Implementation via transfers with identical but unknown distributions

We consider mechanism design environments in which agents commonly know that types are identically distributed across agents, 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 explore problems of partial and full implementation, as well as robustness. First, we characterize the transfers which are incentive compatible under the assumption of common knowledge of identicality, 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 the transfer schemes which achieve full implementation whenever it is possible. Finally, we study the robustness properties of the implementing transfers with respect to misspecifications of agents’preferences and with respect to lower orders beliefs in rationality.