Relations Between Fully-Revealing Equilibria of Multiple-Sender Signaling and Screening Models

We explore the relation between certain multiple-sender cheap-talk signaling games and the corresponding screening or mechanism design games. The existence of fully-revealing equilibria in the signaling game implies the existence of implementable mechanisms that mechanisms that yield a full-information optimal policy for the principal. If the private information revealed to the agents is collectively sufficient to identity the state of the world, the converse is also true. That is, the existence of an implementable mechanism that yields a full-information optimal policy for the principal implies that a fully-revealing equilibrium in the signaling game exists. This suggests that the perceived advantage of the signaling approach-that no commitment by the principal is assumed-may be over-stated. In the setting considered the equilibrium concept for the signaling games allows commitment to be replicated through the beliefs the principal forms in-off-the equilibrium-path events. We also present two sufficient conditions for the existence of full-information optimal mechanisms. The first condition is that no single agents information is essential to identifying the state. The second condition requires the existence of a punishment that the principal finds desirable for some state of the world and the agents find undesirable in all state of the world. When either of these conditions holds, fully-revealing equilibria in the signaling and screening game exist.