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...

We study a duopoly where the two price setting firms have symmetric information. The firms produce substitute goods with a state dependent common value. The information that is available to both firms about the unknown state of nature is also available to the consumers, who also have access to...