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A Constructive Proof that Learning in Repeated Games Leads to Nash Equilibria

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  • Leoni Patrick L

    (University of Southern Denmark)

Abstract

This paper extends the convergence result in Kalai and Lehrer (1993a, 1993b) to a class of games where players have a payoff function continuous for the product topology. Provided that 1) every player maximizes her expected payoff against her own beliefs, 2) every player updates her beliefs in a Bayesian manner, and 3) prior beliefs of other players' strategies have a grain of truth, we construct a Nash equilibrium such that, after some finite time, the equilibrium outcome of the above game is arbitrarily close to the constructed Nash equilibrium.

Suggested Citation

  • Leoni Patrick L, 2009. "A Constructive Proof that Learning in Repeated Games Leads to Nash Equilibria," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-20, January.
    • Handle: RePEc:bpj:bejtec:v:8:y:2009:i:1:n:29
    DOI: 10.2202/1935-1704.1462
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    2. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    3. John H. Nachbar, 2005. "Beliefs in Repeated Games," Econometrica, Econometric Society, vol. 73(2), pages 459-480, March.
    4. Sandroni, Alvaro, 1998. "Necessary and Sufficient Conditions for Convergence to Nash Equilibrium: The Almost Absolute Continuity Hypothesis," Games and Economic Behavior, Elsevier, vol. 22(1), pages 121-147, January.
    5. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    6. Sandroni, Alvaro, 1998. "Does Rational Learning Lead to Nash Equilibrium in Finitely Repeated Games?," Journal of Economic Theory, Elsevier, vol. 78(1), pages 195-218, January.
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