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Bayesian learning and convergence to Nash equilibria without common priors

Yaw Nyarko

Economic Theory, 1998, vol. 11, issue 3, 643-655

Abstract: Consider an infinitely repeated game where each player is characterized by a "type" which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria.

JEL-codes: C70 C73 D81 D82 D83 D84 (search for similar items in EconPapers)
Date: 1998-05-05
Note: Received: March 3, 1995; revised version: February 17, 1997
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