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Characterizing Pure-strategy Equilibria in Large Games

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Author Info
Fu, Haifeng
Xu, Ying
Zhang, Luyi
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.

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File URL: http://mpra.ub.uni-muenchen.de/8025/
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7514.

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Date of creation: 12 Oct 2007
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Handle: RePEc:pra:mprapa:7514

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Related research
Keywords: Large games; Pure strategy equilibrium; Characterization;

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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  1. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653. [Downloadable!] (restricted)
  2. Kim, Taesung & Yannelis, Nicholas C., 1997. "Existence of Equilibrium in Bayesian Games with Infinitely Many Players," Journal of Economic Theory, Elsevier, vol. 77(2), pages 330-353, December. [Downloadable!] (restricted)
  3. Rath, Kali P. & Yeneng Sun & Shinji Yamashige, 1995. "The nonexistence of symmetric equilibria in anonymous games with compact action spaces," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 331-346. [Downloadable!] (restricted)
  4. Yu, Haomiao & Zhang, Zhixiang, 2007. "Pure strategy equilibria in games with countable actions," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 192-200, February. [Downloadable!] (restricted)
  5. M Ali Khan & Yeneng Sun, 2002. "Non-Cooperative Games with Many Players," Economics Working Paper Archive 482, The Johns Hopkins University,Department of Economics. [Downloadable!]
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  6. Blonski, Matthias, 2005. "The women of Cairo: Equilibria in large anonymous games," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 253-264, April. [Downloadable!] (restricted)
  7. Khan, M. Ali & Sun, Yeneng, 1999. "Non-cooperative games on hyperfinite Loeb spaces1," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 455-492, May. [Downloadable!] (restricted)
    Other versions:
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