This paper investigates simultaneous learning about both nature and others' actions in stochastic games, and identifies a set of suffcient conditions assuring that equilibrium actions played by Bayesian agents become eventually arbitrarily close to a Harsanyi-Nash equilibrium. We assume that players have prior beliefs about both nature' drawings and other players' strategies, which are not necessarily exact. Provided that 1) every player maximizes his own expected sum of discounted one-period utility against their own beliefs, 2) every player updates his beliefs in a Bayesian manner, 3) prior beliefs about both nature' drawings and other players' strategies have a grain of truth and 4) beliefs about nature' drawings are independent of actions taken by the players during the game, we show that after some finite time the equilibrium outcome of the above game is arbitrarily close to a Harsanyi-Nash equilibrium, where priors beliefs are assumed to be exact. Therefore, the result strictly extends the results in Kalai and Lehrer [8] to stochastic games with learning about nature as well as others' actions, and it provides a learning theory for the concept of Harsanyi-Nash equilibrium in such games.
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Fudenberg, D. & Levine, D.K., 1991.
"Self-Confirming Equilibrium ,"
Working papers
581, Massachusetts Institute of Technology (MIT), Department of Economics.
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