The Structure of Joint Posterior Beliefs

Abstract

We analyze information structures in environments with privately informed agents and a partially informed mediator who provides public signals. Necessary and sufficient conditions, termed internal and external consistency, are derived for the rationalizability of joint posteriors. Analyzing the geometry of the feasible set of posteriors shows that informational constraints alone can generate non-convexity. We also characterize the convexity of the feasible set in the single-agent setting. Applications to belief depolarization, information design, Bayesian persuasion, and potential games are discussed.