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

Abstract

Models of incomplete information have played a major role in the fields of political science and political economy. The models have almost exclusively been signaling models, and their substantive focus is frequently on situations in which the extensive form is not dictated by institutional requirements or procedures. We explore the relation between multiple-sender signaling games and the corresponding screening or mechanism design games without transfers and establish an equivalence result. If there is a fully-revealing equilibrium in the signaling game there is also a full-information optimal mechanism that yields the principal’s optimal policy in every state. The converse, that fully-revealing equilibria exist in the signaling game if a full-information optimal mechanism exists, is true if and only if the mechanism involves only the selection of policies that are optimal for some belief about the state. We also present two straightforward sufficient conditions for the existence of full-information optimal mechanisms. When either holds, fully-revealing equilibria in the signaling and screening games exist. The perceived advantage of the signaling over the screening approach – that no commitment by the principal is assumed – may be over-stated as flexibility in specifying off the path beliefs can mimic commitment.