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Parameterized games of perfect information

Author

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  • János Flesch

    (Maastricht University)

  • Arkadi Predtetchinski

    (Maastricht University)

Abstract

Considered are perfect information games with a Borel measurable payoff function that is parameterized by points of a Polish space. The existence domain of such a parameterized game is the set of parameters for which the game admits a subgame perfect equilibrium. We show that the existence domain of a parameterized stopping game is a Borel set. In general, however, the existence domain of a parameterized game need not be Borel, or even an analytic or co-analytic set. We show that the family of existence domains coincides with the family of game projections of Borel sets. Consequently, we obtain an upper bound on the set-theoretic complexity of the existence domains, and show that the bound is tight.

Suggested Citation

  • János Flesch & Arkadi Predtetchinski, 2020. "Parameterized games of perfect information," Annals of Operations Research, Springer, vol. 287(2), pages 683-699, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-018-3087-5
    DOI: 10.1007/s10479-018-3087-5
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    References listed on IDEAS

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    6. Carlos Alós-Ferrer & Klaus Ritzberger, 2016. "The Theory of Extensive Form Games," Springer Series in Game Theory, Springer, number 978-3-662-49944-3, June.
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    8. 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.
    9. 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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    1. Sam Ganzfried, 2021. "Human strategic decision making in parametrized games," Papers 2104.14744, arXiv.org, revised Nov 2021.
    2. Sam Ganzfried, 2022. "Human Strategic Decision Making in Parametrized Games," Mathematics, MDPI, vol. 10(7), pages 1-23, April.

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