from the entrant at a low wholesale price, it can monopolize the downstream market. As a result, final consumer prices are higher than absent exclusive dealing. Hence, Simpson and Wickelgren (2007) find that exclusive contracts have either anticompetitive or neutral effects. In contrast to their analysis, we show that for moderate degrees of downstream competition it is optimal for the entrant to induce not just a single downstream firm to breach the contract but both. For moderate degrees of competition, downstream firms can make sufficiently high profits when breaching and are therefore able to afford the damage payment to the incumbent, even if the other downstream firm breaches as well. The entrant prefers both downstream firms to breach instead of only one as it then receives a higher demand. However, to render breach of contract by both downstream firms profitable, the entrant must set its wholesale price lower than it would set it absent exclusive contracts. Therefore, for moderate degrees of downstream competition both downstream firms breach the contract and buy from the entrant at a lower wholesale price than absent exclusive dealing contracts. This leads to lower final consumer prices. As a consequence, the result that exclusive contracts are anticompetitive without efficiency gains reverses. Our

analysis reveals that this procompetitive effect is more likely to occur, the larger the entrant's efficiency advantage is.2 The main effect at work in our model is similar to the one described by Aghion and Bolton (1987). They consider the case with a single buyer and allow the incumbent to set liquidated damages. Aghion and Bolton (1987) show that under these assumptions it is possible for the incumbent to induce the buyer to sign an exclusive contract. The buyer may breach the exclusive contract later on if the entrant is so efficient that it still finds it profitable to enter and set a sufficiently low wholesale price, which enables the buyer to pay the agreed upon liquidated damages to the incumbent. Our paper differs from the one by Aghion and Bolton (1987) in that we allow for downstream competition and consider expectation damages.3 As we point out later, our assumptions are natural but make it more difficult to obtain the result that exclusive contracts have a competition enhancing effect. Nevertheless, we show that the result is present for a general class of demand functions, thereby complementing and extending the finding by Aghion and Bolton (1987). Our result stands in stark contrast to the previous literature, which asserts that exclusive dealing has anticompetitive, or at best neutral effects, if no efficiencies are generated. As is well-known, “Chicago School” scholars (e.g., Bork, 1978, and Posner, 1976) argue for a neutral effect. They consider situations in which downstream firms are independent monopolists (or final consumers). As mentioned above, in this case the incumbent cannot compensate for signing exclusive contracts, given no efficiencies are generated. Rasmusen et al. (1991) and Segal and Whinston (2000) challenge this argument by pointing out that the entrant may not be able to reach minimum efficient scale when selling only to a fraction of downstream firms, implying that downstream firms exert a negative externality on each other when signing. The incumbent can induce the downstream firms to sign by exploiting this externality.4 Fumagalli and Motta (2006) analyze the case in which downstream firms are not independent monopolists but perfect Bertrand competitors and argue for a neutral effect. With perfect downstream competition the entrant needs to sell only to a single downstream firms to reach minimum efficient scale, which removes the negative externality that signing downstream firms exert on each other. To bring out this effect, Fumagalli and Motta (2006) assume that downstream firms face a fixed fee of being active in the downstream market. This implies that downstream firms who buy from the incumbent and have a high wholesale price stay inactive, which enables a downstream firm that buys from the entrant to earn high profits.5 Abito and Wright (2008), Wright (2008), and Kitamura (2010) point out that a different picture emerges once the assumption on the fixed fee of being active is dropped. They show that it then becomes easier for the incumbent to induce downstream firms to sign if downstream competition increases. The reason is that signed downstream firms stay active, thereby

2 As shown by Mathewson and Winter (1987) and Bernheim and Whinston (1998) if two incumbent manufacturers compete for exclusive dealing contracts, the effects of these contracts can also be procompetitive. However, the mechanisms leading to these effects— that manufacturer competition for exclusive representation is tougher than standard competition, or that exclusive dealing reduces the incentive conflict of a risk-averse retailer— are different from the one identified in this paper, in which exclusive dealing can have procompetitive effects as it forces the entrant to set a lower wholesale price in order to render breach of contract profitable for the downstream firms. 3 In addition, we allow the incumbent to set its wholesale prices after the number of signing downstream firms is determined and entry occurred, while Aghion and Bolton (1987) assume that the incumbent can commit to a wholesale price in the exclusive contract. 4 Doganoglu and Wright (2010) show that a similar argument obtains with network effects among downstream firms, given that the incumbent is allowed to make discriminatory offers. 5 As shown by Wright (2009), this argument holds for the case of linear wholesale prices but extends only partly to two-part tariffs.

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exerting competitive pressure on non-signing downstream firms, which limits the profits of the latter.6 In this paper, we challenge the conclusion emanating from the previous literature that exclusive contracts that do not lead to efficiency gains are anticompetitive or have at best a neutral effect. We find that even if exclusive dealing contracts are used by incumbent firms for exclusionary and therefore anticompetitive purposes, they can have procompetitive effects. What makes this result particularly relevant is that it holds for moderate degrees of product differentiation which are present in many industries. We will provide anecdotal evidence from the microprocessor industry, i.e., the case Intel vs. AMD, in which contract breach of downstream buyers occurred. The rest of the paper proceeds as follows. Section 2 sets out the model. In Section 3 we present our result with a general demand function. Section 4 provides an application with a linear demand function. Section 5 presents a real life example of our results and Section 6 concludes. 2. The model In this section we outline the model, which follows Simpson and Wickelgren (2007), but allow for general degrees of product differentiation. Everything described below is common knowledge to all agents. We analyze an industry with an upstream and a downstream market. In the upstream market an incumbent firm I and a potential entrant E produce a homogeneous input good. In the downstream market two differentiated firms i and j process the input good at a one-to-one technology and compete in prices for final consumers. For tractability reasons we assume that downstream firms i and j are symmetric. Downstream firm i's demand function when setting a price pi and when the rival sets a price pj is given by D(pi, pj;γ), with ∂D(pi, pj;γ)/∂pi b 0, ∂D(pi, pj;γ)/∂pj ≥ 0 and | ∂D(pi, pj;γ)/∂pi| ≥ | ∂D(pi, pj;γ)/ ∂pj|. A downstream firm's demand is falling in its own price, it is rising in its rival's price, and the absolute effect of its own price is larger than the effect of its rival's price. In this demand function, γ ∈ [0,1) is a parameter representing the degree of downstream competition or product differentiation, that is, ∂D(pi, pj;γ)/∂pi b 0 is weakly decreasing and ∂D(pi, pj;γ)/∂pj ≥ 0 is strictly increasing in γ. For γ = 0, the two products are independent, implying that each downstream firm is a monopolist, that is, ∂D(pi, pj;0)/∂pj = 0 and | ∂D(pi, pj;0)/∂pi| is minimal. As γ → 1, the two products become perfect substitutes, implying perfect
 Bertrand competition, that is, lim ∂D pi ; p j; γ =∂p j ¼ ∞ and lim ∂D γ→1 γ→1
 pi ; p j; γ =∂pi ¼ −∞ as long as both demands are strictly positive. We impose the technical assumptions ∂2D(pi, pj;γ)/∂p2i ≤ 0 (or not too positive) and ∂2D(pi, pj;γ)/(∂pi ∂pj) ≥ 0, which guarantee that each downstream firm's profit function is concave and that equilibrium prices are strategic complements, i.e., ∂pi/∂ pj N 0. They also ensure that firm i's profit is increasing in the cost of firm j. We also make the natural assumption that firms i's profit is decreasing in its own marginal costs. Finally, we assume that there is a unique equilibrium in the downstream market.7 The timing of the game is as follows (see also Table 1). In the first stage, I makes simultaneous nondiscriminatory exclusive contract offers to the downstream firms.8 An exclusive contract is a compensation x from I to the downstream firms in exchange for the downstream firms' commitment to purchase exclusively from I. After observing these offers, the downstream firms simultaneously decide whether to 6 A similar argument is put forward in earlier works by Stefanidis (1998), Yong (1999), and Simpson and Wickelgren (2001). In these papers, though, the authors assume that the incumbent can commit to a certain wholesale price when offering the exclusive contract. 7 As shown by Vives (1999), a sufficient condition for this to hold is ∂2D(pi, pj;γ)/ ∂p2i + ∂2D(pi, pj;γ)/(∂pi ∂pj) ≤ 0. 8 Our results would not change if we assumed that I makes sequential or discriminatory offers.

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Table 1 Time line. Stage 1

Stage 2

Stage 3.1

Stage 3.2

Stage 3.3

I offers excl. contract E enters or not I sets prices wf, wc i,j can breach i,j buy input i,j accept or reject E sets price we i,j compete

accept or reject them. In the second stage, E decides on entry. In stage 3.1, active upstream firms set wholesale prices to each available downstream firm. I is able to discriminate between those downstream firms that have signed the exclusive contract (captive downstream firms) and those who have not (free downstream firms). It offers a wholesale price wc to captive downstream firms and a wholesale price wf to free downstream firms. E offers a wholesale price we to free downstream firms.9 Captive downstream firms can become free by breaching and paying expectation damages to I in stage 3.2. In accordance with common law I's expectation damages are based on its lost profits. It needs to be restored to the position it would have been in had the contract been performed.10 We assume that, in case both downstream firms breach, each one pays half of the expectation damages. In stage 3.3, I and E produce the input good. Free downstream firms purchase the input good from E if we ≤ wf and from I if we N wf. Captive downstream firms purchase from I at wc.11 Downstream firms compete for consumers by setting prices pi and pj. To simplify the notation, we denote the downstream price vector by p(wi,wj) = [pi(wi,wj), pj(wj,wi)]T when needed as an argument in firm i's demand and by p(wj,wi) = [pj(wj,wi), pi(wi,wj)]T when needed as an argument in firm j's demand. Upstream firms I and E incur a constant marginal cost of cI and cE. We assume that E is more efficient than I, i.e., cE b cI, but that it incurs a sunk cost f when entering. We further assume that E is sufficiently efficient that it can cover this fixed costs f when selling to both downstream firms at a wholesale price of w′ E , where w′ E is the wholesale price that E must charge to induce a downstream firm to breach provided 12 the rival downstream firm does not breach. we impose
 Therefore,  ′ 
 ′     ′ that 2 w E −cE D p w E ; w E ; γ N f, where D p w′ E ; w′ E ; γ is a downstream firm's demand given that both downstream firms face an input price of w′ E and set their downstream prices accordingly.13 Our equilibrium concept is subgame perfection. To avoid the epsilon notation on prices and compensations, we assume that the downstream firms sign the exclusive contract when they are indifferent between signing or not, they breach the exclusive contract when they are indifferent between breaching or not, and they buy from E when they are indifferent between buying from E or I.

  Finally, we assume that D pðcI ; cI Þ; γ ðpðcI ; cI Þ−cI Þ≥D p w′ I ; cI ;   ′   γÞ p w I ; cI −cI , where w′ I solves the maximization problem maxwD(p(w,cI);γ)(w − cI). This assumption implies that a downstream firm is better off when it competes in the downstream market 9 As Simpson and Wickelgren (2007), we restrict our attention to the case of linear wholesale prices. For a brief discussion on two-part tariffs see the Concluding remarks section. 10 In accordance with Simpson and Wickelgren (2007) we consider the situation in which breaching downstream firms are subject to expectation damages. In contrast, Aghion and Bolton (1987), Innes and Sexton (1994) and Spier and Whinston (1995) assume that the incumbent and the downstream firms can sign contracts with liquidated damages. As we discuss in more detail towards the end of the next section, the mechanism driving our results is also at work in case of liquidated damages. For a general discussion on the difference between expectation and liquidated damages, see Brodley and Ma (1993). 11 Our results are invariant to renegotiations, that is, even if I could change wc after the downstream firms decided to breach or not, our results would be unchanged. 12 For a formal definition of w′ E see the online appendix available at http://ssrn.com/ abstract=1908630. 13 A similar assumption is imposed by Simpson and Wickelgren (2007) who assume 2(cI − cE)D(p(cI,cI);γ) N f. It is easy to show that w′ E →cI if downstream firms are perfect Bertrand competitors. Therefore, our assumption generalizes the one of Simpson and Wickelgren (2007) to the case of differentiated products.

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on the basis of its true costs cI than on costs w′ I NcI , given that the rival faces costs cI, where w′ I is set to maximize a profit function with a different mark-up. This assumption simplifies the proofs but is not crucial for our general effect to hold. It is easy to verify that the assumption is satisfied for many commonly used demand functions such as the linear one considered in Section 4, CES, or Hotelling.14

that downstream competition is sufficiently strong and both downstream firms have signed the exclusive contract.

3. The effect in general form

Proof. See Appendix A

We first look at the equilibrium in the downstream market when downstream firm i faces a wholesale price wi while downstream firm j faces a wholesale price wj. Firm i's profit function is

Lemma 1 shows that for intermediate values of γ the entrant sets a wholesale price below cI to induce the downstream firms to breach. Intuitively, the profit the incumbent obtains per downstream firm in case both downstream firms signed the exclusive contract is given by Eq. (2) minus the upfront payment D(p(cI,cI);γ)(p(cI,cI) − cI). If both downstream firms breach, each firm has to pay this amount to the incumbent as expectation damages. This implies that the downstream firms only breach when they can obtain sufficiently high profits in the downstream market. If the entrant sets a wholesale price of cI, the profit of a downstream firm in case of contract breach is given by D(p(cI,cI);γ)(p(cI,cI) − cI). If γ is relatively high, this amount does not cover the expectation damages. Hence, if downstream competition is relatively high, the entrant must set a wholesale price below cI to render breach of contract by both downstream firms profitable. Lemma 1 also shows that if the downstream firms are sufficiently differentiated, it is more profitable for the entrant to induce both downstream firms to breach instead of only one. The explanation for this result is as follows. For moderate degrees of downstream competition, both downstream firms still obtain a sizable profit even if the rival firm also breaches. By contrast, when downstream competition is very intense, the negative externality that breaching downstream firms exert on each other is so strong that each downstream firm only obtains a very small profit when the rival firm also breaches. Hence, with an increasing degree of downstream competition the wholesale price that the entrant needs to set in order to induce contract breach by both downstream firms decreases, implying that the profit of the entrant also decreases. As shown by Simpson and Wickelgren (2007), for intense downstream competition it is then more profitable for the entrant to induce only one downstream firm to breach the exclusive contract. In summary, Lemma 1 shows for a general class of demand functions, that there exists a region in which downstream competition is sufficiently strong such that both downstream firms sign the exclusive contract, but sufficiently weak such that the entrant optimally induces both downstream firms to breach the exclusive contracts at a wholesale price below cI. From Lemma 1 we know that for moderate degrees of downstream competition both downstream firms obtain the input good at a wholesale price we b cI. This results in final consumer prices of p(we,we). As explained above, if exclusive contracts were not allowed, both downstream firms would obtain the input good at a wholesale price of cI resulting in final consumer prices of p(cI,cI). Since we b cI, we have p(we,we) b p(cI,cI) leading to the following result:


 πi ¼ D pi ; p j; γ ðpi −wi Þ: The first-order conditions are given by
 ∂D pi ; p j; γ ∂pi


 ðpi −wi Þ þ D pi ; p j; γ ¼ 0; i≠j;

i; j ¼ 1; 2 :

ð1Þ

These first-order conditions characterize the equilibrium of the downstream game. Due to our assumptions we have the natural properties that in equilibrium dpi/dwi N 0 and dpi/dwj N 0. Since γ → 1 implies ∂D(pi,pj)/∂pi → − ∞, we obtain that profits become zero when wholesale prices are the same, i.e., for wi = wj = w, pi = pj → w. By contrast, when γ = 0, implying that the downstream firms are independent monopolists, profits are largest. If exclusive contracts are not allowed, all downstream firms are free and the incumbent and the entrant compete in stage 3.1 for the free downstream firms. Since the entrant is more efficient, in equilibrium it will make all sales at a price of we = cI while the incumbent will not sell anything. The resulting profit for a downstream firm is D(p(cI,cI);γ)(p(cI,cI) − cI). The same outcome occurs if no downstream firm signs the exclusive contract. If instead downstream firms sign the exclusive contract, the incumbent will set wholesale prices that maximize its profits. These wholesale prices are independent of whether the downstream firms will breach the contract or not as the incumbent becomes subject to expectation damages in case of contract breach. Formally, the incumbent's maximization problem is max w


 2D pðw; wÞ; γ ðw−cI Þ:

ð2Þ

Let us denote the wholesale price w that solves the above problem by wI, with wI N cI. It follows that the incumbent obtains the monopoly profit. Therefore, it can offer positive upfront payments to the downstream firms for signing the exclusive contract. The profit the downstream firms obtain when rejecting the incumbent's offer, i.e., the upfront payment that the incumbent has to offer them for signing the exclusive contract, is decreasing in γ and, in the limit, as γ → 1, it becomes zero. In addition, the double marginalization problem reduces with an increasing degree of downstream competition. Therefore, as formally shown by Simpson and Wickelgren (2007), the incumbent can profitably induce both downstream firms to sign the exclusive contract if downstream competition is sufficiently strong. We can now determine whether the entrant induces downstream firms to breach, and, if so, what its optimal pricing decision is, given 14 In general, it is well-known from the literature on strategic delegation or vertical restraints (e.g., Fershtman and Judd, 1987; or Bonanno and Vickers, 1988) that competing on the basis of higher costs than the true costs can be beneficial for a firm as it induces the rival firm to react less aggressively. However, this argument relies on the fact that, at the true input costs of a firm, a change in these costs has only a second-order effect on the optimal choice of this firm but a first-order effect on the choice of the rival firm. By contrast, in our case wc is set according to a different maximization problem implying that it is biased upwards to a large extent.

Lemma 1. If downstream competition is moderate, there exists a subgame perfect equilibrium in which both downstream firms first sign and then breach the exclusive contract and buy from the entrant at a wholesale price below the incumbent's marginal cost we b cI.

Proposition 1. If downstream competition is moderate, exclusive contracts lead to a reduction in final consumer prices, implying that exclusive contracts enhance consumer surplus and welfare. The result shows that even though exclusive contracts are used for anticompetitive purposes, they may have procompetitive effects. This result is new in the literature. The received literature mainly analyzes the question if exclusive contracts can profitably be used or not, and shows that if the answer is yes, this is to the detriment of consumers. This leads to the conclusion that these contracts can never improve welfare, provided they do not create efficiencies. In contrast, our result shows that this is not necessarily the case, i.e., exclusive contracts can lead to a rise in welfare even if no efficiencies are generated.

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As pointed out in the Introduction section, our result relies on a similar effect as the one discovered by Aghion and Bolton (1987). In contrast to us, they consider liquidated damages instead of expectation damages. Further, they concentrate on the case where there is no competition between downstream firms, i.e., γ = 0. Using a modified version of Aghion and Bolton (1987), one can show that in our framework liquidated damages allow the incumbent to induce downstream firms to sign exclusive contracts, even if γ = 0. The explanation is that even without downstream competition the incumbent can offer a compensation payment so that the overall profit of a downstream firm, i.e., the compensation payment plus the downstream profit, equals the profit that the downstream firm would obtain if it did not sign the exclusive contract. In the latter case, the downstream firm would get the input at the incumbent's marginal costs. In the exclusive contract, the incumbent sets the liquidated damages such that they are equal to the profit that a downstream firm can obtain when buying at the entrant's marginal costs. On the equilibrium path, each downstream firm signs the exclusive contract, the entrant enters and sets its wholesale price equal to its marginal costs in order to induce contract breach by the downstream firms. Since wholesale prices are then equal to the entrant's marginal costs and not the incumbent's, exclusive contracts have a procompetitive effect.15 The considered modification of Aghion and Bolton (1987) shows that the effect highlighted in our paper carries over when considering liquidated instead of expectation damages and becomes even more prominent because it applies for a larger range of γ. In fact, it is relatively straightforward to see that a similar argument as the one just explained does not only hold for γ = 0 but also for higher degrees of downstream competition. In fact, the argument holds up to a certain threshold of γ, above which the entrant prefers to induce only one downstream firm to breach the exclusive contract. By contrast, with expectation damages the incumbent cannot induce downstream firms to sign for low levels of downstream competition. Our analysis nevertheless shows that there is always a region of γ, in which the procompetitive effect materializes. This region is the one of moderate degrees of downstream competition, which is supposedly present in most markets. We now briefly discuss the cases of weak and strong downstream competition. If downstream competition is weak, the allowance of exclusive dealing is competitively innocuous. Either the incumbent cannot pay the downstream firms to accept exclusive contracts, or the entrant can induce both downstream firms to breach at a wholesale price equal to cI. In both cases welfare is unaffected by the allowance of exclusive contracts. The effect of exclusive dealing on welfare is not clear when downstream competition is intense. In this case the entrant induces only a single downstream firm to breach. Even though it sets a lower wholesale price to this firm than it would set absent exclusive contracts, the captive downstream firm still faces a higher wholesale price. If the breaching firm is able to monopolize the downstream market, this will lead to higher final consumer prices than absent exclusive dealing. Exclusive contracts then have anticompetitive effects. As shown by Simpson and Wickelgren (2007), this effect dominates if γ → 1. Our analysis so far shows that for a general class of demand functions exclusive contracts can have competition enhancing effects. However, the analysis does not allow us to draw conclusions on how large the specific regions for γ are. This depends on the exact shape of the demand function. Therefore, we provide an application with a linear demand function in the next section.

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We assume that demand is defined by the standard representative consumer model (see e.g., Vives, 1999), where a consumer's utility is given by


 q2i þ q2j þ 2γqi q j U qi ; q j ¼ qi þ q j − þ v: 2 Here, qi is the amount of consumption from downstream firm i and v is the consumption of an outside good whose marginal utility is normalized to one. The parameter γ ∈ [0,1) again reflects the degree of product differentiation between the downstream firms. For γ = 0 the two goods are independent, while for γ → 1 they become perfect substitutes. If consumers maximize this utility subject to an income constraint, the inverse demand of downstream firm i becomes pi = 1 − qi − γqj. Both downstream firms receive positive demand only if their prices are sufficiently close to each other. If their prices strongly diverge, the higher priced downstream firm receives no demand, while the lower priced downstream firm captures the entire market. Specifically, downstream firm i's demand function is given by

qi ¼

8 > > > > > < > > > > > :

1−pi 1−γ−pi þ γp j   1−γ 2 0

if if if

0 −1 þ γ þ p j γ 1−γ þ γp j

b b ≤

pi ≤ pi b

−1 þ γ þ p j ; γ 1−γ þ γp j ; pi :

We measure the entrant's efficiency advantage by θ, where cI = θwm(cE) + (1 − θ)cE.16 Here, wm(cE) denotes the monopoly wholesale price when a firm's marginal cost is cE, i.e., wm(cE) = (1 + cE)/2. Hence, θ = 0 implies that the entrant has no efficiency advantage, while θ = 1 implies that the entrant's efficiency advantage is just drastic. To simplify the exposition we assume that θ ≥ 0.121 and f = 0.17 These two assumptions rule out the case in which entry is not profitable for E. To simplify the exposition we make the additional refinement on our solution concept that, if multiple equilibria arise, the downstream firms play the equilibrium that is Pareto dominant from their perspective. We use this assumption because in stage 3.2 of the game, the breaching stage, multiple equilibria can arise in which either both downstream firms breach or none of them breaches the exclusive contract.18 In this framework, we can explicitly determine the number of downstream firms to which the entrant sells and the respective wholesale prices for different degrees of downstream competition. Before doing so the following definition is useful. We define the strictly increasing function b θðγÞ : ½0:711; 0:904→½0:121; 1 as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 32−48γ−80γ 2 þ 96γ 3 þ 16γ 4 −36γ 5 þ 4γ7 þ 32 2γ 4 −3γ 5 þ γ 6   2ð2−γ Þ 4−12γ 2 þ 5γ4 −γ6 for 0:711 ≤γ ≤ 0:731; and

2−


pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2ð2−γÞ ð2−γÞð1−γ Þ þ 3γ−γ2 −2 ð1 þ γ Þð5−3γ Þ 4γ−2γ2 −1 for 0:731b γ ≤0:904:

We can now state the following result19:

4. An application with linear demand In this section we show that with a commonly used linear demand function exclusive contracts are procompetitive in a sizable range, in which the degree of product differentiation between the downstream firms is moderate. 15

We thank an anonymous referee for pointing out this analogy to us.

16

This notation of the efficiency advantage follows Abito and Wright (2008). Here and in the following, numbers are rounded up to three decimals. This is consistent with Segal and Whinston (2000) who use the concept of perfectly coalition-proof Nash equilibrium, developed by Bernheim et al. (1987), when dealing with multiple Nash equilibria. 19 The proofs of Lemma 2 and Proposition 2 are contained in an online appendix available at http://ssrn.com/abstract=1908630. 17 18

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θ

Lemma 2. • The entrant sells to both downstream firms if (i) γ ∈ [0,0.711) or (ii) γ ∈ [0.711,0.904) and θ≥ b θðγ Þ. • The entrant sells to one downstream firm if (i) γ ∈ [0.711,0.904) and θbb θðγÞ or (ii) γ ∈ [0.904,1). • The entrant sets we = cI if γ ∈ [0,0.618) and we b cI if γ ∈ [0.618,1). The lemma shows that dependent on the degree of downstream competition the entrant sells either to both or to one downstream firm. If downstream competition is not too intense, the entrant sells to both downstream firms, while if downstream competition is very intense, the entrant sells to only one downstream firm. Additionally, Lemma 2 shows that if γ ∈ [0.711,0.904) the entrant only sells to both downstream firms if its efficiency advantage is sufficiently high. The intuition for this result is that the entrant's profit gain through the increase in demand when both downstream firms breach is the larger, the higher its efficiency advantage is. In order to induce both instead of only one downstream firm to breach, it has to set a lower wholesale price. If its efficiency advantage is larger, it is more important for the entrant to sell a high quantity than to set a high price. Hence, it optimally sells to both downstream firms instead of only one if it is sufficiently efficient. Equipped with these results, we can assess the effects of exclusive dealing on welfare and consumer surplus. As before, we compare the situation in which exclusive contracts are prohibited with the equilibrium in which exclusive contracts are allowed. We obtain the following result. Proposition 2. The effect of exclusive contracts on welfare and consumer surplus is neutral when γ ∈ [0,0.618), positive when (i) γ ∈ [0.618,0.711) or (ii) γ ∈ [0.711,0.904) and θ ≥ b θðγÞ , and negative when (i) γ ∈ [0.711,0.904) and θbb θðγ Þ or (ii) γ ∈ [0.904,1). The different ranges are depicted in Figure 1. Proposition 2 shows that with a commonly used demand function, exclusive dealing is procompetitive in a sizable range. In particular, with this demand function the range of parameters for which exclusive dealing is procompetitive is approximately as large as the region for which exclusive dealing is anticompetitive. Therefore, our effect identified for the general model of the last section applies for a relatively large parameter range. 5. An example: Intel vs. AMD In this section we provide an example from the semiconductor industry that supports our results that contract breach occurs in real world and that more efficient competitors sell at lower wholesale prices to induce buyers to breach. Our anecdotal evidence is drawn from a recent antitrust case on exclusive dealing, Intel vs. AMD.20 Intel is the world's leading microprocessor manufacturer. It implemented a series of conditional rebates to several computer manufacturers like Dell, HP, NEC, Acer and Lenovo as well as to the large European retailer of consumer electronics Media Saturn. For example, the rebates were only granted to HP and NEC when purchasing no less than 95%, respectively, 80% of its central processing unit (CPU) needs for business desktops from Intel. Dell's rebate was conditional on exclusively buying CPUs from Intel. Acer and Lenovo received a payment from Intel conditional on postponing the launch of AMD-based notebooks. In front of the EU Commission Intel argued that the impact of its exclusive deals on competition was minor since its major competitor AMD grew during the investigation period. In particular, it argued that “the intense price competition between Intel and AMD, and the discounts granted by Intel in response to competition, produced very substantial consumer benefits in the form of lower consumer prices”.21 Actual market developments also showed that output increased and prices decreased. 20

For a detailed description of the Intel case, see DeGraba and Simpson (2010). Intel's reply to the 26 July 2007 SO, paragraph 711. See also EU Commission Decision of May 13th 2009, COMP/37.990 Intel, paragraph 1634. 21

1

procompetitive

neutral anticompetitive 0.121

0

0.618 0.711

0.904 1

γ

Fig. 1. Competitive Effects of Exclusive Dealing

We can now contrast the stylized facts with the predictions of our model. Our model predicts that procompetitive effects of exclusive deals arise when competition in the downstream market is moderate and breach of contract possible. Further, the potential upstream competitor must be sufficiently efficient. In fact, all these conditions seem to apply in the Intel vs. AMD case: Competition among computer manufacturers can be described as moderate; there are several large manufacturers, which are to a certain degree differentiated. Further, the downstream firms HP and Dell switched a part of their orders to AMD despite of their exclusive deals with Intel. That is, several downstream firms breached the exclusive contracts.22 Even if they expected to lose a significant amount of their rebates, this obviously did not prevent them from buying from AMD. In addition, the EU Commission cites several computer manufacturers that regarded AMD as being more efficient than Intel.23 These are overall telltale signs that the effect identified in this paper was at work in the microprocessor industry. Without a full proof of foreclosure, the EU Commission condemned Intel to a record fine of 1.06 billion EUR and prohibited it to make use of exclusive deals in the future. Our result suggests that this decision has been unwarranted from a consumer surplus perspective as the exclusive deals might have had procompetitive effects. Intel has lodged an appeal to the Court of First Instance.

6. Concluding remarks In this paper we have shown that naked exclusion has procompetitive effects if downstream firms can breach exclusive contracts and competition between them is moderate. In this situation, both downstream firms sign the exclusive contract with the incumbent but later on they breach it and buy from the entrant. Because downstream firms have to pay damages to the incumbent when breaching, the entrant must set its wholesale price sufficiently low to make breach of contract profitable. In particular, the entrant must set its wholesale price lower than in case absent exclusive contracts. Since downstream firms obtain the input at a lower price, they also set a lower price to final consumers. As a consequence, naked exclusion leads to a rise in consumer

22

See DeGraba and Simpson (2010), pp. 33. In the Commission Decision of May 13th 2009, COMP/37.990 Intel, paragraph 158, the Commission states that Dell explicitly pointed out to Intel how AMD was a growing threat to their own products: “AMD is a great threat to our business. Intel is increasingly uncompetitive to AMD which results in Dell being uncompetitive to [Dell competitors]. We have slower, hotter products that cost more across the board in the enterprise with no hope of closing the performance gap for 1–2 years”. Similar remarks can be found in paragraphs 151, 152 and 154. 23

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surplus and welfare. This result has implications for antitrust policy as it shows that even absent efficiency gains exclusive contracts can have competition enhancing effects. A limitation of our model is that we assumed that entry costs are sufficiently small, so that the entrant finds it profitable to enter. We imposed this assumption to show our effect in the simplest way. Dropping this assumption would affect our results in that exclusive contracts would more likely lead to entry deterrence and therefore render exclusive dealing more likely to be anticompetitive. However, another interpretation of our model is that exclusive contracts put pressure on upstream entrants to become more efficient in order to be able to profitably induce downstream firms to breach the exclusive contracts with the incumbent upstream firms. This interpretation is particularly valid for industries which are characterized by high innovation and growth rates. Following Simpson and Wickelgren (2007) we confined our attention to linear upstream prices.24 If upstream firms could offer two-part tariffs, the analysis would change in two respects. On the one hand, the incumbent would be able to avoid double marginalization implying that, when downstream firms sign exclusive deals, the incumbent earns the monopoly profit of the industry regardless of the degree of downstream competition. This makes exclusive dealing more profitable for the incumbent and raises the damage payment that downstream firms have to pay in case of contract breach. On the other hand, because the damage payment is higher in the two-part tariff case, the entrant needs to offer an even lower wholesale price with exclusive dealing than without in order to render breaching profitable, given that negative fixed fees are not possible, e.g., due to moral hazard issues. Thus, exclusive dealing may again have procompetitive effects leading to even lower wholesale prices than in case of linear upstream pricing. Therefore, the effect identified in this paper carries over to the case of twopart tariffs as long as the entrant is sufficiently efficient. Appendix A. Proof of Lemma 1 The proof proceeds in several steps. First, we calculate the compensation x2, which the incumbent has to offer so that both downstream firms sign the exclusive contract. Second, we calculate the compensation x1, which I has to offer so that exactly one downstream firm signs the exclusive contract. Third, we determine for which degrees of competition the incumbent optimally induces both downstream firms to sign the exclusive contract. Finally, we analyze if the entrant then induces one or both downstream firms to breach and what its optimal wholesale price is. In the following, we denote the number of signed downstream firms by S ∈ {0,1,2}. The compensation x2 must equal the additional profit that a downstream firm can make when rejecting the contract given that the other downstream firm accepts it: f

c

x2 ¼ πijS¼1 −πijS¼2 : f Here, πi|S = 1 denotes a downstream firm's profit when rejecting the c contract while the rival downstream firm accepts it. πi|S = 2 denotes a downstream firm's profit when both accept it. For any compensation above x2 accepting is strictly preferred by the downstream firms but I makes lower profits. If both downstream firms accept the exclusive contract, I's maximization problem is25

max w


 2D pðw; wÞ; γ ðw−cI Þ:

24 As noted by Simpson and Wickelgren (2007), the case of two-part tariffs is much more complicated and therefore beyond the scope of this paper. 25 In the following we use D(pi, pj;γ) as a short-cut for max{0, D(pi, pj;γ)}, that is, we do not explicitly write out if a demand function becomes zero. We do so to reduce the notational burden.

435

Let us denote the solution to this problem w⁎ = wI. When both downstream firms are captive, I charges the monopoly wholesale price to them as it receives the same profits from them whether they breach the contract or not. I's profit is then ΠI|S = 2 = 2D(p(wI,wI);γ)(wI − cI) and a downstream firm's profit, excluding the compensation payment, is πci|S = 2 = D(p(wI,wI);γ)(p(wI,wI) − wI). Now suppose that one downstream firm rejects the contract. In the subsequent price game I and E compete for free downstream firms. Note that the captive downstream firm can also become free by breaching the contract. The standard Bertrand argument implies that I offers a wholesale price wf = cI and E offers a wholesale price we ≤ cI to free downstream firms. It could be optimal for E to set we b cI to induce the captive downstream firm to breach. In order to verify this, we determine whether the captive downstream firm has an incentive to breach if E sets we = cI. If the captive downstream firm does not breach the contract, its input price is wc. Since I gets the same profit from the captive downstream firm whether it breaches or not, wc is argmaxwD(p(w,cI);γ)(w − cI). This yields we N cI. The captive downstream firm's profit when not breaching is D(p(wc,cI);γ)(p(wc,cI) − wc). If the captive downstream firm instead breaches, its profit is D(p(cI,cI);γ)(p(cI,cI) − cI) net the damage payment D(p(wc,cI); γ)(wc − cI) that it has to pay to I. Thus, breaching is profitable for the captive downstream firm if


 D pðcI ; cI Þ; γ ðpðcI ; cI Þ−cI Þ−D pðwc ; cI Þ; γ ðwc −cI Þ≥D pðwc ; cI Þ; γ  ðpðwc ; cI Þ−wc Þ or

 D pðcI ; cI Þ; γ ðpðcI ; cI Þ−cI Þ≥D pðwc ; cI Þ; γ ðpðwc ; cI Þ−cI Þ; which is satisfied by our assumption of Section 2. Hence, the captive downstream firm breaches the contract when E sets we = cI, so that it is optimal for E to set we = cI and no lower wholesale price. E finds it optimal to enter since by assumption 2(cI − cE)D(p(cI,cI);γ) N f. As the captive downstream firm breaches, the downstream firm that did not sign the contract makes profits equal to πfi|S = 1 = D(p(cI,cI);γ)(p(cI,cI) − cI). We can deduce that I has to offer

 x2 ¼ D pðcI ; cI Þ; γ ðpðcI ; cI Þ−cI Þ−D pðwI ; wI Þ; γ ðpðwI ; wI Þ−wI Þ as compensation to each downstream firm for accepting the exclusive contract. We now derive the compensation x1 that I has to offer to induce a single downstream firm to sign the exclusive contract. This compensation must equal the additional profit that a downstream firm can make when rejecting the exclusive contract provided the other downstream firm rejects it, i.e., f

c

x1 ¼ πijS¼0 −πijS¼1 : f Here, πi|S = 0 denotes a downstream firm's profit when both firms reject c the contract, while πi|S = 1 denotes a downstream firm's profit when it signs the contract while the rival firm rejects it. If both downstream firms reject the contract, E enters and the subsequent price game between the upstream firms results in simple Bertrand duopoly wholesale prices, i.e., both upstream firms set wholesale prices equal to cI. Thus, when both downstream firms reject the contract, they make profits f equal to πi|S = 0 = D(p(cI,cI);γ)(p(cI,cI) − cI). From the analysis above we know that a downstream firm's profit c when it signs the contract, while the rival firm rejects it, is πi|S =1 = D(p(cI,cI);γ)(p(cI,cI) − cI) − D(p(wc,cI);γ)(wc − cI). We can deduce that I must offer


 x1 ¼ D pðwc ; cI Þ; γ ðwc −cI Þ

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as compensation in order to induce one downstream firm to sign the exclusive contract. This implies that for x N x2, there exists a subgame perfect equilibrium of the continuation subgame in which both downstream firms sign the exclusive dealing contract.26 In what follows we focus on this equilibrium. We now compare the net profits that I makes when inducing both downstream firms, one or neither downstream firm to sign the exclusive contract. When it induces both downstream firms to sign the exclusive contract, its net profit is

wE = cI, the condition for both downstream firms to breach would be violated. However, by lowering wE below cI, the left-hand side of Eq. (4) rises. This is because the first term increases due to the assumption that a downstream firm's profit rises as its marginal costs fall, while the second term does not change and the third term falls in absolute value. By continuity reasons, it follows that there must exist an interval of γ, such that for all values of γ in this interval Eq. (4) is satisfied with a wholesale price wE b cI. We denote the infimum of this interval by γ. b . First note that at γ ¼ γ b condiWe now show that γ lies above γ tion (3) can be written as

h


 i 2 D pðwI ; wI Þ; γ ðwI −cI Þ þ D pðwI ; wI Þ; γ ðpðwI ; wI Þ−wI Þ−D pðcI ; cI Þ; γ ðpðcI ; cI Þ−cI Þ :



 b ðpðcI ; cI Þ−cI Þ ¼ D pðwI ; wI Þ; γ b ðpðwI ; wI Þ−wI Þ D pðcI ; cI Þ; γ
 b ðwI −cI Þ: þ D pðwI ; wI Þ; γ

It offers x2 to each downstream firm as compensation for signing and receives the monopoly profit whether the downstream firms breach or not. When it induces one downstream firm to sign its net profit is zero. It pays x1 as compensation for signing to one downstream firm, makes zero profit and receives a damage payment equal to x1 because the signed downstream firm breaches. Since I and E are perfect Bertrand competitors but E is more efficient, I also makes zero net profit when inducing neither downstream firm to sign. Hence, I makes use of exclusive contracts only if it is able to profitably induce both downstream firms to accept the exclusive contract, i.e., if

 D pðwI ; wI Þ; γ ðpðwI ; wI Þ−cI Þ≥D pðcI ; cI Þ; γ ðpðcI ; cI Þ−cI Þ:

ð3Þ

If the products are independent of each other, i.e., if γ = 0, the righthand side is larger than the left-hand side since no double marginalization takes place. To the converse, if the products are (almost) perfect substitutes, i.e., if γ → 1, the right-hand side is zero since p(cI,cI) → cI, while the left-hand side is still positive since p(wI,wI) → wI N cI. Thereb, at fore, there must exist at least one intermediate value of γ, denote it γ which Eq. (3) holds with equality. If there are multiple γ satisfying b be the largest. It follows that there exists a subgame perfect Eq. (3), let γ equilibrium in which both downstream firms sign the exclusive conb. tract if γ ≥ γ If both downstream firms signed the exclusive contract, I charges the monopoly wholesale price wc = wI to captive downstream firms and the Bertrand duopoly price wf = cI to free downstream firms. Hence, E is constraint in its pricing decision to free downstream firms by we ≤ cI. It may choose to induce both downstream firms or one downstream firm to breach. To induce both downstream firms to breach it needs to set a wholesale price we ≤ wE, where wE is defined by

 D pðwE ; wE Þ; γ ðpðwE ; wE Þ−wE Þ−D pðwI ; wI Þ; γ ðwI −cI Þ
 −D pðwI ; wE Þ; γ ðpðwI ; wE Þ−wI Þ ¼ 0:

ð4Þ

E optimally sets its wholesale price so that the downstream firms are indifferent between breaching or not. The first term denotes the profit that a downstream firm obtains when breaching provided the other downstream firm also breaches, the second term denotes the damage payment to I in case of contract breach, which is half the profit that I makes when none of the downstream firms breaches, and the third term denotes the profit that a downstream firm makes when not breaching provided the other downstream firm breaches. If γ = 0, it is easy to see that both downstream firms breach when E sets wE = cI since D(p(cI))(p(cI) − cI) N D(p(wI))(p(wI) − cI). If, however, γ becomes sufficiently large, E can no longer induce both downstream firms to breach by setting wE = cI. To see this note that the first term of Eq. (4) goes to zero when downstream competition becomes very intense as p(wE,wE) → wE, while the two last terms of Eq. (4) are negative. Thus, when γ is sufficiently large and E sets 26 If, in addition, x2 ≥ x1, then this subgame perfect equilibrium is also unique. In the linear example considered in Section 4 this is indeed the case.

ð5Þ

However, γ is defined by



 D pðcI ; cI Þ; γ ¼ D pðwI ; cI Þ; γ ðpðwI ; cI Þ−wI Þ þ D pðwI ; wI Þ; γ  ðwI −cI Þ:

ð6Þ

Eqs. (5) and (6) differ in the first term on the right-hand side. We know that D(p(wI,cI);γ)(p(wI,cI) − wI) b D(p(wI,wI);γ)(p(wI,wI) − wI). In addition, we know that for γ = 0, the left-hand sides of Eqs. (5) and (6) are bigger than the respective right-hand sides while for γ → 1, b is defined as the largest γ for which the reverse holds true. Since γ b. Eq. (5) holds, it follows that for γ to fulfill Eq. (6) we must have γ N γ Finally, we need to show that the profit of E when inducing both firms to breach is larger than when inducing only one firm to breach. To show this consider a value of γ slightly above γ. Then, the entrant's wholesale price to induce both downstream firms to breach is cI − , with  N 0 but small, and the profit of E is 2(cI −  − cE)D(p(cI − , cI − )). Now suppose there exists a we ∈ (cI − , cI], denoted by w′ e , such that only one downstream firm breaches. The profit of E is then  ′    w e −cE p w′ e ; wI . Since cI − bw′ e bwI it follows that 2D(p(cI − ,    cI − )) is strictly larger than D p w′ e ; wI . By contrast, the difference ′ between cI −  andw e is negligible sincew′ e ≤cI and  is small. It follows that E strictly prefers to induce both downstream firms to breach at a wholesale price below cI for values of γ slightly above γ. ■ References Abito, Jose M., Wright, Julian, 2008. Exclusive dealing with imperfect downstream competition. International Journal of Industrial Organization 26, 227–246. Aghion, Philippe, Bolton, Patrick, 1987. Contracts as a barrier to entry. American Economic Review 77, 388–401. Bernheim, B. Douglas, Whinston, Michael D., 1998. Exclusive dealing. Journal of Political Economy 106, 64–103. Bernheim, B. Douglas, Peleg, Bezalel, Whinston, Michael D., 1987. Coalition-proof Nash equilibria: concepts. Journal of Economic Theory 42, 1–12. Bonanno, Giacomo, Vickers, John, 1988. Vertical separation. The Journal of Industrial Economics 36, 257–265. Bork, Robert H., 1978. The Antitrust Paradox. Basic Books, New York. Brodley, Joseph F., Ma, Ching-to Albert, 1993. Contract penalties, monopolizing strategies, and antitrust policy. Stanford Law Review 45, 1161–1213. DeGraba, Patrick, Simpson, John D., 2010. Theories of Harm in the Intel Case. available at SSRN: http://ssrn.com/abstract=1705753. Doganoglu, Toker, Wright, Julian, 2010. Exclusive dealing with network effects. International Journal of Industrial Organization 28, 145–154. Fershtman, Chaim, Judd, Kenneth L., 1987. Equilibrium incentives in oligopoly. American Economic Review 77, 927–940. Fumagalli, Chiara, Motta, Massimo, 2006. Exclusive dealing and entry, when buyers compete. American Economic Review 96, 785–795. Innes, Robert, Sexton, Richard J., 1994. Strategic buyers and exclusionary contracts. American Economic Review 83, 566–584. Kitamura, Hiroshi, 2010. Exclusionary vertical contracts with multiple entrants. International Journal of Industrial Organization 28, 213–219. Mathewson, G. Frank, Winter, Ralph A., 1984. An economic theory of vertical restraints. The RAND Journal of Economics 15, 27–38. Mathewson, G. Frank, Winter, Ralph A., 1987. The competitive effects of vertical agreements: comment. American Economic Review 77, 1057–1062. Posner, Richard A., 1976. Antitrust Law: An Economic Perspective. University of Chicago Press, Chicago. Rasmusen, Eric B., Ramseyer, J. Mark, Wiley Jr., John S., 1991. Naked exclusion. American Economic Review 81, 1137–1145.

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