Persuasion and Optimal Stopping

We study how a principal can jointly shape an agent's timing and action through information. We develop a revelation principle: with intertemporal commitment, the problem simplifies to choosing a joint distribution over stopping times and beliefs, delivering a tractable first-order approach, and an anti-revelation principle: without commitment, informative interim recommendations are necessary and sufficient to implement the optimal commitment outcome. We apply the method to analyze (i) moving the goalposts, where inching rather than teleporting the goalposts can be achieved without commitment; (ii) dynamic binary persuasion, where optimal policies combine suspense generation with action-targeted Poisson news; and (iii) dynamic linear persuasion with a continuum of states, where a tail-censorship policy with expanding disclosure intervals is optimal.