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, CKI). 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 the CKI 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 the transfer schemes which achieve full implementation whenever it is 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 entailed by the CKI assumption. This approach enables us to uncover a fairly surprising result: the possibility of full implementation is characterized by the strength of the preference interdependence of the two agents with the least amount of preference interdependence, regardless of the total number of agents, and of their preferences. Finally, we study the robustness properties of the implementing transfers with respect to both misspecifications of agents' preferences and with respect to lower orders beliefs in rationality.