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

Abstract

D. Blackwell and L. Dubins (1962, Ann. Math. Statist. 38, 882-886) showed that opinions merge when priors are absolutely continuous. E. Kalai and E. Lehrer (1993, Econometrica 61, 1019-1045) use this result to show that players in a repeated game eventually play like a Nash equilibrium. We provide an alternative proof of merging of opinions that clarifies the role of absolute continuity while casting doubt on the relevance of the result. Persistent disagreement, the opposite of merging, allows the construction of a sequence of mutually favorable "bets." By a law of large numbers, both agents are certain they will win these bets on average. This certain disagreement violates absolute continuity. Journal of Economic Literature Classification Numbers: C11, C69, C72, D83. © 1999 Academic Press.