Mechanism design with multidimensional, continuous types and interdependent valuations

We consider the mechanism design problem when agents' types are multidimensional and continuous, and their valuations are interdependent. If there are at least three agents whose types satisfy a weak correlation condition, then for any decision rule and any ε > 0 there exist balanced transfers that render truthful revelation a Bayesian ε-equilibrium. A slightly stronger correlation condition ensures that there exist balanced transfers that induce a Bayesian Nash equilibrium in which agents' strategies are nearly truthful.