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Pure strategy Nash equilibria of large finite-player games and their relationship to non-atomic games

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  • Carmona, Guilherme
  • Podczeck, Konrad

Abstract

We consider Nash equilibria of large anonymous games (i.e., each player's payoff depends on his choice and the distribution of the choices made by others). We show that pure strategy Nash equilibria exist in all sufficiently large finite-player games with finite action spaces and for generic distributions of players' payoff functions. We also show that equilibrium distributions of non-atomic games are asymptotically implementable in terms of Nash equilibria of large finite-player games. Extensions of these results to games with general compact metric action spaces are provided.

Suggested Citation

  • Carmona, Guilherme & Podczeck, Konrad, 2020. "Pure strategy Nash equilibria of large finite-player games and their relationship to non-atomic games," Journal of Economic Theory, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:jetheo:v:187:y:2020:i:c:s002205312030020x
    DOI: 10.1016/j.jet.2020.105015
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    Cited by:

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    3. Ghislain H. Demeze-Jouatsa & Roland Pongou & Jean-Baptiste Tondji, 2021. "A Free and Fair Economy: A Game of Justice and Inclusion," Papers 2107.12870, arXiv.org.
    4. Demeze-Jouatsa, Ghislain-Herman & Pongou, Roland & Tondji, Jean-Baptiste, 2021. "A Free and Fair Economy: A Game of Justice and Inclusion," Center for Mathematical Economics Working Papers 653, Center for Mathematical Economics, Bielefeld University.
    5. Ghislain Herman Demeze-Jouatsa & Roland Pongou & Jean-Baptiste Tondji, 2024. "Justice, inclusion, and incentives," Journal of Theoretical Politics, , vol. 36(2), pages 101-131, April.
    6. Enxian Chen Bin Wu Hanping Xu, 2024. "The equilibrium properties of obvious strategy profiles in games with many players," Papers 2410.22144, arXiv.org.
    7. Carmona, Guilherme & Podczeck, Konrad, 2022. "Strict pure strategy Nash equilibrium in large finite-player games when the action set is a manifold," Journal of Mathematical Economics, Elsevier, vol. 98(C).

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    More about this item

    Keywords

    Large games; Pure strategy; Nash equilibrium; Asymptotic implementation; Generic property;
    All these keywords.

    JEL classification:

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

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