Signaling With Commitment

We study the canonical signaling game, endowing the sender with commitment power. We provide a geometric characterization of the sender's attainable payoffs, described by the topological join of the graphs of the sender's interim payoff functions associated with different sender actions. We compare the sender's payoffs in this setting with two benchmarks. In the first, in addition to committing to her actions, the sender can commit to provide the receiver with additional information. In the second, the sender can only commit to release information, but cannot commit to her actions. We illustrate our results with applications to job market signaling, communication with lying costs, and disclosure.