A direct proof of the existence of pure strategy equilibria in large generalized games with atomic players

Consider a game with a continuum of players where only a finite number of them are atomic. Objective functions and admissible strategies may dependon the actions chosen by atomic players and on aggregate information about theactions chosen by non-atomic players. Only atomic players are required to haveconvex sets of admissible strategies and quasi-concave objective functions. In thiscontext, we prove the existence of pure strategy Nash equilibria, a result that ex-tends Rath (1992, Theorem 2) to generalized games and gives a direct proof of aspecial 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 José; Torres-Martínez, Juan Pablo
• Tipo de recurso: Work document
• Fecha de publicación: 2010
• Institución: Universidad de los Andes
• Repositorio: Séneca: repositorio Uniandes
• Idioma: eng
• OAI Identifier: oai:repositorio.uniandes.edu.co:1992/8167
• Acceso en línea: http://hdl.handle.net/1992/8167
• Palabra clave: Generalized games; Non-convexities; Pure-strategy Nash equilibrium; Equilibrios de Nash; Teoría de los juegos; C72, C62
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/