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Continuous Fictitious Play via Projective Geometry

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  • Ulrich Berger

    (Vienna University of Economics)

Abstract

Using insights from the theory of projective geometry one can prove convergence of continuous fictitious play in a certain class of games. As a corollary, we obtain a kind of equilibrium selection result, whereby continuous fictitious play converges to a particular equilibrium contained in a continuum of equivalent equilibria for symmetric 4x4 zero-sum games.

Suggested Citation

  • Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0303004
    Note: Type of Document - pdf file; pages: 15; figures: included
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0303/0303004.pdf
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    References listed on IDEAS

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    1. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    2. Ulrich Berger, 2002. "Best response dynamics for role games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 527-538.
    3. Vijay Krishna & Tomas Sjostrom, 1995. "On the Convergence of Fictitious Play," Harvard Institute of Economic Research Working Papers 1717, Harvard - Institute of Economic Research.
    4. Metrick, Andrew & Polak, Ben, 1994. "Fictitious Play in 2 x 2 Games: A Geometric Proof of Convergence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 923-933, October.
    5. Vijay Krishna & Tomas Sjöström, 1998. "On the Convergence of Fictitious Play," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 479-511, May.
    6. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    7. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
    8. van Damme, E.E.C., 1983. "Refinements of the Nash Equilibrium Concept," Other publications TiSEM 116b3ec4-be4d-48c2-ad1b-8, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Ulrich Berger, 2003. "A general model of best response adaptation," Game Theory and Information 0303008, University Library of Munich, Germany.
    2. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    3. Ulrich Berger, 2003. "Fictitious play in 2xn games," Game Theory and Information 0303009, University Library of Munich, Germany.

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    More about this item

    Keywords

    Continuous Fictitious Play; Best Response Dynamics; Learning; Projective Geometry;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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