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The possibility of impossible stairways: Tail events and countable player sets

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  • Voorneveld, Mark

Abstract

In classical game theory, players have finitely many actions and evaluate outcomes of mixed strategies using a von Neumann-Morgenstern utility function. Allowing a larger, but countable, player set introduces phenomena that are impossible in finite games: Even if players have identical payoffs (no conflicts of interest), (1) this payoff may be minimized in dominant-strategy equilibria, and (2) games so alike that even the consequences of unilateral deviations are the same, may have disjoint sets of payoff-dominant equilibria. Moreover, a class of games without (pure or mixed) Nash equilibria is constructed.

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  • 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.
    • Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:403-410
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    Cited by:

    1. Rachmilevitch, Shiran, 2020. "A note on discontinuity and approximate equilibria in games with infinitely many players," Economics Letters, Elsevier, vol. 193(C).
    2. Khan, M. Ali & Qiao, Lei & Rath, Kali P. & Sun, Yeneng, 2020. "Modeling large societies: Why countable additivity is necessary," Journal of Economic Theory, Elsevier, vol. 189(C).
    3. Conrad Kosowsky, 2023. "Nash Equilibrium and Axiom of Choice Are Equivalent," Papers 2306.01790, arXiv.org.
    4. Kutay Cingiz & János Flesch & P. Jean-Jacques Herings & Arkadi Predtetchinski, 2020. "Perfect information games where each player acts only once," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 965-985, June.
    5. Voorneveld, Mark, 2019. "An axiomatization of the Nash equilibrium concept," Games and Economic Behavior, Elsevier, vol. 117(C), pages 316-321.
    6. Rachmilevitch, Shiran, 2016. "Approximate equilibria in strongly symmetric games," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 52-57.

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