Rank-Preserving Multidimensional Mechanisms

We show that the mechanism design problem for a monopolist selling multiple heterogeneous objects with ex ante symmetric values for the buyer is equivalent to the mechanism design problem for a monopolist selling identical objects with decreasing marginal values. We apply this equivalence result to (a) give new sufficient conditions under which an optimal mechanism is revenue monotone in both the models; (b) derive new results on optimal deterministic mechanisms in the heterogeneous objects model; and (c) show that a uniform price mechanism is robustly optimal in the identical objects model when the monopolist knows the average of the marginal distributions of the units.