Optimal persuasion via bi-pooling - Itai Arieli; Yakov Babichenko; Rann Smorodinsky; Takuro Yamashita (Theoretical Economics, 2023)
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 mean-preserving contractions of any given prior over an interval takes the form of a bi-pooling distribution. By implication, every Bayesian persuasion problem with an interval state-space admits an optimal bi-pooling distribution as a solution, and conversely, for every bi-pooling distribution, there is a Bayesian persuasion problem for which that distribution is the unique solution
Keywords: C72; D82; D83; 330; Bayesian persuasion; bi-pooling; extreme points; information disclosure; mean preserving contraction; price function; signaling