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A Learning Theory for the Harsanyi's Doctrine in Repeated Games

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  • Patrick Leoni

Abstract

This paper investigates simultaneous learning about both nature and others' actions in repeated games, and identifies a set of sufficient conditions assuring that equilibrium actions converge to a Nash equilibrium. Players have each an utility function over infinite histories continuous for the product topology. Nature' drawing after any history can depend on any past actions, or can be independent of them. Provided that 1) every player maximizes her expected payoff against her own beliefs, 2) every player updates her beliefs in a Bayesian manner, 3) prior beliefs about both nature and other players' strategies have a grain of truth, and 4) beliefs about nature are independent of actions chosen during the game, we show that after some finite time the equilibrium outcome of the above game is arbitrarily close to a Nash equilibrium. Those assumptions are shown to be tight.

Suggested Citation

  • Patrick Leoni, "undated". "A Learning Theory for the Harsanyi's Doctrine in Repeated Games," IEW - Working Papers 196, Institute for Empirical Research in Economics - University of Zurich.
    • Handle: RePEc:zur:iewwpx:196
    as

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    File URL: https://www.zora.uzh.ch/id/eprint/52091/1/iewwp196.pdf
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    References listed on IDEAS

    as
    1. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
    2. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-545, May.
    3. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    4. 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.
    5. John C Harsanyi, 1997. "Games with incomplete information played by "bayesian" players," Levine's Working Paper Archive 1175, David K. Levine.
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    Cited by:

    1. Bruno S. Frey & Simon Luechinger & Alois Stutzer, 2007. "Calculating Tragedy: Assessing The Costs Of Terrorism," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 1-24, February.

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    More about this item

    Keywords

    Repeated Games; Continuous Payo�; Bayesian Learning; Harsanyi's Doctrine;
    All these keywords.

    JEL classification:

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

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