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 multi-dimensional 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.