Collusion on Exclusion Edward M. Iacobucci Faculty of Law, University of Toronto Ralph A. Winter Sauder School of Business, UBC October 12, 2012

Abstract Can duopolists sustain tacit collusion not only on pricing but on strategies to exclude entrants?

This question is at the heart of antitrust policy towards joint

dominance. We address the question in a model that joins the dynamic theory of oligopoly pricing with the theory of exclusionary contracts. The model yields as a starting point a simple principle: overlapping contracts, not long term contracts per se, can exclude an entrant. Exclusionary contracts may be pro…table for duopolists even in circumstances where a monopolist incumbent would choose not to exclude, for two reasons.

First, overlapping contracts carry an additional bene…t for a

duopoly: the contracts facilitate collusion by limiting the number of free buyers available to a …rm defecting from cooperative pricing.

Second, the overlapping

contract deterrence strategy is less costly for a duopoly: an entrant into a duopoly anticipates a smaller market share, so that fewer long term contracts su¢ ce to deter entry. The facts inferred from a recent consent order are consistent with predictions of the model. We are grateful to Ken Corts, Scott Hemphill, Patrick Rey, Tom Ross and participants at the Law and Economics Workshop at the University of Chicago for helpful comments.



Competition policy restricts …rm conduct in two areas.

First, the law prohibits ex-

plicit collusion among competitors and restricts practices that facilitate collusive pricing.

Second, the law restricts practices that exclude or disadvantage potential rivals.

The economic foundations for competition policy in the …rst of these areas, collusive behavior, have long been understood. The economic literature has also analyzed a dominant …rm’s incentive for exclusionary practices, including exclusionary contracts, AghionBolton (1987) being the seminal contribution. At the intersection of these two areas is the adoption of exclusionary contracts by an oligopoly. Can oligopolists, competing over time, sustain an implicit agreement not just on prices but on contracts to exclude entrants? This question is relatively unexplored to date in economic theory. Yet the question is at the heart of a highly contentious area of antitrust law. In the U.S., rival …rms engaged in exclusionary conduct without explicit coordination do not violate antitrust law if individually they are not dominant.1 The Federal Trade Commission has attempted to characterize oligopolists’behavior that is interdependent but not collusive as “unfair”under the law, but these attempts have failed.2 In Canada, antitrust authorities historically required explicit collusion for a …nding of abuse of joint dominance, but have recently departed from this approach and contemplate such a …nding even without explicit coordination.3 In Europe, whether uncoordinated oligopolies can be found to have abused a collectively dominant position is also a matter of controversy, with the European Commission suggesting in a discussion paper that “the existence of an agreement or other links in law is not indispensable to a …nding of a collectively dominant position. Such a …nding may be based on other connecting factors and depends on an economic assessment, and, 1

See, e.g., American Bar Association (2007).


See, e.g., E. I. DuPont de Nemours & Co. v. FTC, 729 F.2d 128 (1984).


The antitrust authorities apparently relied on this new approach in negotiating a consent order with

waste disposal companies that were dominant on Vancouver Island, British Columbia (Commissioner of Competition and Waster Services (CA) Inc. and Waste Management of Canada Corporation, 16 June 2009, CT-2009-003 (Comp.Trib.) "Waste Services"). We discuss Waste Services below. Commentators have objected to this development as overreaching on the part of the Bureau (see, e.g., Banicevic and Katz, 2010).


in particular on an assessment of the structure of the market in question” (2005, para. 26). In the …nal version of its guidance on exclusionary abuse of dominance, however, the Commission expressly avoids commenting on the requirements for collective dominance (2009, para. 4). In short, the abuse of joint dominance is an area unsettled in the law and in need of economic foundations. A theory of the abuse of joint dominance must integrate the dynamic theory of collusion with the theory of exclusionary contracts. This paper takes a step towards this integration. We draw on the basic dynamic duopoly theories, in which cooperative pricing can be sustained as an equilibrium if the discount rate is su¢ ciently low (Tirole (1988), Shapiro (1989)). And we draw on the exclusionary contracts model of RasmusenRamseyer-Wiley (1991) and Segal and Whinston (2000) (RRW-SW). A dynamic theory of cooperation not just on pricing but on exclusionary contracts is potentially very complex.

We therefore adopt the simplest set of assumptions allowing us to address our

central question. The model yields as a starting point a simple principle: overlapping or nonsynchronous contracts, not long term contracts per se, exclude an entrant if o¤ered to a su¢ ciently large fraction of buyers.

Long term contracts are not enough to exclude an entrant,

because if long term contracts were synchronous, starting and ending in the same period, then at the end of the common contract period the incumbent(s) and entrant would be symmetrically positioned to compete over existing buyers. Pro…ts would disappear. But when contracts are nonsynchronous, the incumbent(s) can maintain enough buyers in long term contracts that an entrant cannot achieve minimum e¢ cient scale by splitting the remaining buyers.4

We restrict contracts with buyers to being either spot market

contracts or in…nite term contracts. A minimum number of buyers must be retained in long term contracts to deter entry. In the equilibrium with this minimum number of long term contracts, each buyer accepting a long term contract is pivotal in the sense that her decision to accept a long term contract is necessary for entry deterrence (as in Segal and Whinston). The incumbent(s) must compensate long term buyers with the present value 4

An alternative interpretation consistent with our model is that contracts are synchronous but prior

to the end of each contract period the incumbent has a …rst-mover advantage in o¤ering new contracts to buyers that are already contracted.


of the consumer surplus lost from accepting the contract and sustaining entry deterrence. Calculating this cost for the minimum necessary entry-deterring fraction of buyers in long term contracts, and comparing this cost with the bene…ts of maintaining cooperative pricing equilibrium determines whether entry is pro…tably deterred. We …nd that exclusionary contracts may be pro…table for duopolists even in circumstances where a monopolist incumbent would choose not to exclude, for two reasons. First, overlapping contracts carry an additional bene…t for a duopoly in facilitating collusion, as Dana and Fong (2011) show in a model of staggered contracts.5 To understand why, set entry aside and consider the ability of a duopoly to sustain cooperative pricing. The cooperative equilibrium can be sustained if the bene…ts of cheating on cooperative pricing are no greater than the present value of pro…ts from cooperating. The bene…ts of cheating are reduced by nonsynchronous contracting because this strategy limits the number of free buyers available to a …rm defecting from cooperative pricing. Nonsynchronous contracts thus reduce the temptation to cheat on a tacit agreement on prices – an extra bene…t from nonsychronous contracts that would not be captured by a single incumbent.

The exclusionary bene…ts of nonsynchronous contracts arise both for

a single incumbent and for duopoly incumbents, but only duopoly incumbents capture the facilitating-practice bene…t. If the number of nonsynchronous contracts necessary to sustain cooperative pricing is high, the exclusionary bene…ts of the long term contracts may even come for free. The second reason that a duopoly may exclude where a monopolist would not is that the number of (costly) long term contracts that su¢ ce to deter entry into the market is smaller in the case of duopoly incuments.

The prospective entrant into an existing

duopoly foresees a smaller market share compared to a monopolized market simply because it must share the market with two other …rms instead of one. A smaller number of nonsynchronous contracts therefore su¢ ces to prevent the entrant from achieving enough scale to justify entry. To compare the incentives for exclusionary contracting with duopoly incumbents with the case of a single incumbent, we delineate the parameters of the model under which exclusion is pro…table in each case. Two parameters in addition to the discount rate de5

See also Green and Le Coq (2010) for similar reasoning. Green and Le Coq is discussed below.


termine whether cooperation can be sustained in the dimensions of pricing and exclusion. The …rst is the net cost of inducing buyers into long term contracts, which is the e¢ ciency loss from monopoly pricing relative to the monopoly pro…t. The second is the degree of economies of scale on the part of the entrant, as measured by the market share that the entrant must capture to cover costs. Greater economies of scale mean that entry can be excluded with a smaller number of costly long term contracts. The economic literature on contracts as exclusionary has focussed on naked exclusion contracts (RWW-SW) or long term contracts with stipulated damages (Aghion-Bolton). The best form of contracts adopted by …rms for the joint purposes of collusion and exclusion, we suggest, is neither. If long term contracts involved naked exclusion, then a …rm considering defecting from a cartel agreement knows that –even if it does cheat –it will retain in the future the positive net cash ‡ows from buyers that it has previously attracted to the naked exclusion contracts. The incentives to cheat are higher that they would be without this cash ‡ow stream. On the other hand, duopolists that have adopted contracts with meet-or-release (MOR) clauses ensure in the simplest setting that a defector on the cartel price loses the entire stream of future pro…ts (Salop 1986). It is a credible commitment to respond to cheating with a general price o¤er equal to unit cost; if MOR clauses have been adopted then the defector’s existing customers would have the right to prices equal to costs.

The duopolists achieve the goal of collusion more e¢ ciently, i.e. with

fewer costly long term contracts,with MOR contracts than naked exclusion contracts.6 And the duopolists achieve exclusion equally well with the MOR contracts. In the next section of this paper, we review the two literatures that we draw upon in our theory, the literature on collusive pricing and the literature on exclusionary contracts. 6

The bene…cial e¤ect of meet-or-release contracts in this paper contrasts with the e¤ect of simple

long term contracts in Green and Le Coq (2010). In Green and Le Coq, long term contracts have two o¤setting e¤ects on the feasibility of collusion, which the authors call the “gain-cutting e¤ect” and “the protection e¤ect”. The gain cutting e¤ect is that “any contract reduces the demand to be met in the spot market, reducing the short-term gain from defection", as in the current paper. The protection e¤ect is that the defecting …rm’s rival “cannot take away the sales the …rm has covered by contracts made before the defection". The protection e¤ect makes cheating more attractive and collusion less sustainable. The meet-or-release contracts that we propose (and which are adopted in our case example) eliminate the protection e¤ect. This leaves an unambiguously positive of contracts on the sustainability of collusion.


Section 3 develops our model and section 4 then examines a recent competition policy case that illustrates the incentive to collude on exclusion.


Related Literature



The starting point of this paper is an idea with a long history in economics. Cooperative pricing can be sustained as an equilibrium outcome of an in…nitely repeated game.7 In the simplest formulation of this proposition, duopolists play grim trigger strategies. These strategies involve setting monopoly price in each period until either player has deviated from monopoly pricing, following which the player adopts noncooperative Bertrand pricing (Shapiro (1988), Tirole (1988)).

Cooperation is an equilibrium outcome when the

short run bene…ts of cheating on cooperative pricing are less than the present value of sustaining cooperative pricing. For a given number of …rms in the industry, cooperation can be sustained if the discount rate is low enough. The vast literature on dynamic pricing in oligopolies develops extensions of this basic idea.

These extensions include the

question of the maximal degree of collusion sustainable by credible threats for arbitrary values of the discount factor (Abreu 1986) and the problem of detection and optimal punishment given uncertainty in demand or costs (Green and Porter (1984), Harrington and Skrzypacz (2011)). Harrington (2006) o¤ers an excellent overview of cartel theory, including collusion in repeated games. Two papers in this literature hold particular relevance for this paper.


(1989) considers a quantity-setting game in which tacit coordination achieves not only cartel outcome but deters entry. An equilibrium exists in Harrington’s model in which incumbent …rms credibly threaten to respond to entry with a period of aggressive competition. Harrington considers only quantities as strategies. In our model, the focus is equilibria in which incumbent …rms collude on prices as well as contracts to deter entry. Firms deter entry through contracts, as in the recent exclusion literature, rather than threats about post-entry competitive behavior. 7

The more general theorem that cooperation can be sustained by repeated interactions is captured in

the classic model of an in…nitely-repeated prisoners’dilemma. See Fudenberg and Tirole (1993).


Dana and Fong (2011) is the …rst paper to demonstrate the power of nonsychronous contracts in aiding collusion. Firms in the Dana-Fong model o¤er contracts with long but (in the main section of their paper) …nite terms. Consumers with …nite lives enter and leave the market at a constant rate.

Dana and Fong consider the feasibility of

collusion as part of a stationary equilibrium. Collusion is enhanced by staggered, long term contracts because with contracts of length k > 1, only a proportion 1=k of buyers are free from long term contractual obligations as their contracts are renewed in each period. The bene…ts from cheating on collusive pricing are thus reduced to a fraction 1=k of the bene…ts that would be available with 1 period contracts. We build on the essential idea of Dana and Fong in this paper by considering the role of nonsynchronous contracts in entry deterrence, not just collusion.

In the deterrence of entry through contracts,

staggering, or more generally nonsychronicity, is essential even with a single incumbent. Nonsychronicity prevents a potential entrant from simply waiting for the date at which all contracts end, eliminating any incumbency advantage due to long term contracts. Our model integrates the cartel-stabilizing e¤ect of nonsychronicity, which Dana and Fong introduce, with the entry deterrence role of nonsychronicity.



The early Chicago School was skeptical about the anticompetitive e¤ects of exclusive contracts, arguing that buyers would not agree to a contract that exposes them to greater market power on the part of the seller (Bork 1983). Parties will choose a contract that maximizes the total surplus they extract from the contract, and if the compensation that sellers must pay to buyers for accepting an exclusive contract is less than the pro…t obtained from the contract, it was argued, the contract must be e¢ cient. Subsequent commentary accepted the basic insight that buyers would require compensation for contracts’exclusionary e¤ects, but showed that sellers may …nd it pro…table to compensate buyers for such e¤ects with a loss in total e¢ ciency. The key, as Aghion and Bolton (1987) showed, is the use of contracts to extract rents from parties outside the contract.

In the basic Aghion-Bolton model, an incumbent seller and buyer in ef-

fect collude to extract rents from entrants by striking exclusive contracts with stipulated damages clauses.

When entrant’s realized cost is low enough that it does enter, it is 6

able to entice the buyer to breach the exclusive contract and pay liquidated damages. The entrant must o¤er the buyer a particularly attractive price to induce breach, given an obligation to pay signi…cant liquidated damages. A higher stipulated damage in the incumbent-buyer contract induces a lower price on the part of the entrant, and in this sense implements a transfer from the entrant to the buyer. This transfer compensates the buyer for entering into an exclusive contract in the …rst place. The optimal such contract excludes e¢ cient entry under some realizations of the entrant’s random cost. Aghion and Bolton (1987) o¤er another reason why buyers may agree to exclusivity. If there are multiple buyers, externalities may induce each buyer to agree to exclusivity even if it is not in buyers’collective interest to do so. If entrants require a certain scale, the decision of one buyer to accept exclusivity may hinder the entrant’s e¤orts to achieve scale, which in turn negatively a¤ects other buyers. This collective action problem among buyers may lead to exclusion. Rasmusen, Ramseyer and Wiley (1991) (RRW), and later Segal and Whinston (2000) (SW) in their re…nement of RRW (collectively RRW-SW), showed that sellers may …nd it pro…table to compensate a subset of buyers for the welfare losses from “naked” exclusionary contracts (contracts that oblige the buyer only to purchase from the incumbent seller without specifying prices, thus enabling monopoly prices in the future). If a su¢ ciently large subset of buyers agrees to such compensation, a potential entrant cannot achieve minimum e¢ cient scale and thus will not …nd it pro…table to enter and compete. The seller pays the exclusive buyers a lump sum to agree to exclusion, and then charges remaining free buyers monopoly prices. Sellers in equilibrium compensate a subset of buyers fully for forgoing competition and signing naked exclusion contracts (SW).8 Sellers make negative pro…ts on sales to buyers that sign exclusive contracts because full compensation for facing monopoly pricing, the loss of consumer surplus, exceeds monopoly pro…ts by the amount of the deadweight loss. But sellers make pro…ts overall from exclusion because of the monopoly prices charged to free buyers. Fumagalli and Motta (2006)/ Wright (2009) and Simpson and Wickelgren (2007) 8

In the coalition-proof equilbrium restriction adopted by SW, the only equilibrium is one in which

each buyer accepting a long term contract sees her acceptance as pivotal to exclusion of the entrant. Each buyer must therefore be compensated with the full value of the consumer surplus she loses from facing monopoly prices instead of competitive (Bertrand) prices.


showed that the results in RRW-SW depend on whether the buyers are …nal consumers, or instead are intermediate goods producers who themselves compete downstream. Fumagalli and Motta argued that if, for example, downstream buyers engage in Bertrand competition, then even a single free buyer could allow an e¢ cient entrant to achieve scale: if the more e¢ cient entrant o¤ers a lower price than the incumbent, the buyer can capture all of the ultimate downstream market, and thus will purchase all inputs at the intermediate stage.9 Simpson and Wickelgren (2007) consider not only competition downstream but also buyers’ incentives to breach naked exclusionary contracts. In the case of …nal consumers (downstream buyers that do not compete), which is the focus of RRW-SW and our model, Simpson and Wickelgren argue that naked exclusionary contracts cannot exclude because buyers have an incentive to breach. Stipulated damages cannot exceed expectation damages under the penalty doctrine of U.S. law, the authors argue. If an entrant o¤ers competitive prices then buyers, even if they have to pay expectation damages to sellers, are willing to breach since lost pro…ts to the sellers from the contract (expectation damages) are smaller than lost consumer surplus from monopoly prices. Because buyers will breach to buy from a competitive entrant, Simpson and Wickelgren suggest, naked exclusionary strategies will not be successful when buyers are independent. This article contributes to the literature on exclusion by extending the RRW-SW framework to the case of two incumbent sellers. This allows us to address the question at the core of the economic foundations of joint dominance: can two incumbent sellers collude not only on prices but on contracts to exclude a third …rm from entering? We show that in fact two incumbent sellers may be even more likely than one to exclude an entrant.

A second contribution is to highlight the role of nonsychronicity of contract

terms in entry deterrence.

Even in the case of a single incumbent, it is not the long

terms of contracts that deter entry as the existing literature would suggest. Long term contracts deter entry because they allow staggering or more generally nonsynchronicity. Addressing our central question requires a combination of the approach to methods adopted in the literature on collusion and the literature on exclusion. Given the com9

Wright (2009) re…nes and extends the Fumagalli and Motta analysis. Wright shows that when

upstream …rms are allowed to set two-part prices, exclusion will be an equiliibrium if scale economies are large or if the entrant does not have a large cost advantage. Abito and Wright (2008) extend the analysis and sharpen some predictions by introducing product di¤erentiation.


plexity inherent in combining exclusion and collusion, we adopt the simplest possible framework of exclusion and collusion that is found in each literature. Regarding collusion, we assume reversion to Bertrand pricing following the event of cheating. Regarding exclusion, we assume, as in RRW-SW, that the seller can make discriminatory o¤ers, o¤ering long term contracts to some buyers but not others. We depart from the existing literature on exclusionary contracts, however, in abandoning the assumption of naked-exclusion contracts. Naked exclusion contracts are suboptimal for the purpose of cartel stabilization as discussed in the introduction. A naked exclusion contract leaves the cheater on a cartel agreement with the positive cash ‡ows from monopoly pricing to those buyers it has locked up in long term contracts before the cheating decision. This positive cash ‡ow enhances the incentive to defect, compared to a contract or facilitating practice that would leave the defecting …rm with zero cash ‡ows. One alternative such contract is the meet-or-release clause: the buyer (in exchange for an up-front fee) agrees to provide the seller with the option to meet any alternative price that becomes available to the buyer or to release the buyer from the contract.10 To elaborate, if duopolists in a market have both adopted MOR contracts, then it is a credible threat by each …rm in a duopoly attempting tacit collusion to respond to cheating with a price o¤er equal to unit cost for all future periods. That is, such price o¤ers by both …rms for all periods following any price o¤er below the collusive price, is part of a subgame perfect Nash equilibrium. When both …rms in a duopoly adopt MOR contracts with buyers, the consequence of this reaction to cheating is that all cash ‡ows, including those from currently contracted buyers, are lost.

The discipline imposed on

a cheater is maximized since pro…ts following cheating are zero – as in the traditional model of colluding on price but not in a model with naked exclusion contracts. MOR contracts impose the maximum penalty on cheaters and are thus optimal for the purpose of collusion. Moreover, the MOR contracts have the same exclusionary power as nakedexclusion contracts.

Accordingly, we adopt the assumption of MOR contracts, rather

than the suboptimal naked-exclusion contracts. SW show that in the RRW model the unique coalition-proof exclusionary equilibrium involves the signing of long term contracts to the minimal subset of buyers su¢ cient for 10

Salop (1986) provided the …rst analysis of the cartel-stabilizing e¤ect of these contracts.



Each contracted buyer in equilibrium recognizes her acceptance decision as

pivotal in establishing exclusion, which means that the buyers require full compensation for the loss in consumer surplus under the resulting monopoly price as compared to competitive pricing. The parallel proposition in our model is that if long term contracts are entered into in equilibrium, the number of such contracts is the minimum su¢ cient to sustain both collusion and exclusion, with the buyer in each contract fully compensated for the loss in consumer surplus from monopoly pricing. Note that the Simpson-Wickelgren objection to the RRW-SW analysis of the use of naked exclusion contracts as exclusionary instruments does not apply to meet-or-release contracts. (This objection, as discussed above, is that with damages limited to expectation damages under the penalty doctrine of U.S. contract law, buyers will breach and thus break the exclusionary equilibrium.) In meet-or-release contracts, the buyer has no incentive to breach by accepting the entrant’s o¤er without …rst o¤ering the supplier the option to meet the o¤er.11



3.1 3.1.1

Background Theories Long Term Contracts as Exclusionary: the RRW-SW static model

We brie‡y set out an adaptation of the static RRW-SW model as a starting point for our model. We change the assumption of naked exclusion contracts to meet-or-release 11

The Simpson-Wickelgren objection is suspect even within the RRW-SW framework. Simpson and

Wickelgren argue that paying expectation damages would not deter a buyer from breaching an exclusive contract, and that damages cannot exceed expectation damages under U.S. law.

But they do not

consider an alternative remedy for breach that is available to the seller: restitution. Restitution damages are essentially the return of a price paid for services not delivered or obligations not met. Restitution damages are available under the law even when these damages exceed expectation damages. (A supplier being sued for a price refund after failing to deliver a service cannot, for example, argue for a reduction in damages because the buyer paid more than the product is now worth to the buyer.) Sellers in the RWW-SW framework have initially paid buyers an amount that compensates fully for exclusivity in the future. If buyers breach, sellers could sue for the return of the up-front payment. This would leave the buyer with zero surplus from breaching.


contracts in this review. (This makes essentially no di¤erence for the RRW-SW static model but does for our subsequent dynamic model.) An incumbent monopolist in a market, selling to a measure of buyers (normalized to 1), faces a potential entrant. The model has three stages. In stage 1, the incumbent o¤ers buyers meet-or-release contracts –contracts that impose on the supplier the choice of meeting any future price o¤er to the buyer or releasing the buyer from the contract. In exchange for this option, the contract provides for an immediate payment from the incumbent. In stage 2, the entrant decides whether or not to enter. In stage 3, active …rms make price o¤ers for the buyers free of contractual obligations as well as for buyers who have signed exclusive contracts. Then each contracted buyer chooses whether to invoke her right to present the incumbent with the choice between meeting the price o¤er of the entrant, if the entrant is in the market, or releasing the buyer. And, if presented with the option, the incumbent then chooses whether to meet the entrant’s price o¤er or to release the buyer. We consider equilibria in which, if the incumbent is indi¤erent between meeting its rival’s price o¤er or releasing the buyer, it meets the price. Finally, transactions take place. Each buyer has a demand function q( ) with q 0 ( ) < 0. The buyer’s surplus is given R1 by S(p) = p q(s)ds: The incumbent and rival share the same average cost function, c(Q) with c(Q) = c for Q > Q ; for some minimum e¢ cient scale Q , and c0 (Q) < 0

at all Q < Q .

We solve the game backwards.

If stage 3 involves both …rms in the

market, then it is clear that in any equilibrium in the subgame of pricing, the invocation by the buyer of the meet-or-release clause and the optimal response by the incumbent involves the retention of contracted buyers by the incumbent. That is, no equilibrium can involve a price o¤er by the entrant to contracted buyers that will not be matched by the incumbent.12 The entrant supplies only to free buyers in stage 3 and at most to half 12

The incumbent’s equilibrium o¤er to the free buyers is never greater than the entrant’s o¤er. The

incumbent’s marginal cost function in supplying quantity to the free buyers is bounded above (weakly) by the entrant’s cost function. The incumbent’s equilibrium share of free buyers is therefore never less than the entrant’s share. Exercising the option of adding of contracted buyers leaves the incumbents’ marginal cost (over total quantity supplied) no greater than the entrant’s marginal cost. Any price o¤er that the entrant would make in equilibrium would be met with a “meet” decision by the incumbent. Note that our results hold equally well for equilibria in which the entrant does not bother making o¤ers to contracted buyers that it knows will be matched.


of these buyers. Following RRW-SW, the entrant comes into the market in stage 2 if and only if it anticipates nonnegative pro…ts from splitting demand by free buyers in stage 3. = (pm

c)q(pm ) be monopoly pro…t per buyer; x = S(c)


S(pm ) be the additional

surplus captured by a buyer in the event of entry; and e = S(c)

[ + S(pm )] > 0 be

the e¢ ciency loss (loss in total surplus) per buyer from monopoly pricing. Finally, let s = Q =[q(c)] be the minimum share of buyers that an entrant must capture in order to achieve e¢ cient scale. This model has many Nash equilibria, including the o¤er by the incumbent and acceptance by all buyers of long term contracts at zero payment.13 SW restrict attention, as we will, to subgame perfect Nash equilibria in which no coalition of buyers could make themselves better o¤ by changing their acceptance decisions. The re…nement leaves as the only possible exclusionary equilibrium the set of actions in which the monopolist o¤ers compensation x ;which is the full loss of consumer surplus from monopoly, to each of the minimum proportion of buyers, a , su¢ cient to exclude entry. It is a best response for each buyer o¤ered the contract to accept because the buyer is fully compensated for the impact on her surplus of the acceptance decision; and for the monopolist there is no less costly set of exclusionary contract o¤ers.14

The minimum share of buyers that must

accept long term contracts in order for entry to be deterred is the level a such that if the entrant –anticipating that it will capture half the free buyers upon entry –just achieves 13

Acceptance of a long term contract at zero compensation is a Nash equilibrium because assuming all

other buyers are accepting the contract, the cost to a single buyer of accepting the contract is zero. The single buyer’s acceptance decision has no impact on the entry decision. 14

The following is a simple proof that no less costly set of exclusionary contract o¤ers exists. The cost

to the monopolist of the exclusionary strategy of o¤ering a contracts with payment x is a x . Consider any alternative set of contract o¤ers (x1 ; :::xn ). If the alternative is less costly to the incumbent, i.e. Pn if i=1 xi < a x , then # fijxi x g < a . But then rejection of the contracts by the coalition of all buyers in A

fijxi < s g blocks the equilibrium, leading to entry and making buyers in A better

o¤. Rejection by buyers in A and acceptance by the others, and entry, is therefore the only coaltionproof Nash equilibrium in the subgame following the alternative contract o¤ers. O¤er of the alternative contracts is therefore dominated by the o¤er of the minimally su¢ cient number of fully-compensating contracts.


minimum e¢ cient scale. This share is (1=2)(1 a =1

a ) = s , which yields (1)


Exclusion is pro…table if the bene…ts to the incumbent of exclusion exceed the costs. The bene…ts from exclusion are the pro…ts earned from all buyers, . The cost of exclusion is the sum of consumer surplus lost by contracting buyers and for which these buyers must be fully compensated, as explained above. exclusion is

This cost is a x . Hence the condition for

> a x : Since x = e + , this is equivalent to a e < (1

a) :

In other words, the e¢ ciency cost e of entering long term contracts with the necessary fraction of buyers must be less than the bene…t of extracting monopoly pro…ts from the remaining buyers. Equation (1) and the condition (??) yield the condition under which an incumbent monopolist will deter entry in the RRW-SW model s >

1 2(1 + =e)

Note =e = 2 for any linear demand. It follows that in the RRW-SW model with any linear demand, entry deterrence via long term contracts is an equilibrium if and only if the minimum e¢ cient market share is greater than 1=6. 3.1.2

Dynamic Model of Collusion

The simplest model of repeated-game collusion by duopolists (Tirole 1988; Shapiro 1989) involves two …rms with common unit cost c playing an in…nitely-repeated game. The …rms produce identical products, so that the lower-price …rm captures the entire market in any period; when the …rms charge equal prices, the market is split. In general, a strategy set in an in…nitely repeated game consists of a mapping, for each period t, from the history of actions up to the period into an action (a price o¤er) in the period. In addressing the question of whether collusive prices can be sustained in the in…nitely-repeated game, it is standard to consider grim trigger strategies, in which a …rm charges the monopoly price, pm , in period t if in every period preceding t both …rms have charged pm , and otherwise sets price equal to c. In each period, collusion earns each duopolist pro…ts of

=2, where

is the per-period monopoly pro…t. The pair of trigger strategies is an equilibrium, and the collusive outcome sustained as an equilibrium, if the present value of the pro…ts 13

from collusion are greater than the immediate pro…ts from cheating: ( =2) Solving this for in the if






shows that collusive pricing can be sustained as an equilibrium outcome



We consider a market in discrete time in which the demand curve is stationary at q(p). Given the potential complexities within the areas of oligopoly supergames and exclusionary contracts, in combining these two areas we must draw upon the simplest model from each. Three assumptions are central. The …rst is on technology. The incumbent(s) and entrants have access to the same technology in an in…nitely repeated game. We adopt the RRW-SW assumption on costs, which involves increasing returns to scale up to a minimum e¢ cient scale, then constant returns to scale thereafter. This is perhaps the most common representation of economies of scale in the empirical industrial organization literature.16 In our model, the initial diseconomies of scale are overcome once a …rm’s cumulative output over time reaches a minimum level. For example, the initial diseconomies of scale in the cost function can be interpreted as costs of learning; these diseconomies disappear once minimum cumulative output has been reached. At cumulative quantities at or above Q , the average cost is c, whereas at lower cumulative quantities the average cost exceeds c.17 The market share s = Q =q(c) is the minimum e¢ cient market share 15

Of course, in reality successful tacit collusion depends on many factors apart from the discount rate

(Jacquemin and Slade 1989). Adopting the simplest model of dynamic collusion abstracts from other factors, taking a high discount rate as the single factor constraining collusion. 16

. For example, based on their overview of evidence on technology, Scherer and Ross (1990, p.111)

propose “viewing economies of scale in terms of the minimum e¢ cient scale. . . at which all attainable unit cost savings are realized”. 17

An alternative assumption on technology would be that entry requires a one-time investment, with

production then taking place at marginal cost. But in a model with constant marginal cost with a …xed cost of entry, homogenous products and costs, and Bertrand pricing post-entry, deterrence is trivial because of the Bertrand paradox. Even a 1 cent cost of entry would be enough to deter entry because of the anticipation of zero pro…ts post-entry.

The RRW-SW type assumption that economies of scale

disappear once minimum e¢ cient scale is achieved is not only realistic, it is the natural assumption to avoid the trivial, Bertrand-paradox outcome in the case where the entrant and the incumbent have access to the same technology.


(of all buyers, at a competitive price) that an entrant must achieve immediately upon entry to avoid costs above c. Second, we select an equilibrium from the dynamic game that is cooperative pre-entry (in the case of duopoly incumbents) but competitive (Bertrand) post-entry. We recognize the tension in selecting cooperative equilibrium in one subgame and non-cooperative equilibrium in another subgame, but adopt the simplifying assumption in order to focus on the case of an aggressive entrant. Deterrence of an aggressive entrant, i.e. a potential “maverick”to cartel pricing, carries both the strongest incentive and the greatest welfare loss. The assumption captures (in a simple way) the reality that increasing the number of …rms in a market renders cooperative pricing more di¢ cult.18 Our third central assumption captures the idea of overlapping sets of buyers in the market over time. We adopt a simpler approach than a standard overlapping-generations model. A …xed measure of buyers lives in the market each period, with the same proportion entering as new buyers as dying each period. The constant ‡ow of new buyers (“births”) into the market is at a rate b, equal to the number of random “deaths” of buyers in the market. We normalize the constant measure of buyers in the model to be 1. We consider only two time horizons for contracts: in…nite term contracts (until the buyer’s death) or spot market contracts. We adopt this restriction as an assumption, but the in…nite time horizon for long term contracts is an equilibrium even when arbitrary contract lengths are allowed.


Single Incumbent

As a benchmark, we …rst consider the incentives for exclusion by a single incumbent in the dynamic setting. In each period, the timing of actions is illustrated in Table 1. As we enter a period, a fraction (1 b) buyers of each type (free and contracted) is inherited from the previous period; a fraction b new buyers enter. The entry decision is made, and then the active …rms announce prices for free buyers and for contracted buyers. Before the end of the period, whichever …rms are in the market may o¤er long term, meet-or-release 18

In addition, addressing the basic antitrust issue – when do barriers to entry lessen competition? –

requires the case of an aggressive entrant.

Strategies that deter a cooperative entrant do not lessen



contracts to any subset of existing buyers. Then a fraction b of buyers (of each type) dies and the period ends. These assumptions on the timing of actions within each period are the simplest that capture three e¤ects. With buyer turnover, an entrant has access not only to old buyers who have not entered long term contracts, but also to the set of new buyers entering the market. All else equal, a greater rate of buyer turnover will therefore require a higher proportion of long term contracts to exclude the entrant, making entry deterrence more costly. Second, while a …rm cheating on cooperative pricing cannot sell to its rival’s contracted buyers, it can sell to both its own contracted buyers as well as the entire set of entering buyers. Signing up buyers to long term contracts to protect against the incentive to cheat will take this into account. Finally, only …rms currently in the market can o¤er long term contracts –as in the existing literature on exclusionary contracts and, we shall see, in the case study discussed below. b new buyers enter entry decision by entrant price o¤ers to free buyers and contract buyers; long term contract o¤ers acceptance decisions and transactions b buyers of each type die Table 1: Order of Moves in each Period We focus on the deterrence of an aggressive entrant: a …rm whose entry will induce Bertrand competition over free buyers post-entry.

That is, we restrict our attention

to subgame perfect Nash equilibria which involve competitive pricing post-entry. Competition authorities recognize that …rms vary in the extent to which they are likely to cooperate in cooperative pricing versus act as “mavericks” in the context of collusion.19 And competition policy is generally concerned, of course, with the suppression of competition –which in our context is barriers to entry of aggressive competitiors, not potential 19

A maverick is de…ned in the US Horizontal Merger Guidelines as a …rm with “greater incentive to

deviate from the terms of coordination... unusually disruptive and competitive". “Maverick analysis”in antitrust is generally undertaken in the context of collusion or mergers (e.g., Baker 2002), but in principle maverick analysis applies equally well to the exclusion of rivals


entrants that would cooperate post-entry. The restriction also captures in a simple way the empirical reality that collusion is less likely with more incumbents. The assumption is a natural extension of the assumption, in the simplest collusion game, of Bertrand pricing forever as soon as there is any deviation from cooperative pricing. Moreover, the focus on aggressive agents maintains a compelling symmetry in our model between the consequences of failing to exclude and the consequence of failing to collude. In both cases, the consequence of failure is competitive pricing with zero pro…ts. Given the potential complexity of a theory that combines exclusionary contracts with collusion, this symmetry is valuable because it allows a particularly clear delineation of optimal strategies.

To anticipate the duopoly analysis below, we derive the set of

exogenous parameters for which (a) exclusionary contracts would be pro…table in the (hypothetical) case of a duopoly that achieved perfect collusion at zero cost and then (b)the adoption of long term contracts for the purposes of collusion would be pro…table by a (hypothetical) duopoly unthreatened by entry. The intersection of these two sets is then the predicted set of parameters under which the long term contracts are pro…table, since the contracts must achieve both goals to be of any value. With the assumption of an aggressive agent, if the entrant does come into the market then the competition over free buyers is Bertrand.20 The entrant comes into the market if and only if it can achieve minimum e¢ cient scale with half the free buyers immediately available. If scale can be achieved in the …rst period, then cost is equal to c in subsequent periods because the costs greater than c represent one-time investment in entry, such as learning by doing. And if scale cannot be achieved in the …rst period, then any price for which pro…t is nonnegative for the entrant is undercut by the incumbent. Many subgame perfect Nash equilibria emerge in this game, including the o¤er and acceptance of long term contracts by all buyers at zero payment by the incumbent, as in the static game. The restriction to coalition-proof SPNE, however, means that the …rms will maintain only the minimum number of long term contracts that deter entry. Assume that the minimum proportion of buyers, a , that must be maintained in long term contracts to deter entry into the market with one incumbent is an interior solution, 20

That is, we restrict attention to equilibria in which the prices in the post-entry subgames are equi-

librium prices of the static games.


in (0; 1). Note that since a is established at the end of a period it must be low enough that when entering buyers are added to the available buyers, half the total is insu¢ cient to allow the entrant to achieve greater output than Q . That is, a must satisfy 1 [(1 2 In equation (2), the term (1



a ) + b]q(c) = Q

a ) is the number of free buyers inherited from the


previous period and b is the number of newly entered, and therefore free, buyers. When the fraction a of buyers in long term is set so that the demand from sharing these buyers is equal to Q (or Q minus an arbitrarily small number), the entrant is just deterred. This de…nes a . From(2) we have a =

1 2s 1 b


Will it be pro…table to maintain this proportion of buyers in long term contracts? Each long term contract accepted involves payment of the present value to the buyer of the loss in surplus, x , from monopoly pricing each period.

Because of the assumption of

stationarity, the net cost of long term contracts is equivalent (in present value terms) to the payment of a e each period.

In exchange the incumbent receives monopoly pro…t

from the free buyers, which is (1

a ) . Exclusion will be pro…table, therefore, if (1

a ) >a e

which, from (3), is equivalent to =e 1 2s > 1 + =e 1 b



Duopoly Incumbents

Two incumbents in the market will maintain a shared monopoly if they can pro…tably collude on both monopoly pricing and exclusionary contracts. Maintaining the necessary number of costly exclusionary contracts obviously involves externalities between the two duopolists. A multiplicity of equilibria arises because if a2 is the minimum proportion of buyers necessary to maintain in long term contracts, and if a2 is pro…table, then there will be a continuum of equilibria, with one incumbent signing up 18

a2 buyers and the other

incumbent signing (1

)a2 buyers, for some range of

equilibria among these, with


We consider the symmetric

= 1=2.

We consider in turn the pro…tability of exclusion (assuming costless collusion on prices and contracts) and then the pro…tability of collusion (assuming no threat of entry). For long term contracts to be pro…table, parameters must lie in the intersection of the sets for which each goal, exclusion and collusion, is individually pro…table. Exclusion The minimum proportion a2 of buyers necessary to exclude satis…es 1 [(1 3



a2 ) + b]q(c) = Q

since the entrant would capture only 1=3 of the market. This is equivalent to a2 =

1 3s 1 b


Parallel to the single-incumbent analysis above, exclusion is pro…table (assuming collusive pricing) if =e 1 3s > 1 + =e 1 b


Collusion To develop the incentives for collusion, suppose that the duopoly is protected from entry, or “secure”. It is helpful to review the order of the moves within each period and the number of free buyers through the period, when duopolists each enter enough contracts at the end of each period to establish a proportion a buyers in long term contracts at the end of the period. At the beginning of the (next) period, as new buyers enter, the number of free buyers increases to (1


a) + b = (1

a + ab). That is, the relevant

e¤ect of buyer turnover from …rms’ perspectives is to release ab buyers from their long term contracts. Firms simultaneously set prices facing the proportion (1 buyers, each having a(1

a + ab) of free

b)=2 of its own contract buyers. Once prices are set, buyers can

invoke their rights under the meet-or-release clause so that no buyer pays a price higher than the lowest o¤er available to the buyer. Transactions take place. Then at the end of the period, each …rm (if the duopolists maintain a constant a as of the end of the period) signs up ab buyers to replace the contract buyers that died prior to the beginning of the period. 19

A privately e¢ cient implicit agreement on prices and percentage a of long term contracts will maintain a at a level that is just high enough to deter cheating on the agreement. Consider, therefore, the incentives for deviating from a cooperative, pro…t-maximizing agreement on prices and the number of meet-or-release contracts. Deviating from the maximum pro…t outcome in any period could take the form of undercutting the monopoly price during the competition for free buyers, or refusing to o¤er an adequate number of long term contracts. The second of these deviations will not be pro…table if condition (7) holds.

That is, the condition that an exclusionary number of long term contracts

is su¢ cient for no cheating on the o¤er of an adequate number of long term contracts. To determine the incentives for issuing long term contracts it is therefore su¢ cient to consider incentives for cheating on the collusive price. This involves a comparison of the immediate cash ‡ows from cheating with the present value of cash ‡ows from maintaining the cooperative agreement. We develop this comparison below. The comparison of cheating versus cooperating incentives has an implication beyond the stability of the cartel. If it would not be pro…table for duopolists together to maintain collusion by investing a particular proportion of buyers a in long term contracts, then it would be pro…table for an individual duopolist to cheat on the cartel that is maintaining a. This is because cheating would implement the no-collusion outcome. Conversely, if investment in enough contracts to maintain collusion is collectively pro…table, then by de…nition there exists a proportion a that renders cheating on the cartel unpro…table. In short, the no-cheating condition, which we derive below, is identical to the condition that collusion be pro…table. As a preliminary matter, note that the consumer surplus earned each period at a competitive price would be s =

+ e.

When a buyer signs a long term contract, she

is compensated in the current period (period 0) for the following stream of cash ‡ows, starting in period 1: (1

b)s; (1

b)2 s; ::: Discounting this yields the following value for

m, the compensation to each buyer at the beginning of the contract:


1 X


[(1 b) ] s =



1 X

[(1 b) ]t s =




1 (1

(A) cash ‡ows from cheating on the cartel: deviating to a price pm


= ( +e)

(1 b) 1 (1 b)


Regarding collusion on prices,

", for small ", would mean capturing the entire set of free 20

buyers, [(1

a) + ab], for one period, as well as retaining the current-period cash ‡ow

from the …rm’s own contract buyers. There are (1=2)(1 b)a contract buyers for the …rm in the current period. Hence the pro…ts from cheating equal [(1 a)+ab+(1=2)(1 b)a] , which equals a(1


b) =2

(B) present value of cash ‡ows from cooperating: The components of the cash ‡ow stream that would obtain from maintaining the cooperative outcome are the following: (1) current period pro…ts from half the free buyers: (1=2)(1

a + ab)

(2) current pro…ts from its own contracted buyers:21 (1=2)(1


(3) contracting costs this period. The number of new buyers that must be contracted is ab=2. The compensation that must be provided to each contracting buyer is given by (8). The product is (1=2)( + e)

ab(1 b) 1 (1 b)


Adding up the total cash ‡ows in the current period, B(1), B(2) and B(3) yields: (1=2)

(1=2)( + e)

ab(1 b) 1 (1 b)


(4) future periods: If the …rm decides to cooperate, it will earn cash ‡ow given by (11) not just in the current period, but also in every future period.

That is, it earns

half the pro…ts in the market, minus the costs of contracting with half of ab, the newly contracting buyers in each period. The contracting costs are given by (10). Hence the present value of pro…t from cooperating is the product of 1=(1 (1=2)( 21

1 1


( + e)

ab(1 b) 1 (1 b)

Note that B(1) and B(2) add up to 1=2 , as they should.


) and (11): (12)

To develop the no-cheating constraint, de…ne G(a) as (9) minus (12): G(a) = (1 =

a + ab) + (1=2)(1


a ab + 2 2


1 1 ( ) 1 2 1


1 1

(1 + e= )


( + e)

ab(1 b) 1 (1 b)

ab(1 b) 1 (1 b)


from which ~ G(a)

(2= )G(a) = 2




1 1

) 1

(1 + e= )

ab(1 b) 1 (1 b)


The no-cheating constraint is ~ G(a)



~ Note that G(a) is linear, and that when a = 0 a necessary and su¢ cient condition for the RHS of (13) to be negative is that > 1=2, as in the static model. When < 1=2, then ~ ~ G(0) > 0 and because G(a) is linear, a necessary and su¢ cient condition for collusion to be pro…table at some a 2 (0; 1), given the exogenous parameter values b; e= and , is ~ G(1) < 0. In summary, we have the following proposition: Proposition 1 Within the model, 1. a = (1

A monopolist facing potential entry will pro…tably deter entry by maintaining 2s )=(1

b) buyers in long term contracts, providing =e 1 2s > 1 + =e 1 b

2. A duopoly will sustain both cooperative pricing and entry deterrence by maintaining max(a2 ; a ^) in long term contracts, with a2 de…ned by (6) and a ^ de…ned as the root of ~ ~ G(a) = 0 respectively, providing < 1=2, G(1) < 0 and =e 1 3s > 1 + =e 1 b


Each set of values for the four exogenous parameters (s ; b; ; e= ) in this model maps into an outcome for the following decisions: an incumbent would exclude or not exclude; a successfully collusive duopoly would exclude or not exclude; and a duopoly secure against entry would collude or not collude. Tracing the outcomes allows us to determine whether and for which parameters a duopoly would adopt the contracts for the strategic purposes


of collusion and exclusion. And we can compare the strength of duopoly incentives with monopoly incentives for the contract strategy. Figure 1 illustrates the ranges of equilibrium outcomes for various values of the parameters, s and b in the case e= = 0:5 (any linear demand), for

= 0:4. The upward

sloping lines provide the upper boundaries of parameters under which exclusion is profitable for a monopoly and, the higher line, for a duopoly. The horizontal line illustrates the critical value of b, 0:358, below which collusion is pro…table for a secure duopoly. (This value is independent of s .) Referring to Figure 1, in region A competitive, Bertand pricing occurs both in a market with an incumbent monopolist (because it does not pay the monopolist to exclude) as well as with an incumbent duopoly (because the rate of buyer turnover is too high to support the no-cheating constraint under the illustrative discount rate of 0.4. In region B, the same outcomes are realized under both market structures, but if (hypothetically) a duopoly could solve the problem of collusion through some exogenous means the duopoly would exclude the entrant by maintaining enough long term contracts. The monopolist would not exclude. In region C, a monopolist would exclude, but the rate of buyer turnover is too high to support collusion, so competitive pricing is realized in the duopoly case but not the incumbent-monopoly case. In region D, the buyer turnover rate is low enough to support collusion but the minimum e¢ cient scale is so small that to maintain enough long term contracts to exclude the entrant would, even for the duopolists, not be worthwhile. An incumbent monopolist, which would have to maintain even more long term contracts to exclude, would certaintly not do so. Turning to region F, if the minimum e¢ cient scale is large enough then both market structures would …nd exclusion pro…table and given the low buyer turnover rate, collusion is also maintained by an incumbent duopoly. Region E of Figure 1 is most interesting. Here not only the duopoly-collusion condition but also the duopoly-exclusion condition (8) is met. The stronger monopoly-exclusion condition is not met, however. Thus the …gure illustrates that duopolists may exclude even where a monopolist would not since an entrant anticipates a smaller share of the market.


b duopoly excludes (eqn 8)



monopoly excludes (eqn 5)  monopoly excludes  (eqn 5)

C 0 358 0.358

duopolists collude (eqn 15)  duopolists collude  (eqn 15)




s* Figure 1:  Partition of Parameters into Equilibrium Outcomes when discount rate δ  = 0.4;  and efficiency loss/profit = 0.5 (any linear demand)  b rate of buyer turnover b:     rate of buyer turnover s*:   minimum efficient market share A:     entry and competitive outcome with either initial market structure B:     a duopoly that could solve the collusion problem via exogenous means, would exclude; a monopolist would not exclude a  monopolist would not exclude C:     a monopolist excludes; a duopoly breaks down D:     duopolists unthreatened by entry would collude; will not exclude entry E:     duopolists collude and exclude; monopolist does not exclude F:     duopolists collude; both monopolists and duopoly exclude


Case Example

Four testable propositions ‡ow from our theory. First, oligopolists may …nd it pro…table to enter long term contracts with buyers, even when there is an e¢ ciency cost to doing so. In fact, duopolists’incentive to invoke long term contracts may extend even beyond that of a monopolist. Second is the prediction that contracts contain meet-or-release clauses (or, equivalently, right-of-…rst-refusal clauses). Third, the adoption of long term contracts explained by our theory would be observed in concentrated markets and under conditions consistent with the ability of oligopolists to maintain cooperative pricing. They would not be observed in markets with competitive structures. Fourth, prices paid by buyers should be lower early in the contractual relationship rather than later. In our greatly simpli…ed model, the prediction is extreme: the …rst payments by buyers are actually negative as the sellers pay contracting buyers up front for the meet-or-release option. Waste Services is a 2008 Canadian case in the market for commercial waste disposal services in several communities on Vancouver Island.22 The case was settled, but basic facts of the case can be inferred from the Consent Agreement.23 Two …rms were jointly dominant in geographic markets in which a single …rm had historically been found liable for abuse of dominance (exclusionary practices with the e¤ect of a substantial lessening of competition).24 The Consent Agreement required the …rms to refrain from a list of practices including the following: setting contract terms greater than 2 years or renewal terms greater than 1 year; limited termination notice periods for buyers ending substantially before the contract end; rights of …rst refusal; obligations to divulge information about o¤ers from third parties; and substantial liquidated damages. The Consent Agreement included requirements to provide notice of and reasons for any increase in price. Long term contracts were clearly used by the two …rms in this matter, and it is fair 22

Commissioner of Competition and Waste Services (CA) Inc. and Waste Management of Canada

Corporation, 16 June 2009, CT-2009-003 (Comp.Trib.) 23

The Consent Agreement is available on the Competition Tribunal’s webpage: http://www.ct- . None of the Competition Commissioner’s conclusions was admitted to by the …rms that were party to the agreement. Winter assisted the Competition Bureau in this matter, but all of the facts upon which we rely in this paper are public. 24

See Director of Investigation and Research v. Laidlaw Waste Systems Ltd. (1992), 40 C.P.R.

(3d) 289 (Comp.Trib.).


to infer that the e¤ective terms of the contracts were extended through the requirement that a buyer inform the supplier of the desire to terminate in a narrow window of time ending well before the contract termination date. Small businesses such as restaurants will not always keep track of di¢ cult-to-locate termination notice dates on waste-disposal contracts, reducing the likelihood of contracts terminating even if appropriate for the buyer and thus extending the e¤ective term of the contracts. Clause 3 (c) of the Consent Agreement states that “All clauses of a Contract relating to term and termination shall be stated clearly and in plain language on the same page as the customer’s signature, and any additional pages shall be initialed by the customer.” It is fair to infer from this clause that the early-noti…cation clauses for termination of the contracts were not plain, clear or prominent in the contracts. And of course the substantial liquidated damages give the long term contracts commitment power in the sense of deterring the buyer from easily switching to a new entrant. Moreover, it is clear from the nature of the market that the long term contracts are not explained by the dominant e¢ ciency explanation of such contracts as protecting investors in speci…c assets against appropriation of returns from the investment (Joskow 1987, Williamson 1979). Investment in a garbage truck, the capital needed to enter the waste collection industry, is not speci…c to any particular buyer.25 Thus, the facts of the case (as can be inferred from the Consent Agreement) are consistent with the implications of our theory that …rms enter long term contracts, even when there is no e¢ ciency incentive to so; these contracts contain meet-or-release clauses; and the incentive for such contracts is especially strong in a concentrated market. The fourth implication of our theory, regarding the rise in prices during the contracts, is also supported by evidence that can be inferred from the Consent Agreement in this case. The requirement in the Agreement that the supplier of services provide notice and explanation of price increases during the term of the contract indicates that prices did increase during the contract terms to an extent that was not justi…ed by costs. One could develop a theory of naïve buyers who consistently entered incomplete contracts and were 25

Evidence in a case like this could include analysis of whether the length of contracts in the

industry in other locations or in other time periods with di¤erent market structures, to identify whether long term contracts were ubiquitous (supporting an e¢ ciency explanation of some sort) or limited to markets with dominant or jointly dominant …rms. No such evidence is on the public record in this case.


surprised by the price increases. But our theory shows that even with fully forwardlooking buyers (indeed, especially with forward-looking buyers) prices will be relatively low during the initial contracts. This is true a fortiori when …rms compete to attract buyers with low initial prices, given the common knowledge that prices will increase as buyers are committed to the contracts.



This paper has linked two theories, the supergame theory of duopolies and the theory of exclusionary contracts, as a …rst step towards the economic foundations of an important area of antitrust: the abuse of joint dominance. Whether a small number of …rms, not explicitly colluding, can be treated as jointly dominant is controversial in antitrust law. Canadian antitrust enforcers have concluded that collusion is not a pre-requisite to joint abuse of dominance, and there is debate in Europe, while U.S. antitrust law does not recognize abuse of dominance ("monopolization") in this context. We …nd that in some circumstances an even stronger basis for intervention exists for joint dominance than for each of the antitrust areas of which it is the intersection. Exclusionary contracts may be more pro…table or more extensively used by a cartel than by a single dominant …rm because nonsychronous contracts provide an additional bene…t of allowing the collusive outcome for the cartel; and because the cartel need contract with a smaller number of buyers for the contracts to successfully exclude.

An additional reason for a duopoly to be more

aggressive in excluding entrants, not incorporated in the model, is that cartel stability is decreasing in the number of cartel members. For example, allowing a third …rm into the market might rule out the collusive outcome as an equilibrium where allowing a second …rm would not. This force is ruled out in our model by the assumption of competitive play in any post-entry game but deserves exploration in a more general model. Our analysis suggests that legal intervention to prohibit exclusionary contracts may be justi…ed in cases of joint dominance, whereas there is no basis for intervention in the case of tacit collusion over prices alone. Cooperative pricing is not susceptible of a remedy, so tacit collusion is not illegal, nor or should it be. Exclusionary contracts, however, are remediable.


Our model yields several testable implications. Three of these …nd support in the case we examine: the use of long term contracts by a duopoly even in the absence of e¢ ciency bene…ts to the contracts; and an increasing price path during the contract; and meetor-release clauses in the contracts.

Another implication, that long term contracts are

used more in concentrated markets even where the markets are not monopolies, deserves investigation. Finally, our analysis suggests a need for more research on the theory of cartels in which strategy spaces extend beyond prices, quantities and investment to include richer contracts. One example of a useful generalization to the theory here is the introduction of randomness in entrants’costs or in cartel stability. We have assumed that the entrant will with certainty have the same costs as the incumbents. It could be that with positive probability the entrant’s costs are higher or lower. If the entrant has lower costs, then the contracts that the incumbents o¤er must have more exclusionary features than the meet-or-release contracts that we have described. With a simple meet-or-release contract, the more e¢ cient entrant can undercut the incumbents and sell to all existing and new buyers. Incumbents would want to adopt contracts that allow them to punish the other incumbent for cheating on collusion, while at the same time not allowing more e¢ cient entrants to win buyers. One possibility is for the incumbents to commit to match prices in their contracts, rather than include meet-or-release clauses in their contracts. Such a contract would threaten the other duopolist with reversion to competitive conditions in the event of cheating on the collusive arrangement, but would also prevent a more e¢ cient entrant from undercutting the incumbent. The sellers would have to compensate buyers for the foreclosure of more e¢ cient competitors, and thus would have to pay more to foreclose than they would in the basic model where only equally e¢ cient sellers enter. But this could be a pro…table strategy given the exploitation of free buyers that exclusion permits. This strategy would be vulnerable to renegotiation, but if renegotiation were costless among all parties, more e¢ cient entrants would not be kept out of the market with any strategies. In any case, the assumption that the incumbents and entrants have access to the same technology is reasonable for many markets in which competition policy issues arise. In the extension of the model to incorporate potential variation in costs, the two


incentives for staggered, long term contracts would both in‡uence the optimal use of such contracts.

In our simpler model, by contrast, the optimum use of long term contracts

is determined as the minimum of the number su¢ cient for each role: cartel stability and entry deterrence. A second extension would incorporate the case of cooperative pricing in the post-entry subgame. Investment by the incumbent in long term contracts prior to the entry decision could either exclude or accomodate the potential entrant. In either case, the post-entry subgame would involve sequences of investments in long term contracts by the two …rms, supporting cooperation in pricing decisions. A rich set of questions remain to be explored in the extension of strategies in dynamic oligopoly games to incorporate contracts.


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Hawk, Barry and Giorgio Motta, “Oligopolies and Collective Dominance: A Solution in Search of A Problem,” Treviso Conference on Antitrust Between EC Law and National Law, Eighth Edition, Fordham Law Legal Studies Research Paper No. 1301693, available at SSRN: Harrington, Joseph, "How Do Cartels Operate?," Foundations and Trends in Microeconomics, August 2006. Harrington, Joseph, “Collusion and Predation under (Almost) Free Entry,” International Jour- nal of Industrial Organization, Vol. 7, September 1989, pp. 381-401. Harrington, Joseph and Andrzej Skrzypacz, "Private Monitoring and Communication in Cartels: Explaining Recent Collusive Practices," American Economic Review, forthcoming (2011) Heeb, Randal, William E. Kovacic, Robert C. Marshall, and Leslie M. Marx, “Cartels as Two-Stage Mechanisms: Implications for the Analysis of Dominant-Firm Conduct," Chicago Journal of International Law, Vol. 10, No.1 (Summer 2009). Jacquemin, Alexis, and Margaret E. Slade, “Cartels, Collusion, and Horizontal Merger.” In Handbook of Industrial Organization Volume I, Richard Schmalensee, and Robert D. Willig, eds. (Amsterdam: North Holland, 1989). Joskow, Paul L., "Contract Duration and Relationship-Speci…c Investments: Empirical Evidence from Coal Markets," American Economic Review, Vol. 77, No. 1 (Mar., 1987), pp. 168-185 Rasmusen, Eric B., J. Mark Ramseyer, and John S. Wiley, JR, “Naked Exclusion,”The American Economic Review, December 1991, Vol.81 No.5, 1137-1145. Salop, S.C., 1986, “Practices that (credibly) facilitate oligopoly co-ordination,”in: J.E. Stiglitz and G.F. Mathewson, eds., New developments in the analysis of market structure (MIT Press, Cambridge, MA). Scherer, F. and David Ross, Industrial market structure and economic performance, 1990 30

Segal, Ilya R. and Michael D. Whinston, "Naked Exclusion: Comment," The American Economic Review, March 2000, Vol.90, No.1, 296-309. Shapiro, Carl, "Theories of Oligopoly Behavior," Ch. 6 in Handbook of Industrial Organization, North-Holland, 1989. Simpson, John and Abraham Wickelgren (2007) Naked Exclusion, E¢ cient Breach, and Downstream Competition, American Economic Review Tirole, Jean, The Theory of Industrial Organization, MIT Press 1988. Vitzilaiou, Lia and Constantinos Lambadarios, “The Slippery Slope of Addressing Collective Dominance Under Article 82 EC,” GCP: The Antitrust Chronicle, October 2009, Release 1, 1-10. Williamson, Oliver E. , Transaction-cost economics: The governance of contractual relations. Journal of Law and Economics, 22(2) (1979): 233-261. Wright, Julian 2009. "Exclusive Dealing and Entry, When Buyers Compete: Comment." American Economic Review, 99(3)


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