Private Bayesian Persuasion
We consider a multi-agent Bayesian persuasion problem where an informed sender tries to persuade a group of receivers to adopt a certain product. The sender is allowed to commit to a signaling policy where she sends a private signal to every receiver. The payoff to the sender is a function of the subset of adopters. We characterize an optimal signaling policy and the maximal revenue to the sender for three different types of payoff functions: supermodular, symmetric submodular, and a supermajority function. Moreover, using tools from cooperative game theory we provide a necessary and sufficient condition under which a public signaling policy is optimal.