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We show that the mechanism-design problem for a monopolist selling multiple,heterogeneous objects to a buyer with ex ante symmetric and additive values isequivalent to the mechanism-design problem for a monopolist selling identicalobjects to a buyer with decreasing marginal values. We derive three new resultsfor the identical-objects model: (i) a new condition for revenue monotonicityof stochastic mechanisms, (ii) a sufficient condition on priors, such thatprices in optimal deterministic mechanism are not increasing, and (iii) asimplification of incentive constraints for deterministic mechanisms. We usethe equivalence to establish corresponding results in the heterogeneous-objectsmodel.

Rank-preserving Multidimensional Mechanisms: an equivalence between identical-object and heterogeneous-object models