Implementation with Uncertain Evidence

Abstract: We study a full implementation problem where a socially desirable outcome depends on a state of the world which is unknown to the designer but (commonly) known to a set of agents. The designer may ask the agents to present hard evidence which they privately draw from a distribution depending on the state. We identify a necessary and sufficient condition for implementation in (mixed-strategy) Bayesian Nash equilibria called No Perfect Deceptions (NPD). When agents also face uncertainty about the state and are informationally small (McLean and Postlewaite (2002)), a generalization of the NPD condition (GNPD) is sufficient for implementation and necessary when the information size is zero. Our implementing mechanisms accommodate the case with two or more agents, invoke no integer/modulo games, and impose transfers that in equilibrium vanish with the agents' information size.