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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. 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).
    3. 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).
    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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