Implementation via Transfers with Identical but Unknown Distributions

Joint with Mariann Ollar (Univ. of Edinburgh).

We consider standard mechanism design settings, in which we only maintain it common knowledge that 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 explore problems of partial and full implementation, as well as robustness: First, we characterize the transfers which are incentive compatible under the assumption of identicality, and provide necessary and sufficient conditions for partial implementation in these settings. Second, we characterize the transfers which achieve full implementation via direct mechanisms, as well as the conditions on the environment which make it possible. Finally, we study robustness properties of the implementing transfers with respect to mispecifications of both agents beliefs and of their preferences, as well as for implementation based on lower orders of rationality.