IDEAS home Printed from https://ideas.repec.org/a/the/publsh/4305.html
   My bibliography  Save this article

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

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20210853/31441/896
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arve, Malin & Zwart, Gijsbert, 2023. "Optimal procurement and investment in new technologies under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 147(C).
    2. Yuya Wakabayashi & Ryosuke Sakai & Shigehiro Serizawa, 2022. "A Characterization of the Minimum Price Walrasian Rule with Reserve Prices for an Arbitrary Number of Agents and Objects," ISER Discussion Paper 1161, Institute of Social and Economic Research, Osaka University.
    3. Nicolas Gruyer, 2009. "Optimal Auctions When A Seller Is Bound To Sell To Collusive Bidders," Journal of Industrial Economics, Wiley Blackwell, vol. 57(4), pages 835-850, December.
    4. Yeon-Koo Che & Ian Gale, 1994. "Auctions with budget-constrained buyers: a nonequivalence result," Working Papers (Old Series) 9402, Federal Reserve Bank of Cleveland.
    5. Scott Fay & Robert Zeithammer, 2017. "Bidding for Bidders? How the Format for Soliciting Supplier Participation in NYOP Auctions Impacts Channel Profit," Management Science, INFORMS, vol. 63(12), pages 4324-4344, December.
    6. Hanming Fang & Peter Norman, 2014. "Toward an efficiency rationale for the public provision of private goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 375-408, June.
    7. Jeremy Bulow & Paul Klemperer, 1994. "Auctions vs. Negotiations," NBER Working Papers 4608, National Bureau of Economic Research, Inc.
    8. Bogetoft, Peter & Nielsen, Kurt, 2003. "Yardstick Based Procurement Design In Natural Resource Management," 2003 Annual Meeting, August 16-22, 2003, Durban, South Africa 25910, International Association of Agricultural Economists.
    9. Shunda, Nicholas, 2009. "Auctions with a buy price: The case of reference-dependent preferences," Games and Economic Behavior, Elsevier, vol. 67(2), pages 645-664, November.
    10. Koessler, Frédéric & Skreta, Vasiliki, 2016. "Informed seller with taste heterogeneity," Journal of Economic Theory, Elsevier, vol. 165(C), pages 456-471.
    11. Siao-Leu Phouratsamay & Safia Kedad-Sidhoum & Fanny Pascual, 2021. "Coordination of a two-level supply chain with contracts," 4OR, Springer, vol. 19(2), pages 235-264, June.
    12. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    13. Paulo Monteiro, 2009. "Abstract types and distributions in independent private value auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 497-507, September.
    14. Stefano Galavotti, 2014. "Reducing Inefficiency in Public Good Provision Through Linking," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(3), pages 427-466, June.
    15. Leandro Arozamena & Estelle Cantillon, 2004. "Investment Incentives in Procurement Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(1), pages 1-18.
    16. Yiding Feng & Jason Hartline & Yingkai Li, 2020. "Simple Mechanisms for Agents with Non-linear Utilities," Papers 2003.00545, arXiv.org, revised Oct 2022.
    17. Strausz, Roland, 2006. "Deterministic versus stochastic mechanisms in principal-agent models," Journal of Economic Theory, Elsevier, vol. 128(1), pages 306-314, May.
    18. Jean-Michel Benkert, 2015. "Bilateral trade with loss-averse agents," ECON - Working Papers 188, Department of Economics - University of Zurich, revised Jul 2022.
    19. Stephen Leider & William S. Lovejoy, 2016. "Bargaining in Supply Chains," Management Science, INFORMS, vol. 62(10), pages 3039-3058, October.
    20. Kos, Nenad & Messner, Matthias, 2013. "Extremal incentive compatible transfers," Journal of Economic Theory, Elsevier, vol. 148(1), pages 134-164.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:the:publsh:4305. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.