Best Garbling is No Garbling: Persuasion in Real Time

We study continuous-time persuasion where a sender controls both how informative a signal is over time and when to stop providing information to a receiver. Given an exogenous signal process, the sender can both garble the evolving signal path and delay the receiver's decision at a convex, increasing cost of time. We show that, although both instruments are available, any optimal persuasion scheme is fully transparent: the sender keeps the signal fully informative and persuades solely by choosing when to stop.