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Rank-preserving multidimensional mechanisms: An equivalence between identical-object and heterogeneous-object models

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  • Bikhchandani, Sushil
  • Mishra, Debasis

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.

Suggested Citation

  • Bikhchandani, Sushil & Mishra, Debasis, 2024. "Rank-preserving multidimensional mechanisms: An equivalence between identical-object and heterogeneous-object models," Journal of Economic Theory, Elsevier, vol. 222(C).
    • Handle: RePEc:eee:jetheo:v:222:y:2024:i:c:s0022053124001297
    DOI: 10.1016/j.jet.2024.105923
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    Keywords

    Rank-preserving mechanism; Revenue maximization; Multidimensional mechanism design;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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