Robust Persuasion of a Privately Informed Receiver

Abstract

This paper studies robust Bayesian persuasion of a privately informed receiver in which the sender only has limited knowledge about the receiver's private information. The sender is ambiguity averse and has a maxmin expected utility function. We show that when the sender faces full ambiguity, i.e., the sender has no knowledge about the receiver's private information, full information disclosure is optimal; when the sender faces local ambiguity, i.e., the sender thinks the receiver's private beliefs are all close to the common prior, as the sender's uncertainty about the receiver's private information vanishes, the sender can do almost as well as when the receiver does not have private information. We also fully characterize the sender's robust information disclosure rule for various kinds of ambiguity in an example with two sates and two actions.

Keywords: Bayesian Persuasion, Ambiguity Aversion, Maxmin Utility, Private Information, Robustness

JEL Classification: D81, D82, D83