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

Autores:
Riascos Villegas, Álvaro; Torres-Martínez, Juan Pablo
Palabras clave:
Generalized games, Non-convexities, Pure-strategy Nash equilibrium
Archivo:
Año:
2010
Mes:
Mayo
Número:
13