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Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides

Author

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  • Bernard de Meyer

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Alexandre Marino

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

The recursive formula for the value of the zero-sum repeated games with incomplete information on both sides is known for a long time. As it is explained in the paper, the usual proof of this formula is in a sense non constructive: it just claims that the players are unable to guarantee a better payoff than the one prescribed by formula, but it does not indicates how the players can guarantee this amount. In this paper we aim to give a constructive approach to this formula using duality techniques. This will allow us to recursively describe the optimal strategies in those games and to apply these results to games with infinite action spaces.

Suggested Citation

  • Bernard de Meyer & Alexandre Marino, 2005. "Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00193996, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00193996
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00193996v1
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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. Bernard de Meyer & Ehud Lehrer & Dinah Rosenberg, 2009. "Evaluating information in zero-sum games with incomplete information on both sides," Post-Print halshs-00390625, HAL.
    3. De Meyer, Bernard, 2010. "Price dynamics on a stock market with asymmetric information," Games and Economic Behavior, Elsevier, vol. 69(1), pages 42-71, May.
    4. Fabien Gensbittel & Miquel Oliu-Barton, 2020. "Optimal Strategies in Zero-Sum Repeated Games with Incomplete Information: The Dependent Case," Dynamic Games and Applications, Springer, vol. 10(4), pages 819-835, December.
    5. Bernard De Meyer & Ehud Lehrer & Dinah Rosenberg, 2010. "Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 851-863, November.

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