Slow persuasion

TL;DR

This paper explores the optimal way to persuade over time when information is revealed gradually, showing how constraints limit information flow and can lead to less-than-full disclosure even with aligned interests.

Contribution

It introduces a novel viscosity dynamic programming approach to characterize equilibrium in slow persuasion models with gradual information release.

Findings

Graduality constraints reduce information provision compared to unconstrained cases.

The gap in information provision narrows as the constraint becomes less strict.

Less-than-full information can be optimal even with aligned preferences but different priors.

Abstract

What are the value and form of optimal persuasion when information can be generated only slowly? We study this question in a dynamic model in which a 'sender' provides public information over time subject to a graduality constraint, and a decision-maker takes an action in each period. Using a novel 'viscosity' dynamic programming principle, we characterise the sender's equilibrium value function and information provision. We show that the graduality constraint inhibits information provision relative to unconstrained persuasion. The gap can be substantial, but closes as the constraint slackens. Contrary to unconstrained persuasion, less-than-full information may be provided even if players have aligned preferences but different prior beliefs.