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

31 Pages Posted: 1 Feb 1997

See all articles by Ronald I. Miller

Ronald I. Miller

NERA Economic Consulting

Chris William Sanchirico

University of Pennsylvania Law School; University of Pennsylvania Wharton School - Business Economics and Public Policy Department

Date Written: November 1996

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 agentsi 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 irational learning leads to Nash equilibrium.i 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 ibets.i 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.

JEL Classification: D83

Suggested Citation

Miller, Ron I. and Sanchirico, Chris William, The Role of Absolute Continuity in Merging of Opinions and Rational Learning (November 1996). Available at SSRN: https://ssrn.com/abstract=2201 or http://dx.doi.org/10.2139/ssrn.2201

Ron I. Miller (Contact Author)

NERA Economic Consulting ( email )

1166 Avenue of the Americas, 34th Floor
New York, NY 10036
United States

Chris William Sanchirico

University of Pennsylvania Law School ( email )

3501 Sansom Street
Philadelphia, PA 19104
United States
215-898-4220 (Phone)

HOME PAGE: http://www.law.upenn.edu/faculty/csanchir/

University of Pennsylvania Wharton School - Business Economics and Public Policy Department

3641 Locust Walk
Philadelphia, PA 19104-6372
United States

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