A Characterization of Virtual Bayesian Implementation

Abstract

We provide a characterization of virtual Bayesian implementation in environments satisfying no-total-indifference. A social choice function in such environments is virtually Bayesian implementable if and only if it satisfies incentive compatibility and a condition we term virtual monotonicity. The latter is weaker than Bayesian monotonicity - a condition which is known to be necessary for Bayesian implementation. We argue that virtual monotonicity is weak in the sense that it is generically satisfied in environments with at least three alternatives. This implies that in most environments virtual Bayesian implementation is as successful as it can be (incentive compatibility is the only condition needed).

Keywords: Virtual monotonicity, virtual Bayesian implementation, incentive compatibility, type diversity, decentralization, incomplete information

JEL Classification: C72, D78, D82