Accelerator and Brake: Dynamic Persuasion with Dead Ends

This paper studies dynamic persuasion in a strategic-experimentation relationship in which the principal has a single-peaked preference over the agent's stopping time. Excessive experimentation may end in a dead end. The principal privately observes project quality, which determines the agent's payoff conditional on success, while both parties learn about feasibility only through the agent's experimentation. We show that an optimal policy uses at most two one-shot disclosures: an accelerator before the principal's ideal stopping time and a brake afterward. A local Arrow--Pratt comparison of induced payoffs over stopping time determines whether the accelerator is concentrated or gradual. Under common discounting, the comparison yields a one-shot accelerator. Under heterogeneous discounting, the one-shot result remains robust unless the agent is sufficiently more impatient than the principal, in which case the ranking reverses over an interval and the accelerator can take a one-shot--gradual--one-shot form.