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Playing games with bounded entropy

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  • Valizadeh, Mehrdad
  • Gohari, Amin

Abstract

We study zero-sum repeated games in which the maximizer (player or team) is restricted to strategies with limited randomness. Particularly, we analyze the maxmin payoff of the maximizer in two models: the first model forces the maximizer to randomize her actions just by conditioning them to the outcomes of an observed random source. In the second model, the maximizer is a team of players who are free to privately randomize their corresponding actions but do not have access to any explicit source of shared randomness needed for coordination. While prior works adopted the method of types to address these problems, we use the idea of random hashing being the core of randomness extractors. In addition, we use a tool for simulation of a source from another source. Utilizing these tools, we simplify and generalize the earlier results. We also study the computational aspects of the solution for the first model.

Suggested Citation

  • Valizadeh, Mehrdad & Gohari, Amin, 2019. "Playing games with bounded entropy," Games and Economic Behavior, Elsevier, vol. 115(C), pages 363-380.
    • Handle: RePEc:eee:gamebe:v:115:y:2019:i:c:p:363-380
    DOI: 10.1016/j.geb.2019.03.013
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    References listed on IDEAS

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    1. Olivier Gossner & Rida Laraki & Tristan Tomala, 2004. "Informationally optimal correlation," Working Papers hal-00587228, HAL.
    2. Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," PSE-Ecole d'économie de Paris (Postprint) hal-00487954, HAL.
    3. Gossner, Olivier & Vieille, Nicolas, 2002. "How to play with a biased coin?," Games and Economic Behavior, Elsevier, vol. 41(2), pages 206-226, November.
    4. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
    5. Ilan Adler, 2013. "The equivalence of linear programs and zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 165-177, February.
    6. Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 413-424, May.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Repeated games; Bounded entropy; Randomness extraction; Source simulation; Entropy minimization; Information theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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