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

Serie

  • Documentos CEDE

Resumen

  • 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.

fecha de publicación

  • 2010-05

Líneas de investigación

  • Generalized Games
  • Non Convexities
  • Pure Strategy Nash Equilibrium

Issue

  • 7091