Private Bayesian Persuasion

Abstract

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