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 h...
- 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/
| Summary: | 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. |
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