Efficient allocations in economies with asymmetric information when the realized frequency of types is common knowledge

We consider a general economy, where agents have private information about their types. Types can be multidimensional and potentially interdependent. We show that, if the realized frequency of types (the exact number of agents for each type) is common knowledge, then a mechanism exists, which is consistent with truthful revelation of private information and which implements first-best allocations of resources as the unique equilibrium. The result requires the single-crossing property on utility functions and the anonymity of the Pareto correspondence.