Persuasion with Ambiguous Receiver Preferences

TL;DR

This paper models a Bayesian persuasion problem where a sender optimally influences receiver beliefs under worst-case type distributions, connecting it to zero-sum games and demonstrating optimal linearization strategies.

Contribution

It introduces a maxmin persuasion framework with a novel connection to zero-sum games and characterizes optimal linearization of prior distributions in both binary and continuous states.

Findings

Sender's optimal strategy involves linearizing the prior to produce a uniform distribution of posterior means.

The model links persuasion problems to zero-sum game frameworks like political spending and auctions.

Optimal distributions have an atom at the lower bound of the support.

Abstract

I describe a Bayesian persuasion problem where Receiver has a private type representing a cutoff for choosing Sender's preferred action, and Sender has maxmin preferences over all Receiver type distributions with known mean and bounds. This problem can be represented as a zero-sum game where Sender chooses a distribution of posterior mean beliefs that is a mean-preserving contraction of the prior over states, and an adversarial Nature chooses a Receiver type distribution with the known mean; the player with the higher realization from their chosen distribution wins. I formalize the connection between maxmin persuasion and similar games used to model political spending, all-pay auctions, and competitive persuasion. In both a standard binary-state setting and a new continuous-state setting, Sender optimally linearizes the prior distribution over states to create a distribution of posterior means that is uniform on a known interval with an atom at the lower bound of its support.