A Direct Proof of the Existence of Pure Strategy Equilibria in Large Generalized Games with Atomic Players

Alvaro Riascos () and Juan Pablo Torres-Martinez

No 7091, Documentos CEDE from Universidad de los Andes, Facultad de Economía, CEDE

Abstract: 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. In this context, we prove the existence of pure strategy Nash equilibria, a result that extends Rath (1992, Theorem 2) to generalized games and gives a direct proof of a special case of Balder (1999, Theorem 2.1). Our proof has the merit of being simple, based only on standard fixed point arguments and finite dimensional real analysis.

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)
Pages: 12
Date: 2010-05-02
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (1)

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Related works:
Working Paper: A direct proof of the existence of pure strategy equilibria in large generalized games with atomic players (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:col:000089:007091

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