Persuasion of a Privately Informed Receiver

Abstract

We study Bayesian persuasion in linear environments with a privately informed receiver. We allow the sender to condition information provided to the receiver on the receiver’s report about his type (private persuasion). We describe implementable outcomes, establish equivalence between public persuasion studied in the prior literature and private persuasion, and draw connections with the stan- dard linear mechanism design with transfers. We also characterize optimal per- suasion rules, establish monotone comparative statics, and consider several appli- cations, such as a competitive market for a good with consumption externalities (e.g., cigarettes) in which a benevolent government designs an educational cam- paign about a payoff-relevant characteristic (e.g., the health risks of smoking).