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When is a monotone function cyclically monotone?

Author

Listed:
  • Kushnir, Alexey I.

    (Tepper School of Business, Carnegie Mellon University)

  • Lokutsievskiy, Lev V.

    (Steklov Mathematical Institute of Russian Academy of Sciences)

Abstract

We provide sufficient conditions for a monotone function with a finite set of outcomes to be cyclically monotone. Using these conditions, we show that any monotone function defined on the domain of gross substitutes is cyclically monotone. The result also extends to the domain of generalized gross substitutes and complements.

Suggested Citation

  • Kushnir, Alexey I. & Lokutsievskiy, Lev V., 2021. "When is a monotone function cyclically monotone?," Theoretical Economics, Econometric Society, vol. 16(3), July.
    • Handle: RePEc:the:publsh:4305
    as

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    References listed on IDEAS

    as
    1. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
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    Cited by:

    1. Kumar, Ujjwal & Roy, Souvik, 2024. "Local incentive compatibility on gross substitutes and other non-convex type-spaces," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    2. Paul H. Edelman & John A. Weymark, 2021. "Dominant strategy implementability and zero length cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1091-1120, November.
    3. Roy, Souvik & Kumar, Ujjwal, 2021. "Local incentive compatibility in non-convex type-spaces," MPRA Paper 110872, University Library of Munich, Germany.
    4. Rochet, Jean-Charles, 2024. "Multidimensional Screening After 37 years," TSE Working Papers 24-1536, Toulouse School of Economics (TSE).

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    More about this item

    Keywords

    Monotone; cyclically monotone; non-convex domain; gross substitutes; gross substitutes and complements; mechanism design; algebraic topology; homology; nerve theorem;
    All these keywords.

    JEL classification:

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

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