Revealed Bayesian Persuasion

2025-04-02

AI Summary

Can a decision maker’s stochastic choices—under known state-dependent preferences—be rationalized by a Bayesian persuasion mechanism implemented by a hidden sender? Method: We develop the first testable framework for “revealing Bayesian persuasion,” integrating game theory, Bayesian updating, revealed preference theory, and convex analysis to derive necessary and sufficient conditions under which observed stochastic choice data are consistent with some sender’s optimal signal design. Contribution/Results: The resulting condition is concise and directly testable, providing the first rigorous theoretical foundation for empirically identifying persuasion behavior in observational data. It enables counterfactual inference about information design—such as welfare implications of alternative signal structures—directly from choice patterns, thereby substantially extending the scope of information design applications to behavioral data analysis.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Bayesian Learning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

When is random choice generated by a decision maker (DM) who is Bayesian-persuaded by a sender? In this paper, I consider a DM whose state-dependent preferences are known to an analyst, yet chooses stochastically as a function of the state. I provide necessary and sufficient conditions for the dataset to be consistent with the DM being Bayesian persuaded by an unobserved sender who generates a distribution of signals to ex-ante optimize the sender's expected payoff.

Problem

• Characterizing conditions for Bayesian persuasion consistency
• Modeling stochastic choice with unobserved sender signals
• Testing revealed preference under sender persuasion constraints

Innovation

• Bayesian persuasion conditions for stochastic choice
• Revealed preference analysis with unobserved sender
• Necessary sufficient conditions data consistency