On the existence of pure strategy equilibria in large generalized games with atomic players

Alvaro Riascos () and Juan Pablo Torres-Martinez

MPRA Paper from University Library of Munich, Germany

Abstract: We consider a game with a continuum of players where only a finite number of them are atomic. Objective functions and admissible strategies may depend on the actions chosen by atomic players and on aggregate information about the actions chosen by non-atomic players. Only atomic players are required to have convex sets of admissible strategies and quasi-concave objective functions. We prove the existence of a pure strategy Nash equilibria. Thus, we extend to large generalized games with atomic players the results of equilibrium existence for non-atomic games of Schemeidler (1973) and Rath (1992). We do not obtain a pure strategy equilibrium by purification of mixed strategy equilibria. Thus, we have a direct proof of both Balder (1999, Theorem 2.1) and Balder (2002, Theorem 2.2.1), for the case where non-atomic players have a common non-empty set of strategies and integrable bounded codification of action profiles. Our main result is readily applicable to many interesting problems in general equilibrium. As an application, we extend Aumann (1966) result on the existence of equilibrium with a continuum of traders to a standard general equilibrium model with incomplete asset markets.

Keywords: Generalized games; Non-convexities; Pure-strategy Nash equilibrium (search for similar items in EconPapers)
JEL-codes: C62 C72 (search for similar items in EconPapers)
Date: 2012-01
New Economics Papers: this item is included in nep-gth and nep-mic
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Citations: View citations in EconPapers (2)

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