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Fictitious Play in Extensive Form Games

Author

Listed:
  • Ebbe Hendon

    (Institute of Economics, University of Copenhagen)

  • Hans Jørgen Jacobsen

    (Institute of Economics, University of Copenhagen)

  • Birgitte Sloth

    (Institute of Economics, University of Copenhagen)

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.

Suggested Citation

  • Ebbe Hendon & Hans Jørgen Jacobsen & Birgitte Sloth, "undated". "Fictitious Play in Extensive Form Games," Discussion Papers 94-06, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:9406
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    References listed on IDEAS

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    1. Wagner, Alfred, 1891. "Marshall's Principles of Economics," History of Economic Thought Articles, McMaster University Archive for the History of Economic Thought, vol. 5, pages 319-338.
    2. Sutton, John, 1993. "Echoes of Edgeworth: The problem of indeterminacy," European Economic Review, Elsevier, vol. 37(2-3), pages 491-499, April.
    3. Hildenbrand, Werner, 1993. "Francis Ysidro Edgeworth: Perfect competition and the core," European Economic Review, Elsevier, vol. 37(2-3), pages 477-490, April.
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    5. Jevons, William Stanley, 1871. "The Theory of Political Economy," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number jevons1871, December.
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    Cited by:

    1. 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, pages 165-193.
    2. Hart, Sergiu, 2002. "Evolutionary dynamics and backward induction," Games and Economic Behavior, Elsevier, vol. 41(2), pages 227-264, November.
    3. 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.
    4. 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.
    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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