Bayesian persuasion with heterogeneous priors

In a world in which rational individuals may hold different prior beliefs, a sender can influence the behavior of a receiver by controlling the informativeness of an experiment (public signal). We characterize the set of distributions of posterior beliefs that can be induced by an experiment, and provide necessary and sufficient conditions for a sender to benefit from persuasion. We then provide sufficient conditions for the sender to benefit from persuasion for almost every pair of prior beliefs, even when there is no value of persuasion under a common prior. Our main condition is that the receiver's action depends on his beliefs only through his expectation of some random variable.