We study robust mechanism design in environments in which agents commonly believe that others’ types are identically distributed, but we do not assume that the actual distribution is common knowledge, nor that it is known to the designer. First, we characterize all incentive compatible transfers under these assumptions. Second, we characterize the conditions under which full implementation is possible via direct mechanisms, that only elicit payoff relevant information, and the transfer schemes which achieve it whenever possible. The full implementation results obtain from showing that the problem can be transformed into one of designing a network of strategic externalities, subject to suitable constraints which are dictated by the incentive compatibility requirements.

Multiplicity of equilibria and the dependence on strong common knowledge assumptions are well-known problems in mechanism design. We address them by studying full implementation via transfer schemes, under general restrictions on agents' beliefs. We show that incentive-compatible transfers ensure uniqueness—and hence full implementation—if they induce sufficiently weak strategic externalities. We then design transfers for full implementation by using information on beliefs in order to weaken the strategic externalities of the baseline canonical transfers. Our results rely on minimal restrictions on agents' beliefs, specifically on moments of the distribution of types, that arise naturally in applications.