An upper bound for the l_1-variation along the road to agreement

摘要

Two agents with a common prior on the possible states of the world participate in a process of information transmission, consisting of sharing posterior probabilities of an event of interest. Aumann's Agreement Theorem implies that such a process must end with both agents having the same posterior probability. We show that the l(1)-variation of the sequence of posteriors of each agent, obtained along this process, must be finite, and provide an upper bound for its value.