Persuasion with Non-Linear Preferences

TL;DR

This paper characterizes optimal persuasion signals in single-peaked utility settings, showing they are supported on a contact set and often involve pooling at most two states, with conditions for full or negative assortative disclosure.

Contribution

It introduces a duality-based framework for optimal signals in persuasion with non-linear preferences, identifying when simple pairwise pooling suffices and characterizing disclosure strategies.

Findings

Optimal signals are supported on a contact set where dual constraints bind.

Pooling at most two states per signal is always optimal under certain conditions.

Conditions are provided for full disclosure and negative assortative disclosure strategies.

Abstract

In persuasion problems where the receiver's action is one-dimensional and his utility is single-peaked, optimal signals are characterized by duality, based on a first-order approach to the receiver's problem. A signal is optimal iff the induced joint distribution over states and actions is supported on a compact set (the contact set) where the dual constraint binds. 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). We provide conditions under which higher actions are induced at more or less extreme pairs of states. Finally, we provide conditions for the optimality of either full disclosure or negative assortative disclosure, where signal realizations can be ordered from least to most extreme. Optimal negative assortative disclosure is characterized as the solution to a pair of ordinary differential equations.