Robustness of Persuasion to Receiver Preferences

2026-05-27

AI Summary

This study investigates the robustness of Bayesian persuasion when the receiver’s preferences are subject to small Knightian (non-probabilistic) uncertainty. By integrating minimax regret and maxmin expected utility criteria with non-probabilistic uncertainty modeling, the paper examines the stability of the sender’s optimal persuasion mechanisms. The central contribution establishes that, under generic conditions, the continuity of Bayesian persuasion mechanisms is equivalent to their robustness against perturbations in the receiver’s preferences, and this property holds generically. The findings demonstrate that most standard persuasion setups inherently possess intrinsic robustness to minor ignorance about the receiver’s preferences.

Abstract

We study the robustness of Bayesian persuasion to uncertainty about the receiver's preferences. We analyze two conceptually distinct notions: continuity, in which only the modeler lacks precise knowledge, but where the model's predictions are nonetheless accurate; and robustness, in which the sender also lacks precise knowledge, but where the outcome is insensitive to this ignorance. We model preference uncertainty as infinitesimally small, non-probabilistic (Knightian) uncertainty, and the sender's behavior as either minimizing the regret or maximizing the minimum utility. We show that continuity holds if and only if robustness holds, and that both notions are generic. Thus, while some instances of Bayesian persuasion are fragile, typical instances are both continuous and robust with respect to a small amount of ignorance.

Problem

• Bayesian persuasion
• preference uncertainty
• robustness
• continuity
• Knightian uncertainty

Innovation

• Bayesian persuasion
• preference uncertainty
• Knightian uncertainty
• robustness
• continuity