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Approximations In Dynamic Zero-Sum Games

Author

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  • Mabel M. TIDBALL

    (INRIA, 2004 Route des Lucioles, BP93, 06902 Sophia-Antipolis Cedex, France)

  • Eitan ALTMAN

Abstract

We develop a unifying approach for approximating a ``limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or ``almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to state approximations of stochastic games, to convergence of finite horizon problems to infinite horizon problems, to convergence in the discount factor and in the immediate reward.

Suggested Citation

  • Mabel M. TIDBALL & Eitan ALTMAN, 1994. "Approximations In Dynamic Zero-Sum Games," Game Theory and Information 9401001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:9401001
    Note: 25 pages, LateX file
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    References listed on IDEAS

    as
    1. Truman Bewley & Elon Kohlberg, 1976. "The Asymptotic Theory of Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 197-208, August.
    2. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
    3. Ward Whitt, 1978. "Approximations of Dynamic Programs, I," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 231-243, August.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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