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Learning in General Games with Nature’s Moves

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  • Patrick L. Leoni

Abstract

This paper investigates simultaneous learning about both nature and others’ actions in repeated games and identifies a set of sufficient conditions for which Harsanyi’s doctrine holds. Players have a utility function over infinite histories that are continuous for the sup‐norm topology. Nature’s drawing after any history may depend on any past actions. 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 construct a Nash equilibrium, that is, realization‐equivalent to the actual plays, where Harsanyi’s doctrine holds. Those assumptions are shown to be tight.

Suggested Citation

  • Patrick L. Leoni, 2014. "Learning in General Games with Nature’s Moves," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:453168
    DOI: 10.1155/2014/453168
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    References listed on IDEAS

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    1. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    2. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    3. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    4. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
    5. 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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