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Parameterized games of perfect information

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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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    11. 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.
    12. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2016. "Equilibrium existence for large perfect information games," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 5-18.
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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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