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Deterministic Differential Games Under Probability Knowledge Of Initial Condition

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  • P. CARDALIAGUET

    ()
    (Laboratoire de Mathématiques, CNRS UMR 6205 Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, 29200 Brest, France)

  • M. QUINCAMPOIX

    ()
    (Laboratoire de Mathématiques, CNRS UMR 6205 Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, 29200 Brest, France)

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    Abstract

    We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝn. This result is the first step for future work on differential games with lack of information.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 10 (2008)
    Issue (Month): 01 ()
    Pages: 1-16

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    Handle: RePEc:wsi:igtrxx:v:10:y:2008:i:01:p:1-16

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    Related research

    Keywords: Differential games; incomplete information; Hamilton-Jacobi-Isaacs equation; Subject Classification: 22E46; Subject Classification: 53C35; Subject Classification: 57S20;

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    Cited by:
    1. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    2. Rainer Buckdahn & Juan Li & Marc Quincampoix, 2013. "Value function of differential games without Isaacs conditions. An approach with nonanticipative mixed strategies," International Journal of Game Theory, Springer, vol. 42(4), pages 989-1020, November.
    3. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.

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