Sender-receiver games with cooperation

We consider generalized sender-receiver games in which the sender also has an action to choose, but this action is payoff-relevant only to himself. We study “cooperate and talk” equilibria (CTE) in which, before sending his message, the sender can commit to delegate his decision to the receiver. CTE are beneficial to the receiver (with respect to no communication) and unlike the equilibria of the plain cheap talk game, preserve him from afterwards regret. While existence of CTE cannot be guaranteed in general, a sufficient condition is that the receiver has a “uniform punishment decision” against the sender.