Persuasion and Optimal Stopping

TL;DR

This paper explores how a principal can influence an agent's timing and actions through information, developing principles for commitment and no-commitment scenarios, and applying these to various dynamic persuasion problems.

Contribution

It introduces a unified framework with revelation and anti-revelation principles for dynamic persuasion, simplifying analysis and characterizing optimal policies under different commitment settings.

Findings

Informed commitment simplifies the problem to choosing joint distributions over stopping times and beliefs.

Without commitment, informative interim recommendations are necessary for optimal persuasion.

Optimal policies include moving goalposts, suspense generation, and expanding disclosure intervals.

Abstract

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.