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

Abstract

We propose a robust solution concept for Bayesian persuasion that
accounts for the Sender's concern that her Bayesian belief about the
environment---which we call the conjecture---may be false.
Specifically, the Sender is uncertain about the exogenous sources
of information the Receivers may learn from, and about strategy selection.
She first identifies all information policies 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. Then, she uses the conjecture to pick the optimal policy among
the worst-case optimal ones. 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 and develop a few new applications.

Keywords: persuasion, information design, robustness, worst-case optimality

JEL Classification: D83, G28, G33