Incentives and the Existence of Pareto-Optimal Revelation Mechanisms

From the characterization of strongly and Bayesian incentive compatible Pareto-optimal mechanisms with transferable utilities, we derive the following results. If there are only two types per individual then a strongly incentive compatible Pareto-optimal mechanism exists. If there are only two individuals (with more than three types) then there are sets of beliefs (open in the class of all beliefs) for which no Bayesian incentive compatible Pareto-optimal mechanism exists. If there are more than two individuals then the class of beliefs for which such mechanisms exist is open and dense in the class of all beliefs.