A Dynamic Non-direct Implementation Mechanism for Interdependent Value Problems, Second Version
Much of the literature on mechanism design and implementation uses the revelation principle to restrict attention to direct mechanisms. This is without loss of generality in a well defined sense. It is, however, restrictive if one is concerned with the set of equilibria, if one is concerned about the size of messages that will be sent, or if one is concerned about privacy. We showed in McLean and Postlewaite (2014) that when agents are informationally small, there exist small modifications to VCG mechanisms in interdependent value problems that restore incentive compatibility. We show here how one can construct a two-stage mechanism that similarly restores incentive compatibility while improving upon the direct one stage mechanism in terms of privacy and the size of messages that must be sent. The first stage essentially elicits that part of the agents' private information that induces interdependence and reveals it to all agents, transforming the interdependent value problem into a private value problem. The second stage is a VCG mechanism for the now private value problem. Agents typically need to transmit substantially less information in the two stage mechanism than would be necessary for a single stage mechanism. Lastly, the first stage that elicits the part of the agents' private information that induces interdependence can be used to transform certain other interdependent value problems into private value problems.