Values of Large Finite Games

Abstract

The competitive equilibrium is a notion based on what each agent can obtain by itself. The value is a notion based on what each individual contributes to society. These notions tend toward coincidence in large exchange economies. For replica exchange economies with transferable utility, the value tends toward the (unique) competitive allocation. The framework of finite economies establishes convergence of the value to a competitive allocation. The framework of continuum economies establishes that the value is a competitive allocation. For large economies, the core converges to the set of competitive allocations, the results can be roughly summarized for large exchange economies; the value is nearly in the core. To capture the idea of a large game, the notion of a technology is introduced, and of a game derived from a technology. This framework is general to include economic environments including exchange, coalition production, hedonic coalitions, club goods, and local public goods; pure public goods generally do not fit within this framework. The framework also allows for indivisibilities and nonconvexities.