We consider a cheap-talk game a la Crawford and Sobel (1982), where the sender's bias parameter is only “approximately common knowledge” in the sense of (a variant of) Monderer and Samet (1989). Compared to the standard case where the structure of the bias parameter is common knowledge,...

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...