Persuasion in the Long Run: When history matters

Hyeonggyun Ko

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arXiv · 2508.01662

Persuasion in the Long Run: When history matters

Hyeonggyun Ko

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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.

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Hyeonggyun Ko. 2025-08-03. Persuasion in the Long Run: When history matters. https://arxiv.org/abs/2508.01662

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