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