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Approximate equilibria in strongly symmetric games

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  • Rachmilevitch, Shiran

Abstract

I study approximate equilibria in games with countably many players and finitely many pure strategies, with an emphasis on symmetric games. In a class of games called strongly symmetric tail function games, the following holds: existence of perfect ϵ-equilibrium (Solan and Vielle, 2001) for all ϵ>0 is equivalent to the existence of Nash equilibrium. In the larger class of strongly symmetric (not necessarily tail function) games, this equivalence no longer holds. The main result is that every strongly symmetric game has a symmetric ϵ proper equilibrium (Myerson, 1978) which is an ϵ-equilibrium (Radner, 1980). This existence result fails to hold in the larger class of weakly symmetric games.

Suggested Citation

  • Rachmilevitch, Shiran, 2016. "Approximate equilibria in strongly symmetric games," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 52-57.
    • Handle: RePEc:eee:mateco:v:66:y:2016:i:c:p:52-57
    DOI: 10.1016/j.jmateco.2016.07.003
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    References listed on IDEAS

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    1. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    2. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Xefteris, Dimitrios, 2015. "Symmetric zero-sum games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 89(C), pages 122-125.
    4. Fey, Mark, 2012. "Symmetric games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 75(1), pages 424-427.
    5. Voorneveld, Mark, 2010. "The possibility of impossible stairways: Tail events and countable player sets," Games and Economic Behavior, Elsevier, vol. 68(1), pages 403-410, January.
    6. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. repec:dau:papers:123456789/6017 is not listed on IDEAS
    8. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
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    Cited by:

    1. Conrad Kosowsky, 2023. "Nash Equilibrium and Axiom of Choice Are Equivalent," Papers 2306.01790, arXiv.org.
    2. Rachmilevitch, Shiran, 2020. "A note on discontinuity and approximate equilibria in games with infinitely many players," Economics Letters, Elsevier, vol. 193(C).

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