Title: Large Games and Economies With Effective Small Groups
Abstract: A model of large games in characteristic form is introduced and a number of results are reported. The game-theoretic results and techniques are related to economic models and results. For the main results, two properties are required: most players have many substitutes and small groups are effective - all or almost all gains to collective activities can be realized by groups bounded in absolute size of membership. From these two properties it follows that: approximate cores of large games are nonempty; approximate cores of large games are typically small, and converge to Walrasian payoffs; asymptotically, the approximate core correspondence is monotonic, that is, a vector of changes in population composition and a corresponding vector of changes in core payoffs point in opposite directions; the core of a continuum limit game with small (finite) groups is nonempty; and when all gains to group formation can be realized by groups bounded in absolute size then the convergence of the core occurs at finite group sizes and the monotonicity of the core correspondence is exact. The totality of the results suggests that a competitive economy is one with many substitutes for all players and/or commodities and with effective small groups.
Creation-Date: March 1992, Revised August 1992
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