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On the values of repeated games with signals

Author

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  • Hugo Gimbert

    (LaBRI - Laboratoire Bordelais de Recherche en Informatique - UB - Université de Bordeaux - École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) - CNRS - Centre National de la Recherche Scientifique)

  • Jérôme Renault

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Sylvain Sorin

    (IMJ - Institut de Mathématiques de Jussieu - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Xavier Venel

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Wieslaw Zielonka

    (LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study the existence of different notions of values in two-person zero-sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value and the uniform value may not exist in general. Then, we show the existence of the value for any Borel payoff function if the players observe a public signal including the actions played. We prove also two other positive results without assumptions on the signaling structure: the existence of the $\sup$-value and the existence of the uniform value in recursive games with non-negative payoffs.

Suggested Citation

  • Hugo Gimbert & Jérôme Renault & Sylvain Sorin & Xavier Venel & Wieslaw Zielonka, 2016. "On the values of repeated games with signals," PSE-Ecole d'économie de Paris (Postprint) hal-01006951, HAL.
    • Handle: RePEc:hal:pseptp:hal-01006951
    DOI: 10.1214/14-AAP1095
    Note: View the original document on HAL open archive server: https://hal.science/hal-01006951
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    References listed on IDEAS

    as
    1. A. Maitra & W. Sudderth, 1998. "Finitely additive stochastic games with Borel measurable payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 257-267.
    2. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with a Single Controller and Incomplete Information," Discussion Papers 1346, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    4. Eilon Solan & Nicolas Vieille, 2000. "Uniform Value in Recursive Games," Discussion Papers 1293, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Jérôme Renault, 2012. "The Value of Repeated Games with an Informed Controller," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 154-179, February.
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    8. Maitra, A & Sudderth, W, 1993. "Finitely Additive and Measurable Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(3), pages 201-223.
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    Cited by:

    1. Daniel Hernández-Hernández & Joshué H. Ricalde-Guerrero, 2022. "Zero-Sum Stochastic Games with Random Rules of Priority, Discrete Linear-Quadratic Model," Dynamic Games and Applications, Springer, vol. 12(4), pages 1293-1311, December.
    2. Renault, Jérôme & Ziliotto, Bruno, 2020. "Hidden stochastic games and limit equilibrium payoffs," Games and Economic Behavior, Elsevier, vol. 124(C), pages 122-139.

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