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Characterizing Pure-strategy Equilibria in Large Games

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Listed:
  • Fu, Haifeng
  • Xu, Ying
  • Zhang, Luyi

Abstract

In this paper, we divide the players of a large game into countable different groups and assume that each player’s payoff depends on her own action and the distribution of actions in each of the subgroups. Focusing on the interaction between Nash equilibria and the best response correspondence of the players, we characterize the pure-strategy equilibria in three settings of such large games, namely large games with countable actions, large games with countable homogeneous groups of players and large games with an atomless Loeb agent space. Furthermore, we also present a counterexample showing that a similar characterization result does not hold for large games under a more general setting.

Suggested Citation

  • Fu, Haifeng & Xu, Ying & Zhang, Luyi, 2007. "Characterizing Pure-strategy Equilibria in Large Games," MPRA Paper 7514, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:7514
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    File URL: https://mpra.ub.uni-muenchen.de/8025/2/MPRA_paper_8025.pdf
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    References listed on IDEAS

    as
    1. Blonski, Matthias, 2005. "The women of Cairo: Equilibria in large anonymous games," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 253-264, April.
    2. Khan, M. Ali & Yeneng, Sun, 1995. "Pure strategies in games with private information," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 633-653.
    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.
    4. Khan, M. Ali & Sun, Yeneng, 2002. "Non-cooperative games with many players," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.),Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 46, pages 1761-1808, Elsevier.
    5. 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.
    6. 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.
    7. 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.
    8. M Ali Khan & Yeneng Sun, 1996. "Non-Atomic Games on Loeb Spaces," Economics Working Paper Archive 374, The Johns Hopkins University,Department of Economics, revised Aug 1996.
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    Citations

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    Cited by:

    1. Fu, Haifeng & Yu, Haomiao, 2015. "Pareto-undominated and socially-maximal equilibria in non-atomic games," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 7-15.
    2. Grant, Simon & Meneghel, Idione & Tourky, Rabee, 2016. "Savage games," Theoretical Economics, Econometric Society, vol. 11(2), May.

    More about this item

    Keywords

    Large games; Pure strategy equilibrium; Characterization;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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