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A Characterization of Subgame-Perfect Equilibrium Plays in Borel Games of Perfect Information

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  • János Flesch

    (Department of Quantitative Economics, Maastricht University, 6200 MD Maastricht, Netherlands)

  • Arkadi Predtetchinski

    (Department of Economics, Maastricht University, 6200 MD Maastricht, Netherlands)

Abstract

We provide a characterization of subgame-perfect equilibrium plays in a class of perfect information games where each player’s payoff function is Borel measurable and has finite range. The set of subgame-perfect equilibrium plays is obtained through a process of iterative elimination of plays. Extensions to games with bounded Borel measurable payoff functions are discussed. As an application of our results, we show that if every player’s payoff function is bounded and upper semicontinuous, then, for every positive epsilon, the game admits a subgame-perfect epsilon-equilibrium. As we do not assume that the number of players is finite, this result generalizes the corresponding result of Purves and Sudderth [24] [Purves RA, Sudderth WD (2011) Perfect information games with upper semicontinuous payoffs. Math. Oper. Res. 36(3):468–473].

Suggested Citation

  • János Flesch & Arkadi Predtetchinski, 2017. "A Characterization of Subgame-Perfect Equilibrium Plays in Borel Games of Perfect Information," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1162-1179, November.
    • Handle: RePEc:inm:ormoor:v:42:y:2017:i:4:p:1162-1179
    DOI: 10.1287/moor.2016.0843
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    References listed on IDEAS

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    9. Cingiz, Kutay & Flesch, János & Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2016. "Doing it now, later, or never," Games and Economic Behavior, Elsevier, vol. 97(C), pages 174-185.
    10. Carlos Alós-Ferrer & Klaus Ritzberger, 2017. "Characterizing existence of equilibrium for large extensive form games: a necessity result," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 407-430, February.
    11. Flesch, J. & Kuipers, J. & Schoenmakers, G. & Vrieze, K., 2013. "Subgame-perfection in free transition games," European Journal of Operational Research, Elsevier, vol. 228(1), pages 201-207.
    12. J. Kuipers & J. Flesch & G. Schoenmakers & K. Vrieze, 2016. "Subgame-perfection in recursive perfect information games, where each player controls one state," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 205-237, March.
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    Cited by:

    1. János Flesch & Arkadi Predtetchinski, 2020. "Parameterized games of perfect information," Annals of Operations Research, Springer, vol. 287(2), pages 683-699, April.
    2. 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.

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