A Learning Theory for the Harsanyi's Doctrine in Repeated Games
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.
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- E. Kalai & E. Lehrer, 2010.
"Rational Learning Leads to Nash Equilibrium,"
Levine's Working Paper Archive
529, David K. Levine.
- Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University.
- Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 925, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Fudenberg, Drew & Levine, David K, 1993.
Econometric Society, vol. 61(3), pages 523-45, May.
- John C Harsanyi, 1997. "Games with incomplete information played by "bayesian" players," Levine's Working Paper Archive 1175, David K. Levine.
- Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
- 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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