Rank-Preserving Multidimensional Mechanisms

We show that the mechanism-design problem for a monopolist selling multiple, heterogeneous objects to a buyer with ex ante symmetric and additive values is equivalent to the mechanism-design problem for a monopolist selling identical objects to a buyer with decreasing marginal values. The equivalence is facilitated by the rank-preserving property, which states that higher-valued objects are assigned with a higher probability. In the heterogeneous-objects model, every symmetric and incentive-compatible mechanism is rank preserving. In the identical-objects model, every feasible mechanism is rank preserving. We provide three applications in which we derive new results for the identical-objects model and use our equivalence result to establish corresponding results in the heterogeneous-objects model.