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Fictitious play in 2xn games

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  • Ulrich Berger

    (Vienna University of Economics)

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    Abstract

    It is known that every continuous time fictitious play process approaches equilibrium in every nondegenerate 2x2 and 2x3 game, and it has been conjectured that convergence to equilibrium holds generally for 2xn games. We give a simple geometric proof of this.

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    File URL: http://128.118.178.162/eps/game/papers/0303/0303009.pdf
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    Bibliographic Info

    Paper provided by EconWPA in its series Game Theory and Information with number 0303009.

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    Length: 11 pages
    Date of creation: 25 Mar 2003
    Date of revision:
    Handle: RePEc:wpa:wuwpga:0303009

    Note: Type of Document - pdf-file; pages: 11; figures: included
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    Web page: http://128.118.178.162

    Related research

    Keywords: Fictitious Play; Learning Process; 2xn Games;

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    References

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    1. Vijay Krishna & T. Sjostrom, 2010. "On the Convergence of Fictitious Play," Levine's Working Paper Archive 417, David K. Levine.
    2. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    3. Monderer, Dov & Sela, Aner, 1997. "Fictitious play and- no-cycling conditions," Sonderforschungsbereich 504 Publications 97-12, Sonderforschungsbereich 504, Universit├Ąt Mannheim;Sonderforschungsbereich 504, University of Mannheim.
    4. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May.
    5. 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.
    6. Harris, Christopher, 1998. "On the Rate of Convergence of Continuous-Time Fictitious Play," Games and Economic Behavior, Elsevier, vol. 22(2), pages 238-259, February.
    7. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November.
    8. Metrick, Andrew & Polak, Ben, 1994. "Fictitious Play in 2 x 2 Games: A Geometric Proof of Convergence," Economic Theory, Springer, vol. 4(6), pages 923-33, October.
    9. Diana Richards, 1997. "The geometry of inductive reasoning in games," Economic Theory, Springer, vol. 10(1), pages 185-193.
    10. Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, EconWPA.
    11. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    12. Foster, Dean P. & Young, H. Peyton, 1998. "On the Nonconvergence of Fictitious Play in Coordination Games," Games and Economic Behavior, Elsevier, vol. 25(1), pages 79-96, October.
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