Slow persuasion

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 characterize 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.