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

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 new condition for revenue monotonicity of stochastic mechanisms, (ii) a sufficient condition on priors, such that prices in optimal deterministic mechanism are not increasing, and (iii) a simplification of incentive constraints for deterministic mechanisms. We use the equivalence to establish corresponding results in the heterogeneous-objects model.