Bayesian Persuasion with Multiple Receivers

This paper investigates the role of persuasion mechanisms in collective decision-making. A persuasion mechanism consists of a family of conditional distributions over the underlying state space and the generated noisy signals. A biased, perfectly informed sender adopts a persuasion mechanism to provide a group of uninformed receivers with signals about the unknown state of the world. We compare public persuasion with private persuasion. We find that the sender can always reach her highest possible expected payoff under public persuasion, regardless of the number of signals or the signals' correlation structure. The sender is worse off under private persuasion. Moreover, we show that private persuasion is always more informative than its public counterpart. As a result, the receivers make better decisions under private persuasion