VIRTUAL IMPLEMENTATION IN INCOMPLETE INFORMATION ENVIRONMENTS WITH INFINITE ALTERNATIVES AND TYPES

This paper considers virtual implementation in both dominant strategy equilibrium and Bayesian strategy equilibrium for incomplete informati on environments with general payoff functions, any number of agents, a nd arbitrary sets of alternatives and types. We characterize virtual i mplementability in private-value models by giving necessary and suffic ient conditions. We show that a social choice function is virtually im plementable in Bayesian (resp. dominant strategy) equilibrium if and o nly if it is Bayesian (resp. dominant strategy) incentive compatible. We also show that incentive compatibility is the necessary and suffici ent condition for a class of common-value economic environments where there are two or mon alternatives that have no valuation externalities . In addition, our mechanism for transferable utility models satisfies budget balancing constraints.