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We consider a two-period model with two sellers and one buyer. Although we assume it is efficient for the buyer to purchase from both sellers in each period, we show that when the buyer's valuations are inter-temporally linked and at least one seller is financially constrained, exclusion can sometimes arise in equilibrium (i.e., the buyer purchases all of its requirements from the same seller in each period). The exclusionary equilibria are supported by contract offers in which the excluding seller's incremental price to supply the contestable part of demand is below its marginal cost and sometimes negative. Our findings contribute to the literatures on market-share contracts, bundling, all-units discounts, and loyalty discounts.

Upstream firms (sellers) often encourage downstream firms (buyers) to promote their products by offering discounts if the buyers' purchases meet or exceed certain quantity or market-share thresholds. Sometimes the discounts apply only to the incremental units purchased by the buyer that exceed the threshold, while in other cases, they apply retroactively to all the units purchased by the buyer once the threshold is reached. Although both types of discounts reduce the buyer's average purchase price, the latter also have the feature that the buyer's out-of-pocket cost “jumps down” when the triggering threshold is reached, implying that the incremental price faced by the buyer at that point is negative. Generally these discounts are a sign of healthy competition, and are often required by buyers as a price of doing business; for example, the lower (negative) incremental prices may create powerful incentives for a retailer to deploy market strategies that expand the volume of sales and increase welfare. In other circumstances, however, they may be anticompetitive; the lower (negative) incremental prices may instead create incentives for a retailer to promote the sale of products on which it is eligible to earn a discount at the expense of other, substitute products that may have been more preferred by final consumers. As we will show in this article, when implemented by a dominant seller, who may have easier access to financing than its rival or rivals, the aforementioned discounts can sometimes exclude equally-efficient rivals, misallocate resources, and lower overall welfare. The potential for the abuse of discounts by a dominant seller has been the subject of several high profile cases and investigations in the U.S. and Europe.1 The concern in these cases and investigations is whether it would be possible for an equally-efficient rival to make a comparable offer when selling its products. In the case of discounts that are aggregated over multiple products (i.e., bundled discounts), for example, an important question is whether a single-product rival would be able to match the attractiveness of the dominant seller's offer, even when the post-discount prices are above cost.2 In the case of quantity or share-based discounts that apply retroactively to all units, the question is whether an equally-efficient rival could profitably compensate buyers for foregoing the rebates they would receive if they were to meet the threshold set by the dominant seller. And, similarly, in the case of a dominant seller selling a “must-stock” item, where competition takes place over only a subset of the buyers' purchases, the question is whether the dominant seller may have an advantage over its smaller rival because it can average its discount over a larger installed base.3 The publicly disclosed fact patterns in the Intel investigation provide a motivating example for the paper. If one assumes that because of prior platform and/or model introductions, there is an installed base for Intel's product (CPU's), so that competition at any point in time between Intel and its rival takes place over only a subset of each buyer's (in this case, original equipment manufacturers) purchase requirements, then the question becomes whether the dominant seller can profitably extend its dominance over the committed portion of the installed base to the contestable part of demand by offering discounts that apply retroactively to all-units purchased by the buyer. We show here that in a two-period model the answer can be ‘yes’ if tomorrow's installed base depends on today's sales (e.g., if switching costs link sales in the two-periods),4 and the rival is financially constrained and thus hampered in its ability to compete for the inter-temporal sales.5 We illustrate our findings in a simple two-period model with two sellers and one buyer. The buyer requires at most two units of product in each period. We assume that in the first period, one of the units is already captive and thus can only be purchased (if at all) from the “incumbent seller,” whereas the other unit is contestable and thus can be purchased either from the incumbent seller or an “entrant seller.” We show that when the buyer's valuations are linked over time, specifically, when the contestable unit from the first period becomes part of the installed base for the seller's product in the second period (and therefore itself becomes captive), and the entrant seller is financially constrained, there are plausible conditions under which exclusion arises as the unique equilibrium outcome (i.e., the buyer purchases only from the incumbent seller). This holds even though it is more efficient for the entrant to supply the contestable unit in the first period. For example, suppose the buyer is willing to pay at most 100 for the captive unit in the first period, 80 for the contestable unit if purchased from the incumbent seller, and 100 for the contestable unit if purchased from the entrant seller. Suppose also that the buyer's valuations are the same in the second period, except now the formerly contestable unit is captive and can only be purchased from the seller that supplied it in the first period. Suppose finally that each seller's marginal cost of production for each unit in each period is 30. In this case, the incumbent can earn a second-period profit of (100–30) + (80–30) = 120 if it supplies both units in the first period, but only a profit of 100–30 = 70 if it does not. Thus, the incumbent increases its second-period profits by 50 if it wins the first-period contestable unit. In contrast, if the entrant supplies the contestable unit in the first-period, then it can earn 100 − 30 = 70 in the second period, which is more than what the incumbent earns on its incremental sale. (Recall that by assumption the buyer prefers to diversify its purchases across the two vendors.) It is precisely because the first-period contestable unit is more valuable when it is supplied by the entrant than when it is supplied by the incumbent that one might ordinarily expect the entrant to win the “bidding” for the right to supply the buyer's requirements for this unit. However, this will not necessarily be the case in this example if the entrant is financially constrained. To see this, suppose, to continue the example, that the entrant must earn non-negative profit in each period and thus cannot “borrow” from its expected second-period profits from supplying the contestable unit in period one. Then, when the entrant cannot commit to its second-period price in period one,6 the best the entrant can do is to offer to supply the contestable unit in period one at a price of 30 (i.e., its marginal cost of production) — which can be dominated by an offer from the incumbent seller to supply the contestable unit in period one at an incremental price of no more than 10. For example, the incumbent seller can profitably offer to supply the first-period captive unit at a price of 120 and the captive plus contestable unit at a price of 110. Given this offer, it is optimal for the buyer to purchase both units from the incumbent, giving the incumbent an expected two-period profit from its sales of (110 − 60) + (100 − 30) + (80 − 30) = 170, which exceeds what its expected two-period profit would be if it did not supply the contestable unit in period one: (100 − 30) + (100 − 30) = 140. In effect, the incumbent sacrifices 20 in profit in the first period in order to gain an extra 50 in profit in the second period, a strategy that is not available to the financially-strapped entrant. In this example, the incumbent offers the contestable unit at a negative incremental price even though a positive incremental price of up to 10 would also suffice (e.g., the incumbent could achieve the same outcome by offering to supply the captive unit at a price of 100 and the captive plus contestable unit at a price of 110). If the marginal cost of production for each unit were instead 15, however, the incumbent would not have a choice. The incremental price of the contestable unit would then have to be negative in order to support exclusion in equilibrium. More generally, we focus in this paper on the role played by negative incremental prices and find that they can arise (under some conditions) in both efficient and exclusionary equilibria. However, whereas they cannot always support efficient equilibria (when these equilibria exist), they can always support exclusionary equilibria (when these equilibria exist). In particular, we find that a common feature of all exclusionary equilibria is that they are supported by contract offers in which the incumbent seller offers to sell the contestable unit at a price that is below its marginal cost. In some cases, it must even offer to sell the contestable unit at a negative price if exclusion is to be supported in equilibrium. That negative incremental prices can arise in both efficient and exclusionary equilibria is an attractive feature of the model. However, it raises the question of whether it is possible ex-ante to distinguish when they will be pro-competitive and when they will be anti-competitive. We examine this question by considering first the consequences in our model of a ban on offers in which a seller charges an incremental price on the contestable unit that is below its marginal cost of production. We then consider the welfare effects of a ban on negative incremental prices. We find that the former always yields the first-best outcome (the buyer will always purchase one unit from each seller in each period). In contrast, we find that the latter does not always eliminate the possibility of exclusion (it would not, for example, eliminate the possibility of exclusion in the numerical setting above). It does, however, reduce the set of circumstances under which exclusionary equilibria arise, and in that sense, it too is welfare improving. The latter is also easier to implement when marginal costs are unknown or not verifiable, considerations that are important in minimizing Type 2 errors. The majority of models of exclusionary conduct come from the literature on exclusive dealing. In many of these models (as in our model), profits are linked over time or across markets, and there are contracting externalities that mitigate the dominant seller's cost of inducing exclusion. First-mover advantages, fixed costs of production, and restrictions on allowable contracts, coupled with coordination failures among buyers, have all been advanced to explain how inefficient exclusion can arise in equilibrium.7 In contrast, in our model, sellers move simultaneously, there are no fixed costs of production, nonlinear contract terms are feasible, and because there is only one buyer, there is no coordination failure among buyers. Instead, switching costs link profits over time, and the inefficient exclusion is made possible by the financial constraints on the incumbent seller's rival. The literatures on market-share contracts, loyalty discounts, and all-units discounts focus mostly on the role of these contracts/discounts in facilitating rent-shifting and dampening competition. They do not, with the exception of the recent work by Calzolari and Denicolo, 2011a and Calzolari and Denicolo, 2011b, who consider the competitive effects of quantity discounts in an asymmetric duopoly with privately informed buyers, consider their potential for inducing exclusion.8 Papers by Spector (2005), Kobayashi (2005), and Heimler (2005) discuss pro-competitive and anti-competitive uses of loyalty discounts but do not rigorously model the market settings in which the discounts arise in the equilibrium of a well-specified game. However, like us, these authors suggest various screens in rule of reason cases that could be used to delineate anti-competitive from permissible loyalty discounts. From this perspective, our paper fits into a growing body of commentary from competition regulators and competition policy experts who have been grappling with the proper standards under which unilateral conduct should be examined (e.g., whether loyalty discounts and other similar practices should be examined through the lens of exclusionary practices or, instead, predatory pricing).9 The rest of the paper proceeds as follows. Section 2 describes the model. Section 3 characterizes necessary and sufficient conditions for equilibria to exist and discusses the role of switching costs and financing constraints in supporting exclusion. Section 4 looks at the sellers' equilibrium contract terms and considers the effects of various restrictions on the space of allowable contracts. Section 5 considers extensions of the model. Section 6 discusses the policy implications of our findings.

We have considered a simple two-period model in which two sellers compete to sell their goods to a single buyer and fully characterized the set of equilibria. Although the efficient outcome calls for the buyer to purchase from both sellers in each period, we showed that under plausible conditions, exclusion can sometimes arise as the unique equilibrium outcome. We showed this despite there being no downstream externalities (there is only one buyer) and complete information about cost and demand parameters. Moreover, we showed that exclusion can arise even though both sellers have the same marginal cost of production and thus are productively equally efficient. We also showed that exclusion can arise whether or not the entrant can compete on the full range of product offerings to the buyer (i.e., whether or not the entrant can compete on both units). The two key assumptions were (a) the entrant is more financially constrained than the incumbent, and (b) the buyer incurs switching costs after its initial round of purchases. These are features of many real-world market settings. A novel aspect of the analysis is that it focuses on how the incumbent is able to support the exclusionary outcomes (when the equilibrium calls for exclusion). We found that while exclusionary equilibria were often but not always supported by negative incremental prices on the incumbent's second unit, all exclusionary equilibria were supported by below-cost pricing on this unit. Moreover, we found that the same outcome could not be achieved by simply equating the incumbent's price on each unit sold, i.e., by offering the same overall discount but with a linear price. Instead, we found that the discount had to be structured in a particular way, for example, with a market-share discount, an all-units discount, or with a loyalty rebate. The scenario we consider comes close in certain respects to the situation instanced by the EC in its Discussion Paper on the Application of Article 82 (at paragraph 143 and section 7.2.2.1), where the incumbent firm offers a “must stock” item which, however, covers only a portion of the buyer's needs. Another portion of the buyer's needs can be fully contested by a challenger whose production costs are on par with that of the incumbent (so, in this respect, the challenger is equally efficient) and, indeed, downstream consumers exhibit a preference for the challenger's product for at least some portion of their needs. By strategically placing the threshold level of commitment in the loyalty rebate schedule, the incumbent creates what the Commission terms a “suction” effect which impels the buyer to actually purchase more than the un-contested portion of its needs. While the example may sound compelling, it is necessary to explain why the incumbent seller would sacrifice a portion of the profits it could earn by not fighting (too aggressively) for the contestable portion of demand. Our model provides the needed link: it shows that because of the link between first period purchases and second period purchases, such first period profit sacrifice can be recouped in the second period when the entrant can no longer compete for the otherwise contestable portion of demand. If the entrant is not so impaired then the initial exclusionary strategy does not make sense to begin with, at least not within the basic common agency model analyzed here, because the increase in the first period share does not enhance profit opportunities in the second period. This discussion also reveals that, since the rationale for exclusionary conduct entails strengthening (or maintaining) market power in the second period, it is flawed to look solely at the ability of the challenger to recompense the buyer for the profits the buyer foregoes if it switches some of the contestable share back to the entrant, when assessing the strength of the “suction” effect. Indeed, if the entrant is sufficiently well-financed it can implement a successful counter-strategy by compensating the buyer's initial losses from the enhanced second-period revenues, or from a loan. This is precisely the point made by Easterbrook (1981) in his seminal article on price predation where he argued that a well-financed pray will be able to survive the period of aggression and benefit from higher prices after that. A predator, who realizes this, eschews predation in the first place, as he would in our model. Our paper brings out the relevance of Easterbrook's insight in the non-predation context: here, and in a predatory setting, banks' incentives to lend to an entrant can be weakened by the very concern that the incumbent seller may engage in exclusionary conduct. Our model allows us to consider the impact on the feasibility of exclusionary strategies in the event of (i) a general prohibition on below-cost pricing, and (ii) a more targeted prohibition on negative incremental prices only, which disallows downward jumps in the buyer's outlay schedule (such downward jumps occur, for example, in contracts with quantity-based all-units discounts). Since incremental costs are generally positive, a negative incremental price would in addition violate a prohibition on below-cost pricing, provided that all of the discount on infra-marginal sales (i.e., sales up to the jump in the outlay schedule) is loaded onto the incremental unit(s). This calculation is consistent with the approach taken in Ortho v. Abbott which, however, unlike the model in the paper, involved bundled discounts across multiple products.26 In our model, the two units offered for sale by the incumbent are essentially interchangeable. Nevertheless, the incumbent's strategy is to induce the customer to purchase both units from him as opposed to buying one unit from the rival. In principle, this is no different from inducing the customer to buy all five different blood tests (as in Ortho) from Abbott, as opposed to splitting the purchases between Abbott and Ortho. As noted earlier, our results were derived in a stylized model in which discounting emerges as a pro-competitive or anti-competitive strategy but in which there is no role for standard, unilateral reasons for discounting (e.g., to mitigate the effects of double marginalization or to enhance the downstream demand of a buyer who may be sensitive to price). It will be important, in future research, to combine these two analytical strands in order to sharpen the policy prescriptions. In these more complex settings, for example, it may be profitable for a buyer to pass on part of the incumbent's discount to final consumers, even when it is exclusionary. Although overall welfare may be lower, the effects on the product's final consumers would then need to be tracked as well.