Persuasion in the Long Run: When history matters

TL;DR

This paper examines how long-term persuasion strategies are affected by receivers' evolving beliefs and potential model misspecification, revealing conditions under which optimal information structures remain effective or need adjustment.

Contribution

It characterizes when Bayesian Persuasion-optimal structures are robust over time despite receivers' belief updates and potential switching behavior.

Findings

When receivers cannot infer the state from actions, they do not switch, maintaining the optimality of BP structures.

If receivers can infer the state, full disclosure can outperform BP-optimal strategies.

The paper highlights the importance of considering belief evolution in long-term information design.

Abstract

We study a long-run persuasion problem where a long-lived Sender repeatedly interacts with a sequence of short-lived Receivers who may adopt a misspecified model for belief updating. The Sender commits to a stationary information structure, but suspicious Receivers compare it to an uninformative alternative and may switch based on the Bayes factor rule. We characterize when the one-shot Bayesian Persuasion-optimal (BP-optimal) structure remains optimal in the long run despite this switching risk. In particular, when Receivers cannot infer the state from the Sender's preferred action, they never switch, and the BP-optimal structure maximizes the Sender's lifetime utility. In contrast, when such inference is possible, full disclosure may outperform BP-optimal. Our findings highlight the strategic challenges of information design when the Receivers' interpretation of signals evolves over time.