The Core of Bayesian Persuasion

TL;DR

This paper characterizes when an analyst can interpret observed agent actions as resulting from learning about a state, combining information design and Bayesian persuasion theories, with applications to network games and data consistency.

Contribution

It introduces a novel characterization linking information design and Bayesian persuasion, utilizing Strassen's theorem and Hall's marriage theorem, to analyze agent learning from observed actions.

Findings

Provides a characterization for rationalizing agent actions as learning about the state.

Applies the framework to ring-network games.

Identifies conditions for data set consistency with public information in Bayesian persuasion.

Abstract

An analyst observes the frequency with which an agent takes actions, but not the frequency with which she takes actions conditional on a payoff relevant state. In this setting, we ask when the analyst can rationalize the agent's choices as the outcome of the agent learning something about the state before taking action. Our characterization marries the obedience approach in information design (Bergemann and Morris, 2016) and the belief approach in Bayesian persuasion (Kamenica and Gentzkow, 2011) relying on a theorem by Strassen (1965) and Hall's marriage theorem. We apply our results to ring-network games and to identify conditions under which a data set is consistent with a public information structure in first-order Bayesian persuasion games.