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Article Excerpt
Summary. This paper analyzes cartel stability when firms are farsighted. It studies a price leadership model a la D' Aspremont et al. (1983), where the dominant cartel acts as a leader by determining the market price, while the fringe behaves competitively. According to D' Aspremont et al.'s (1983) approach a cartel is stable if no firm has an incentive to either enter or exit the cartel. In deciding whether to deviate or not, a firm compares its status quo with the outcome its unilateral deviation induces. However, the firm fails to examine whether the induced outcome will indeed become the new status quo that will determine its profits. Although the firm anticipates the price adjustment following its deviation, it ignores the possibility that more firms may exit (or enter) the cartel. In other words, the firm does not consider the fact that the outcome immediately induced by its deviation may not be stable itself. We propose a notion of cartel stability that allows firms to fully foresee the result of their deviation. Our solution concept is built in the spirit of von Neumann and Morgenstern's (1944) stable set, while it modifies the dominance relation following Harsanyi's (1974) criticism. We show that there always exists a unique, non-empty set of stable cartels.
Keywords and Phrases: Cartel stability, Foresight, Abstract stable set, Coalition formation.
JEL Classification Numbers: C79, D43, D49, L13.
1 Introduction
The importance of cartel stability is manifested through the extent of the literature dedicated to the topic over (at least) the last three decades. By using a conceptually different approach, we aspire to shed some light to the rather debatable aspects of cartel stability.
The classical doctrine about oligopolistic markets is that even though collusive behavior--all firms acting as one monopolist--is more profitable than competitive behavior--each firm maximizing independently its own profits while ignoring the strategic element inherent in the environment--collusion will not prevail. The reason is that given that every one else colludes and maintains a high price, each firm, unilaterally, has an incentive to deviate and free ride on the cartel's collusive efforts. The cartel would price and produce by maximizing aggregate profits, whereas the cheating firm would function as a price taker and set its marginal cost equal to the market price, as set by the cartel.
One of the most influential works studying cartel stability is the one by D' Aspremont et al. (1983). Their model, based on a general price-leadership framework, considers a finite economy where a dominant cartel sets the market price at a joint profit maximizing level, and a competitive fringe free-rides on the profit maximizing efforts of the cartel by overstepping the quota set by the cartel.
Although price-leadership models are studied in earlier works (not necessarily in an attempt to study cartel behavior), the major contribution of D' Aspremont et al. (1983) is the observation that once a member of the cartel deviates and joins the fringe, the remaining cartel is going to adjust its quota (and thus the market price) in a manner that maximizes the new (shrunk by one member) cartel's aggregate profits. Once such an adjustment is captured by the model, the result is that it may no longer be beneficial for a firm to exit the cartel and join the fringe. The profits the potential deviator may enjoy by increasing his output may be offset by the decrease in market price as brought about by the cartel's adjustment. In particular, the authors formally define and show that there always exists a stable cartel. That is, a specific size of a cartel such that it is not profitable for any member to violate the quota anymore and join the fringe (this aspect of cartel stability is defined as internal stability). Moreover, no more fringe members wish to join the cartel either (this aspect of cartel stability is defined as external stability). It is also shown that the result does not hold for the case where the economy consists of an infinite number of firms.
Along the same lines Donsimoni et al. (1986) study the same general model with the additional assumption of linear demand and marginal cost functions. Besides their different approach towards existence, the authors show that under some additional conditions on cost efficiency the stable cartel is unique.
Within the same institutional setting other works modify some of the assumptions of the basic model. Specifically, Donsimoni (1985) allows for product heterogeneity, while Shaffer (1995) studies the case where the fringe does not behave "that competitively" anymore. Instead, the fringe members realize the strategic impact of their actions on the market price by behaving as in a Cournot competition.
Prokop (1999) uses extensive form games to describe the process of collusion. Each firm, consecutively and in an exogenously determined order, decides to enter the cartel or not. The interesting result is that applying subgame perfection to such a dynamic process yields the same results (stable cartel sizes) with the D' Aspremont et al. (1983) approach. Depending on the order of moves, some firms enjoy more profits than others.
The venue we follow in this paper is to assume that binding agreements are not possible, and therefore examine the immunity of cartels against potential deviations. We do not allow for coalitions to form, apart from the cartel itself, and thus all deviations are unilateral. However, unlike previous works we allow each firm, when contemplating a deviation, to compare the ultimate outcome of its action with its status quo instead of some intermediate situation that may not prevail.
1.1 A simple example
The following trivial example intends to clearly point out the myopia embedded in the analysis of stable cartels. The firms' behavior and the various institutional assumptions are identical to those in D' Aspremont et al.'s (1983) model.
Consider a market with N = {1,..., 5} identical firms and let Q = [[summation].sub.i[member of]N] [q.sub.i] indicate the total quantity produced in the market, whereas [q.sub.i] indicates the individual firm's quantity. Let P indicate the market price.
Consider the simple case of a linear demand, Q = 100-P, where the individual cost function is TC([q.sub.i]) = [1/2]10[q.sub.i.sup.2]. When a cartel of size k [less than or equal to] n, denoted by [C.sub.k] [subset] N, forms it behaves like one firm by maximizing aggregate (with respect to its members) profits, and thus, it produces and prices at the point where the marginal revenue (derived from the residual demand) equals marginal cost. The fringe of size n - k, denoted by [F.sub.k] = N/[C.sub.k], behaves competitively by producing at the point where market price is equal to marginal cost of each firm. The firms in the cartel are aware of the fringe's behavior, and this awareness is reflected on their consideration of the residual demand instead of the market demand.
The...
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