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. Symmetric and incentive-compatible mechanisms for heterogeneous objects are rank preserving, i.e., higher-valued objects are assigned with a higher probability. In the identical-objects model, every mechanism is rank preserving. This facilitates the equivalence, which we use in three applications.

翻译：我们证明，垄断者向具有事前对称且可加价值的买家出售多种异质物品的机制设计问题，等价于垄断者向具有递减边际价值的买家出售同质物品的机制设计问题。异质物品的对称且激励相容的机制是保持秩的，即价值更高的物品被分配的概率更高。在同质物品模型中，每个机制都是保持秩的。这一性质促成了上述等价关系，我们将其应用于三个场景。