The Role of Absolute Continuity in “Merging of Opinions” and “Rational Learning”
重新证明Blackwell和Dubins的意见融合定理，指出绝对连续性是其关键条件，但通过构造持续分歧下的互惠赌局，质疑该结果的实际相关性。
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, Econometrica61, 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.