A Network Solution to Robust Implementation: The Case of Identical but Unknown Distributions

We consider mechanism design environments in which agents commonly know that others’ types are identically distributed, but without assuming that the actual distribution is common knowledge, nor that it is known to the designer (common knowledge of identicality). Under these assumptions, we study problems of partial and full implementation, as well as robustness. First, we characterize the transfers which are incentive compatible under these common knowledge assumption, and provide necessary and sufficient conditions for partial implementation. Second, we characterize the conditions under which full implementation is possible via direct mechanisms, as well as transfer schemes which achieve it whenever possible. We do this by pursuing a network approach, which is based on the observation that the full implementation problem in our setting can be conveniently transformed into one of designing a network of strategic externalities, subject to suitable constraints which are dictated by the incentive compatibility requirements.