J.F. Mertens & S. Sorin 
Game-Theoretic Methods in General Equilibrium Analysis [PDF ebook] 

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.