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Fictitious Play in Extensive Form Games

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  • Hendon, Ebbe
  • Jacobsen, Hans Jorgen
  • Sloth, Birgitte

Abstract

This article analyzes the fictitious play process originally proposed for strategic form games by Brown (1951) and Robinson (1951). We interpret the process as a model of preplay thinking performed by players before acting in a one-shot game. This model is one of bounded rationality. We discuss how fictitious play should then be defined for extensive form games and conclude that this is somewhat problematic. We therefore study two alternative definitions. For either of these, under a weak condition of initial uncertainty, a convergence point of a fictitious play sequence is a sequential equilibrium. For generic games of perfect information initial uncertainty also implies convergence of fictitious play.
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Suggested Citation

  • Hendon, Ebbe & Jacobsen, Hans Jorgen & Sloth, Birgitte, 1996. "Fictitious Play in Extensive Form Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 177-202, August.
  • Handle: RePEc:eee:gamebe:v:15:y:1996:i:2:p:177-202
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    Cited by:

    1. Jehiel, Philippe & Samet, Dov, 2005. "Learning to play games in extensive form by valuation," Journal of Economic Theory, Elsevier, vol. 124(2), pages 129-148, October.
    2. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    3. Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
    4. Cressman, R. & Schlag, K. H., 1998. "The Dynamic (In)Stability of Backwards Induction," Journal of Economic Theory, Elsevier, vol. 83(2), pages 260-285, December.
    5. Xu, Zibo, 2016. "Convergence of best-response dynamics in extensive-form games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 21-54.
    6. Vriend, Nicolaas J., 1997. "Will reasoning improve learning?," Economics Letters, Elsevier, vol. 55(1), pages 9-18, August.

    More about this item

    JEL classification:

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

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