Riascos Villegas, Alvaro and TorresMartínez, Juan Pablo (2012): On the existence of pure strategy equilibria in large generalized games with atomic players.

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Abstract
We 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 nonatomic players. Only atomic players are required to have convex sets of admissible strategies and quasiconcave objective functions.
We prove the existence of a pure strategy Nash equilibria. Thus, we extend to large generalized games with atomic players the results of equilibrium existence for nonatomic games of Schemeidler (1973) and Rath (1992). We do not obtain a pure strategy equilibrium by purification of mixed strategy equilibria. Thus, we have a direct proof of both Balder (1999, Theorem 2.1) and Balder (2002, Theorem 2.2.1), for the case where nonatomic players have a common nonempty set of strategies and integrable bounded codification of action profiles.
Our main result is readily applicable to many interesting problems in general equilibrium. As an application, we extend Aumann (1966) result on the existence of equilibrium with a continuum of traders to a standard general equilibrium model with incomplete asset markets.
Item Type:  MPRA Paper 

Original Title:  On the existence of pure strategy equilibria in large generalized games with atomic players 
Language:  English 
Keywords:  Generalized games; Nonconvexities; Purestrategy Nash equilibrium 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62  Existence and Stability Conditions of Equilibrium 
Item ID:  36626 
Depositing User:  Juan Pablo TorresMartínez 
Date Deposited:  13. Feb 2012 16:59 
Last Modified:  14. Feb 2013 02:08 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/36626 