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On the MaxMin Value of Stochastic Games with Imperfect Monitoring

Author

Listed:
  • Dinah Rosenberg

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Eilon Solan

    (TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University)

  • Nicolas Vieille

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study zero-sum stochastic games in which players do not observe the actions of the opponent. Rather, they observe a stochastic signal that may depend on the state, and on the pair of actions chosen by the players. We assume each player observes the state and his own action. We propose a candidate for the max-min value, which does not depend on the information structure of player 2. We prove that player 2 can defend the proposed max-min value, and that in absorbing games player 1 can guarantee it. Analogous results hold for the min-max value. This paper thereby unites several results due to Coulomb.

Suggested Citation

  • Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2001. "On the MaxMin Value of Stochastic Games with Imperfect Monitoring," Working Papers hal-00593645, HAL.
    • Handle: RePEc:hal:wpaper:hal-00593645
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    Cited by:

    1. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    3. Xavier Venel, 2015. "Commutative Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 403-428, February.
    4. Jean-François Mertens & Abraham Neyman & Dinah Rosenberg, 2009. "Absorbing Games with Compact Action Spaces," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 257-262, May.
    5. Levy, Yehuda, 2012. "Stochastic games with information lag," Games and Economic Behavior, Elsevier, vol. 74(1), pages 243-256.
    6. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    7. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

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    Keywords

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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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