Persuasion with Non-Linear Preferences

In persuasion problems where the receiver’s utility is single-peaked in a one-dimensional action, optimal signals are characterized by duality, based on a first-order approach to the receiver’s problem. A signal that pools at most two states in each realization is always optimal, and such pairwise signals are the only solutions under a non-singularity condition on utilities (the twist condition). Our core results provide conditions under which higher actions are induced at more or less extreme pairs of states, so that the induced action is single-dipped or single-peaked on each set of nested pairs of states. We also provide conditions for the optimality of either full disclosure or negative assortative disclosure, where signal realizations can be ordered from least to most extreme. Methodologically, our proofs rely on a novel complementary slackness theorem for persuasion problems.