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

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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," Cahiers de la Maison des Sciences Economiques b05027, Université Panthéon-Sorbonne (Paris 1).
  • Handle: RePEc:mse:wpsorb:b05027
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2005/B05027.pdf
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    1. Bernard De Meyer, 1996. "Repeated Games, Duality and the Central Limit Theorem," Mathematics of Operations Research, INFORMS, vol. 21(1), pages 237-251, February.
    2. DE MEYER , Bernard, 1993. "Repeated Games and the Central Limit Theorem," CORE Discussion Papers 1993003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206.
    4. Bernard De Meyer & Alexandre Marino, 2004. "Repeated market games with lack of information on both sides," Cahiers de la Maison des Sciences Economiques bla04066, Université Panthéon-Sorbonne (Paris 1).
    5. Bernard De Meyer, 1996. "Repeated games, Duality, and the Central Limit Theorem," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00259714, HAL.
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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. repec:hal:journl:halshs-00390625 is not listed on IDEAS
    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.

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    Keywords

    Repeated games; dual games; incomplete information; recurrence formula;

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