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. We derive three new results for the identical-objects model: (i) a sufficient condition on priors, such that prices in optimal deterministic mechanism are not increasing, (ii) a simplification of incentive constraints for deterministic mechanisms, and (iii) a new condition for revenue monotonicity of stochastic mechanisms. We use the equivalence 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。我们针对同质物品模型推导出三个新结果：（i）先验分布的一个充分条件，使得最优确定性机制中的价格不会递增；（ii）确定性机制激励约束的简化形式；（iii）随机机制收入单调性的新条件。我们利用这一等价性在异质物品模型中建立了相应结果。