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.

翻译：我们证明，垄断者向具有事前对称且可加价值的买家销售多种异质商品时的机制设计问题，等价于垄断者向具有递减边际价值的买家销售同质商品时的机制设计问题。这一等价关系通过秩保持性质得以建立——该性质表明，价值更高的商品被分配的概率也更高。在异质商品模型中，所有对称且激励相容的机制均满足秩保持性；在同质商品模型中，所有可行机制均满足秩保持性。我们提供了三个应用场景：针对同质商品模型推导出新结论，并利用等价性结果，在异质商品模型中建立相应结论。