We consider a single object allocation problem with multidimensional signals and interdependent valuations. When agents' signals are statistically independent, Jehiel and Moldovanu [Efficient design with interdependent valuations, Econometrica, 69(5):1237-1259, 2001] show that efficient and Bayesian incentive compatible mechanisms generally do not exist. In this paper, we extend the standard model to accommodate maxmin agents and obtain necessary as well as sufficient conditions under which efficient allocations can be implemented. In particular, we derive a condition that quantifies the amount of ambiguity necessary for efficient implementation. We further show that under some natural assumptions on the preferences, this necessary amount of ambiguity becomes sufficient. Finally, we provide a definition of informational size such that given any nontrivial amount of ambiguity, efficient allocations can be implemented if agents are sufficiently informationally small.

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Zhu, and seminar participants at Bonn, BYU, Harvard, Hitotsubashi, LSE, UBC, and Osaka for their helpful comments. The paper also serves as our response to William Thomson who likes to joke that, while fairness sometimes implies efficiency, the converse is never true. Song gratefully acknowledges financial support by the German Science Foundation (through Collaborative Research Center TRR 190).

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