Implementation via Augmented Revelation Mechanisms

Consider the problem of Bayesian implementation, i.e., of constructing mechanisms with the property that all 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 selectively 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 (where truthful reporting is an equilibrium) will also implement it._x000B__x000B_This principle enables us to obtain necessary conditions for a choice rule to be implementable. In a large variety of environments these conditions are also sufficient. Our approach of augmenting revelation mechanisms is then extended to accomodate alternative implementation concepts including unique implementation and implementation in undominated equilibrium strategies.