Bayesian persuasion with costly messages

Abstract We study a model of Bayesian persuasion in which the Sender commits to a signal structure, privately observes the signal realization, and then sends a message to the Receiver at a cost that depends on both the signal realized and the message sent. Our setup weakens the Sender's commitment to truthfully reveal information in Bayesian persuasion. We provide sufficient conditions for full communication by the Sender in the Sender-preferred equilibrium, and these conditions are satisfied under many commonly studied communication games. Under these conditions, the Sender's (lack of) commitment in the persuasion problem is quantified as a communication cost to induce a belief distribution for the Receiver. We apply this approach to study test design and information provision by lobbyists.

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