### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 643-655 |

Number of pages | 13 |

Journal | Economic Theory |

Volume | 11 |

Issue number | 3 |

State | Published - May 1998 |

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### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Economic Theory*,

*11*(3), 643-655.

**Bayesian learning and convergence to Nash equilibria without common priors.** / Nyarko, Yaw.

Research output: Contribution to journal › Article

*Economic Theory*, vol. 11, no. 3, pp. 643-655.

}

TY - JOUR

T1 - Bayesian learning and convergence to Nash equilibria without common priors

AU - Nyarko, Yaw

PY - 1998/5

Y1 - 1998/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032219887&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032219887&partnerID=8YFLogxK

M3 - Article

VL - 11

SP - 643

EP - 655

JO - Economic Theory

JF - Economic Theory

SN - 0938-2259

IS - 3

ER -