Fu, Haifeng and Xu, Ying and Zhang, Luyi (2007): Characterizing Purestrategy Equilibria in Large Games.
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Abstract
In this paper, we consider a generalized large game model where the agent space is divided into countable subgroups and each player's payoff depends on her own action and the action distribution in each of the subgroups. Given the countability assumption on its action or payoff space or the Loeb assumption on its agent space, we show that that a given distribution is an equilibrium distribution if and only if for any (Borel) subset of actions the proportion of players in each group playing this subset of actions is no larger than the proportion of players in that group having a best response in this subset. Furthermore, we also present a counterexample showing that this characterization result does not hold for a more general setting.
Item Type:  MPRA Paper 

Original Title:  Characterizing Purestrategy Equilibria in Large Games 
Language:  English 
Keywords:  Large games, Pure strategy equilibrium, Characterization 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  8025 
Depositing User:  Haifeng Fu 
Date Deposited:  01. Apr 2008 13:48 
Last Modified:  16. Feb 2013 04:58 
References:  Aliprantis, C.D., Border, K.C., 1999. Infinite Dimensional Analysis: a Hitchhiker’s Guide. 2nd Ed. Berlin: SpringerVerlag. Blonski, M., 2005. The women of Cairo: equilibria in large anonymous games. Journal of Mathematical Economics 41, 253264. Fu, H.F., 2007. From large games to Bayesian games: a unified approach on pure strategy equilibria. Working paper. NUS Khan, M.A., Rath, K.P., Sun, Y.N., 1997. On the existence of pure strategy equilibria in games with a continuum of players. Journal of Economic Theory 76, 1346. Khan, M.A., Sun, Y.N., 1995. Pure strategies in games with private information. Journal of Mathematical Economics 24, 633653. Khan, M.A., Sun, Y.N., 1996. Nonatomic games on Loeb spaces. Proceedings of the National Academy of Sciences of the United States of America 93, 1551815521. Khan, M.A., Sun, Y.N., 1999. Noncooperative games on hyperfinite Loeb spaces. Journal of Mathematical Economics 31, 455492. Khan, M.A., Sun, Y.N., 2002. Noncooperative games with many players. In: Robert Aumann and Sergiu Hart (Eds), Handbook of Game Theory with Economic Applications Volume III , Elsevier Science, Amsterdam; p. 17611808. Kim, T., Yannelis, N.C., 1997. Existence of equilibrium in Bayesian games with infinitely many players. Journal of Economic Theory 77, 330353. Loeb, P.A., Wolff,M., 2000. Nonstandard Analysis for the Working Mathematician. Kluwer Academic Publishers, Amsterdam. Rath, K.P., Sun, Y.N., Yamashige, S., 1995. The nonexistence of symmetric equilibria in anonymous games with compact action spaces. Journal of Mathematical Economics 24, 331346. Skorokhod, A., 1956. Limit theorems for stochastic processes. Theory of Probability and its Applications 1, 261290. Sun, Y.N., 1996. Distributional properties of correspondences on Loeb spaces. Journal of Functional Analysis 139, 6893. Yannelis, N.C., Rustichini, A., 1991. Equilibrium points of noncooperative random and Bayesian games. In: Aliprantis, C.D., Border, K.C., Luxemberg W.A.J. (eds) Positive operators, Riesz spaces, and economics, Springer, Berlin Heidelberg NewYork, pp 2348. Yu, H.M., Zhang, Z.X., 2007. Pure strategy equilibria in games with countable actions. Journal of Mathematical Economics 43, 192200. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/8025 
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Characterizing Purestrategy Equilibria in Large Games. (deposited 07. Mar 2008 17:17)
 Characterizing Purestrategy Equilibria in Large Games. (deposited 01. Apr 2008 13:48) [Currently Displayed]