Implementation via Augmented Revelation Mechanisms

Abstract

Consider the problem of Bayesian implementation, i.e., of constructing mechanisms with the property that all Bayesian equilibrium outcomes agree with a given choice rule. We show that a general procedure is to start with an incentive-compatible revelation mechanism, and then augment agents' message spaces in order to eliminate undesired equilibria. Specifically, we present an Augmented Revelation Principle, which states that if there exists any mechanism that implements a given choice rule, then an augmented revelation mechanism will also implement it. This principle enables us to obtain necessary conditions for implementation. For a large class of environments these conditions are also sufficient.