Mean-preserving contractions are critical for studying Bayesian models of information design. We introduce the class of bi-pooling policies, and the class of bi-pooling distributions as their induced distributions over posteriors. We show that every extreme point in the set of all...

Two firms produce substitute goods of unknown quality. At each stage the firms set prices and a consumer with private information and unit demand buys from one of the firms. Both firms and consumers see the entire history of prices and purchases. Will such markets aggregate information? Will the...

New ways of doing things often get started through the actions of a few innovators, then diffuse rapidly as more and more people come into contact with prior adopters in their social network. Much of the literature focuses on the speed of diffusion as a function of the network topology. In...

Consider a finite, normal form game G in which each player position is occupied by a population of N individuals, and the payoff to any given individual is the expected payoff from playing against a group drawn at random from the other positions.  Assume that individuals adjust their behavior...

We address the question to which degree the private information of a decision maker is revealed through his action, in an environment with compact metrizable state and action space. We show that the decision maker's optimal action reveals his posterior distribution for a generic set of...

In [1], it was shown that in games of perfect information, common knowledge of rationality entails that the backward induction outcome is reached, and is consistent (for short, entails BI). That work has been criticized because it assumes that a player chooses rationally at all his nodes, even...