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

Sushil Bikhchandani; Debasis Mishra

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arXiv · 2209.10137

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

Sushil Bikhchandani·Debasis Mishra

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Abstract

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.

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econ.TH cs.GT

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Sushil Bikhchandani, Debasis Mishra. 2022-09-21. Rank-preserving Multidimensional Mechanisms: an equivalence between identical-object and heterogeneous-object models. https://arxiv.org/abs/2209.10137

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