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The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"

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Author Info
R. I. Miller (both Columbia University)
C. W. Sanchirico (both Columbia University)

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Abstract

Two agents with different priors watch a sequence unfold over time, updating their priors about the future course of the sequence with each new observation. Blackwell and Dubins (1962) show that the agents' opinions about the future will converge if their priors over the sequence space are absolutely continuous: i.e., if they agree on what events are possible. From this Kalai and Lehrer (1993) conclude that the players in a repeated game will eventually agree about the future course of play and thus that "rational learning leads to Nash equilibrium." We provide an alternative proof of convergence that clarifies the role of absolute continuity and in doing so casts doubt on the relevance of the result. From the existence of continued disagreement we construct a sequence of mutually favorable, uncorrelated "bets." Both agents are sure that they win these bets on average over the long run and this disagreement over what is possible violates absolute continuity.

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Publisher Info
Paper provided by EconWPA in its series Game Theory and Information with number 9612001.

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Length: 29 pages
Date of creation: 03 Dec 1996
Date of revision: 04 Dec 1996
Handle: RePEc:wpa:wuwpga:9612001

Note: 29 pages in Acrobat Reader format
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Web page: http://129.3.20.41

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Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis

References listed on IDEAS
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  1. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ronald Miller & Chris Sanchirico, . "Almost Everybody Disagrees Almost All the Time: The Genericity of Weakly Merging Nowhere," Scholarship at Penn Law upenn_wps-1001, University of Pennsylvania Law School. [Downloadable!]
    Other versions:
  2. Mario Gilli, 2002. "Rational Learning in Imperfect Monitoring Games," Working Papers 46, University of Milano-Bicocca, Department of Economics, revised Mar 2002. [Downloadable!]
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