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Two More Classes of Games with the Fictitious Play Property

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  • Ulrich Berger

    (Vienna University of Economics)

Abstract

Fictitious play is the oldest and most studied learning process for games. Since the already classical result for zero-sum games, convergence of beliefs to the set of Nash equilibria has been established for some important classes of games, including weighted potential games, supermodular games with diminishing returns, and 3x3 supermodular games. Extending these results, we establish convergence for ordinal potential games and quasi-supermodular games with diminishing returns. As a by-product we obtain convergence for 3xm and 4x4 quasi-supermodular games.

Suggested Citation

  • Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0408003
    Note: Type of Document - pdf; pages: 17
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0408/0408003.pdf
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    References listed on IDEAS

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    Cited by:

    1. Berger, Ulrich, 2007. "Brown's original fictitious play," Journal of Economic Theory, Elsevier, vol. 135(1), pages 572-578, July.
    2. Ulrich Berger, 2006. "A Generalized Model Of Best Response Adaptation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 45-66.
    3. Leslie, David S. & Collins, E.J., 2006. "Generalised weakened fictitious play," Games and Economic Behavior, Elsevier, vol. 56(2), pages 285-298, August.

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    More about this item

    Keywords

    Fictitious Play; Learning Process; Ordinal Potential Games; Quasi-Supermodular Games;
    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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