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Maxmin computation and optimal correlation in repeated games with signals

Author

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  • Olivier Gossner

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Rida Laraki

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Tristan Tomala

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

For a class of repeated games with imperfect monitoring, the maxmin payoff is obtained as the solution of an optimization problem defined on a set of probability distributions under entropy constraints. The present paper offers a method for solving such problems for the class of 3-player 2 by 2 games.

Suggested Citation

  • Olivier Gossner & Rida Laraki & Tristan Tomala, 2004. "Maxmin computation and optimal correlation in repeated games with signals," Working Papers hal-00242940, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242940
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242940
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    References listed on IDEAS

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    1. Yair Goldberg, 2003. "On the Minmax of Repeated Games with Imperfect Monitoring: A Computational Example," Discussion Paper Series dp345, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. JÊrÆme Renault & Tristan Tomala, 1998. "Repeated proximity games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 539-559.
    3. Olivier Gossner & Penélope Hernández & Abraham Neyman, 2006. "Optimal Use of Communication Resources," Econometrica, Econometric Society, vol. 74(6), pages 1603-1636, November.
    4. Gossner, Olivier & Vieille, Nicolas, 2002. "How to play with a biased coin?," Games and Economic Behavior, Elsevier, vol. 41(2), pages 206-226, November.
    5. Neyman, Abraham & Okada, Daijiro, 1999. "Strategic Entropy and Complexity in Repeated Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 191-223, October.
    6. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
    7. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
    8. MERTENS, Jean-François & ZAMIR, Shmuel, 1981. "Incomplete information games with transcendental values," LIDAM Reprints CORE 445, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Lehrer, Ehud & Smorodinsky, Rann, 2000. "Relative entropy in sequential decision problems1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 425-439, May.
    10. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Post-Print hal-00487960, HAL.
    11. Tristan Tomala & Olivier Gossner, 2004. "Secret correlation in repeated games with signals," Working Papers hal-00587232, HAL.
    12. Jean-François Mertens & Shmuel Zamir, 1981. "Incomplete Information Games with Transcendental Values," Mathematics of Operations Research, INFORMS, vol. 6(2), pages 313-318, May.
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    Cited by:

    1. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 13-30, February.

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