Consider a probability distribution governing the evolution of a descrete-time stochastic process. Such a distribution may be represented as a convex combination of more elementary probability measures, with the interpretation of a two-stage Bayesian procedure. In the first stage, one of the...

A central result in the rational learning literature is that if the true measure is absolutely continuous with respect to the beliefs then, given enough data, the updated beliefs merge with the true distribution. In this paper, we show that, under absolute continuity, weak merging occurs fast...

A player inuences a collective outcome if his actions can change the probability of that outcome. He is Æ-pivotal if this change exceeds some threshold Æ. We study inuence in general environments with N players and arbitrary sets of signals. It is shown that inuence is maximized when players'...

A probability distribution governing the evolution of a stochastic process has infinitely many Bayesian representations of the form mu = integral operator [subscript theta] mu[subscript theta] delta lambda (theta). Among these, a natural representation is one whose components (mu[subscript...