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JEAN-FRANQOIS MERTENS This book presents a systematic exposition of the use of game theoretic methods in general equilibrium analysis. Clearly the first such use was by Arrow and Debreu, with the "birth" of general equi librium theory itself, in using Nash's existence theorem (or a generalization) to prove the existence of a competitive equilibrium. But this use appeared possibly to be merely tech nical, borrowing some tools for proving a theorem. This book stresses the later contributions, were game theoretic concepts were used as such, to explain various aspects of the general equilibrium model. But clearly, each of those later approaches also provides per sea game theoretic proof of the existence of competitive equilibrium. Part A deals with the first such approach: the equality between the set of competitive equilibria of a perfectly competitive (i.e., every trader has negligible market power) economy and the core of the corresponding cooperative game.
List of contents
A The Core and the Bargaining Set.- I General Equilibrium and Cooperative Games: Basic Results.- II Core Convergence in Perfectly Competitive Economies.- III Economies with Atoms.- IV Bargaining Sets.- B The Value.- V The Shapley Value.- VI Value of Games with a Continuum of Players.- VII The TU Value: The Non-differentiable Case.- Addendum: The Shapley value of a perfectly competitive market may not exist.- VIII The Harsanyi Value.- IX Value Equivalence Theorems: The TU and NTU Cases.- X Economic Applications of the Shapley Value.- C The Cooperative Approach to Large Markets and Games.- XI An Axiomatic Approach to the Equivalence Phenomenon.- XII Large Games and Economies with Effective Small Groups.- D The Non-Cooperative Approach.- XIII Strategic Market Games: a Survey of Some Results.- XIV From Nash to Walras Equilibrium.- XV Correlated- and Communication Equilibria.- XVI Notes on Correlated Equilibrium and Sunspot Equilibrium.- XVII Implementation with Plain Conversation.
Summary
Proceedings of the NATO Advanced Study Institute, Long Island, NY, U.S.A., July 1--12, 1991
