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Fictitious play in 2xn games

Author

Listed:
  • Ulrich Berger

    (Vienna University of Economics)

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.

Suggested Citation

  • Ulrich Berger, 2003. "Fictitious play in 2xn games," Game Theory and Information 0303009, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpga:0303009
    Note: Type of Document - pdf-file; pages: 11; figures: included
    as

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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/0303/0303009.pdf
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    References listed on IDEAS

    as
    1. Monderer, Dov & Sela, Aner, 1997. "Fictitious play and no-cycling conditions," Papers 97-12, Sonderforschungsbreich 504.
    2. 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.
    3. 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.
    4. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    5. 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.
    6. Ulrich Berger, 2003. "Continuous Fictitious Play via Projective Geometry," Game Theory and Information 0303004, University Library of Munich, Germany.
    7. Aner Sela, 1999. "Fictitious play in `one-against-all' multi-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 635-651.
    8. Diana Richards, 1997. "The geometry of inductive reasoning in games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 185-193.
    9. Vijay Krishna & Tomas Sjostrom, 1995. "On the Convergence of Fictitious Play," Harvard Institute of Economic Research Working Papers 1717, Harvard - Institute of Economic Research.
    10. 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.
    11. Vijay Krishna & Tomas Sjöström, 1998. "On the Convergence of Fictitious Play," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 479-511, May.
    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.
    13. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
    14. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Fictitious Play; Learning Process; 2xn 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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