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How to play with a biased coin?

Author

Listed:
  • Olivier Gossner

    (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

  • 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 characterize the maxmin of repeated zero-sum games in which player one plays in pure strategies conditional on the private observation of a fixed sequence of random variables. Meanwhile we introduce a definition of a strategic distance between probability measures, and relate it to the standard Kullback distance.

Suggested Citation

  • Olivier Gossner & Nicolas Vieille, 2002. "How to play with a biased coin?," Post-Print hal-00464984, HAL.
    • Handle: RePEc:hal:journl:hal-00464984
    DOI: 10.1016/S0899-8256(02)00507-9
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    References listed on IDEAS

    as
    1. Lehrer Ehud, 1994. "Finitely Many Players with Bounded Recall in Infinitely Repeated Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 390-405, November.
    2. Lehrer, Ehud & Smorodinsky, Rann, 2000. "Relative entropy in sequential decision problems1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 425-439, May.
    3. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 431-456.
    4. 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.
    5. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Olivier Gossner & Rida Laraki & Tristan Tomala, 2004. "Maxmin computation and optimal correlation in repeated games with signals," Working Papers hal-00242940, HAL.
    2. Hernández, Penélope & Urbano, Amparo, 2008. "Codification schemes and finite automata," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 395-409, November.
    3. GOSSNER, Olivier & TOMALA, Tristan, 2003. "Entropy and codification in repeated games with imperfect monitoring," LIDAM Discussion Papers CORE 2003033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Marco Battaglini & Stephen Coate, 2008. "A Dynamic Theory of Public Spending, Taxation, and Debt," American Economic Review, American Economic Association, vol. 98(1), pages 201-236, March.
    5. Valizadeh, Mehrdad & Gohari, Amin, 2019. "Playing games with bounded entropy," Games and Economic Behavior, Elsevier, vol. 115(C), pages 363-380.
    6. repec:dau:papers:123456789/6885 is not listed on IDEAS
    7. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 13-30, February.
    8. Gossner, Olivier & Hörner, Johannes, 2010. "When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 63-84, January.
    9. Mehrdad Valizadeh & Amin Gohari, 2021. "Simulation of a Random Variable and its Application to Game Theory," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 452-470, May.
    10. Neyman, Abraham & Okada, Daijiro, 2009. "Growth of strategy sets, entropy, and nonstationary bounded recall," Games and Economic Behavior, Elsevier, vol. 66(1), pages 404-425, May.
    11. Olivier Gossner & Jöhannes Horner, 2006. "When is the individually rational payoff in a repeated game equal to the minmax payoff?," Discussion Papers 1440, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    13. Hu, Tai-Wei, 2014. "Unpredictability of complex (pure) strategies," Games and Economic Behavior, Elsevier, vol. 88(C), pages 1-15.
    14. Solan, Eilon & Solan, Omri N. & Solan, Ron, 2020. "Jointly controlled lotteries with biased coins," Games and Economic Behavior, Elsevier, vol. 119(C), pages 383-391.

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    More about this item

    Keywords

    biased coin;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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