Implementation with Evidence: Complete Information

This paper studies full-implementation in Nash equilibrium. We generalize the canonical model (Maskin, 1977) by allowing agents to send evidence or discriminatory signals. We first study settings where evidence is hard information that proves something about the state of the world. In such environments, social choice rules that are not Maskin-monotonic can be implementable. We formulate a more general property, evidence-monotonicity, and show that this is a necessary condition for implementation. Evidence-monotonicity is also sufficient for implementation if there are three or more agents and the social choice rule satisfies no veto power. We illustrate how evidence-monotonicity constrains what is implementable even in the presence of rich evidence, and also derive conditions under which various evidentiary structures yield permissive results. The latter part of the paper generalizes these themes to settings where evidence take the form of costly signaling. Columbia University Paris School of Economics and CNRS E-mail addresses: [email protected], [email protected]. Date: First version: December 2008; This version: February 5, 2010. For helpful comments, we thank David Ahn, Vince Crawford, Geoffroy de Clippel, Bob Evans, Jayant Vivek Ganguli, Vijay Krishna, Laurent Lamy, Eric Maskin, François Maniquet, Stephen Morris, Daijiro Okada, Mike Riordan, Hamid Sabourian, Roberto Serrano, Joel Sobel, Joel Watson, and seminar participants at various institutions. This research began when both authors were Members of the Institute for Advanced Study at Princeton. We gratefully acknowledge the Institute’s hospitality and financial support through the Roger W. Ferguson, Jr. and Annette L. Nazareth membership (Kartik) and the Deutsche Bank membership (Tercieux). IMPLEMENTATION WITH EVIDENCE 1