Preparing for the Worst But Hoping for the Best: Robust (Bayesian) Persuasion

We propose a robust solution concept for Bayesian persuasion that accounts for the Sender’s ambiguity over (i) the exogenous sources of information the Receivers may learn from, and (ii) the way the Receivers play (when multiple strategy profiles are consistent with the assumed solution concept and the available information). The Sender proceeds in two steps. First, she identifies all information structures that yield the largest payoff in the “worst-case scenario,†i.e., when Nature provides information and coordinates the Receivers’ play to minimize the Sender’s payoff. Second, she picks an information structure that, in case Nature and the Receivers play favorably to her, maximizes her expected payoff over all information structures that are “worst-case optimal.†We characterize properties of robust solutions, identify conditions under which robustness requires separation of certain states, and qualify in what sense robustness calls for more information disclosure than standard Bayesian persuasion. Finally, we discuss how some of the results in the Bayesian persuasion literature change once robustness is accounted for.