Persuasion Under Higher-Order Uncertainty

We study a general model of persuasion games under higher-order uncertainty about the sender's knowledge of an uncertain state variable. Unlike situations where such uncertainty is absent, we show that higher-order uncertainty eliminates truth-telling as an equilibrium. Instead, equilibrium consists of a convex interval of states where either disclosure or complete non-disclosure occurs, depending on the relative slopes of the ideal action lines of the sender and receiver. When choosing between senders differing in both expertise and preference alignment, we offer conditions where expertise dominates regardless of the degree of preference misalignment. Absent higher-order uncertainty, we provide an algorithm for constructing a truthful equilibrium, as well as necessary and sufficient conditions for equilibrium uniqueness.