Gradual Persuasion and Maximal Inequalities

We consider a gradual persuasion model in which a sender (she) tries to persuade a receiver (he) to take an irreversible adoption action over time. 

We show that the gradual persuasion model can serve as a tool for interpreting and proving classical results in the maximal inequalities literature such as the Hardy-Littlewood martingale inequality, the [Dubins-Gilat '78] maximal maximum martingale, and [Hobson '98] maximal maximum martingale. Moreover, the gradual persuasion perspective provides new insights into the maximal inequalities literature. 

As a corollary from these observations, we show that a sender who is ignorant of the receiver's utility function can persuade the receiver in the gradual persuasion model as if she knew his utility. This remains true even if the sender is partially informed about the state (not necessarily fully informed) and the receiver is partially informed about the state (not necessarily uninformed).

Joint with Itai Arieli and Fedor Sandomirskiy.