When is the sender's equilibrium payoff unique in Bayesian persuasion?
PDF Jan 2022
A sender publicly commits to an experiment to inform a receiver’s decision. We study attainable sender payoffs, accounting for her incentives at the experiment choice stage, and not presupposing a receiver tie-breaking rule when indifferent. We characterize when the sender has a unique equilibrium payoff, which therefore coincides with her optimal value in Kamenica and Gentzkow (2011). A sufficient condition is that every action which is a receiver best response to some belief over a set of states is a unique best response to some other such belief—a generic property in the finite case.