Observable Self-Restraint in Repeated Cheap Talk

Abstract

A long-lived sender repeatedly advises a myopic receiver who observes only the recommendation record. Nonbinding, observable self-restraint, such as a rolling quota on favorable recommendations, makes each favorable recommendation use capacity that could serve future opportunities, inducing selective advice. With two actions, when obedience requires a strictly positive cost of self-restraint, the sender's normalized equilibrium payoff is subject to a ceiling equal to the payoff from the best credible partitional signal minus the expected cost of self-restraint. This bound holds at every discount factor; under an upper-tail condition, rolling quotas approach it as the sender becomes patient. A sufficiently valuable opportunity can also induce an informative violation that ends communication.