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Fictitious play in stochastic games

Author

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  • G. Schoenmakers
  • J. Flesch
  • F. Thuijsman

Abstract

In this paper we examine an extension of the fictitious play process for bimatrix games to stochastic games. We show that the fictitious play process does not necessarily converge, not even in the 2 × 2 × 2 case with a unique equilibrium in stationary strategies. Here 2 × 2 × 2 stands for 2 players, 2 states, 2 actions for each player in each state. Copyright Springer-Verlag 2007

Suggested Citation

  • G. Schoenmakers & J. Flesch & F. Thuijsman, 2007. "Fictitious play in stochastic games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(2), pages 315-325, October.
    • Handle: RePEc:spr:mathme:v:66:y:2007:i:2:p:315-325
    DOI: 10.1007/s00186-007-0158-9
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    References listed on IDEAS

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    1. Vrieze, O.J. & Tijs, S.H., 1982. "Fictitious play applied to sequences of games and discounted stochastic games," Other publications TiSEM da21d287-bc00-4a8e-a18f-0, Tilburg University, School of Economics and Management.
    2. 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.
    3. Vijay Krishna & Tomas Sjöström, 1998. "On the Convergence of Fictitious Play," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 479-511, May.
    4. 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.
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    Cited by:

    1. Leslie, David S. & Perkins, Steven & Xu, Zibo, 2020. "Best-response dynamics in zero-sum stochastic games," Journal of Economic Theory, Elsevier, vol. 189(C).

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