Oligopoly and Competition in Large Markets
In this paper we study questions of oligopoly and competition in a general equilibrium framework. In particular, we consider the Nash equilibria of a model of noncooperative exchange in the context of a measure space of economic agents which incorporates both atoms, representing large traders or organized syndicates of traders, and a nonatomic continuum of infinitesimal individual traders. Benyamin Shitovitz (1973, 1974) introduced this type of measure-theoretic model to study situations in which some but not all agents may have market power. Traditional general equilibrium treatments of such situations (see, for example, Kenneth Arrow and Frank Hahn, ch. 6) have been deficient in that they have simply assumed a priori that certain agents behave as price takers while others act noncompetitively, with no formal explanation being given as to why a particular agent should behave one way or the other. Shitovitz's approach represents an important contribution in pointing to an explicit formulation leading to such differences in behavior. In this paper we seek to explore the use of this type of model in studying issues of oligopoly in a general equilibrium framework. A specific focus of our work is in illuminating how either perfectly or imperfectly competitive behavior may emerge endogenously in this model, depending on the characteristics of the agent and his place in the economy. Shitovitz's analysis concentrated on the core of the economy, that is, the set of allocations which no group of agents can improve upon by using only its own resources to achieve a distribution of commodities which each of its members prefers to the allocation in question. This solution concept has, of course, been widely applied in economics, and the equivalence between the core and competitive equilibria in the absence of large traders or syndicates is well known. (See Werner Hildenbrand for a presentation of these results.) Most of the succeeding work with Shitovitz's mixed measure-theoretic model has also been concerned with the core. (See, for example, Jean Jaskold-Gabszewicz and Jacques Dreze, Jaskold-Gabszewicz, Robert Aumann, Andrew Postlewaite and Robert Rosenthal, and Dreze, Gabszewicz, and Postlewaite.) While Shitovitz's model would seem especially appropriate for studying oligopoly, he concentrated not so much on market power phenomena per se as on the possibility that all the core outcomes would still be competitive allocations despite the presence of atoms. Some of the results he obtained in studying this issue appear so counterintuitive as to seem to call into question the use of this model with atoms and a nonatomic ocean in studying oligopoly. For example, his Theorem B (1973) indicates that if there are two large traders or syndicates with the same endowment densities and preferences over consumption bundle densities, then the core and competitive allocations coincide, no matter what the relative sizes of the two traders. Thus, the presence of an arbitrarily small (but not infinitesimal) rival can be viewed as completely cancelling out the market power of a large trader who might represent all but a tiny fraction of the market's potential supply of a commodity. Of course, if one finds such a result unsatisfying, one need not question the model of atoms and a continuum. Rather, one might object to the use of the core as the solution concept. Our work here indicates *Okuno: University of Illinois and Yokohama National University; Postlewaite: University of Illinois; Roberts: Northwestern University. Part of this work was done while Postlewaite was a visiting faculty member at the University of California-San Diego. We wish to thank George Borts and an anonymous referee for comments. Roberts' research was supported by the National Science Foundation under grant SOC 7620953, while Postlewaite's work was partially supported under grant SOC 77-27403.