IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v114y2024ics0304406824000880.html
   My bibliography  Save this article

An even tighter bound for the Shapley–Folkman–Starr theorem

Author

Listed:
  • Wu, Haoyu
  • Tang, Ao

Abstract

Based on a previous refined Shapley–Folkman lemma, we derive a tighter error bound for the Shapley–Folkman–Starr theorem and apply the result to the course allocation problem.

Suggested Citation

  • Wu, Haoyu & Tang, Ao, 2024. "An even tighter bound for the Shapley–Folkman–Starr theorem," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    • Handle: RePEc:eee:mateco:v:114:y:2024:i:c:s0304406824000880
    DOI: 10.1016/j.jmateco.2024.103028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406824000880
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2024.103028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Starr, Ross M, 1969. "Quasi-Equilibria in Markets with Non-Convex Preferences," Econometrica, Econometric Society, vol. 37(1), pages 25-38, January.
    2. Zhou, Lin, 1993. "A Simple Proof of the Shapley-Folkman Theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 371-372, April.
    3. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    4. Budish, Eric & Reny, Philip J., 2020. "An improved bound for the Shapley–Folkman theorem," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 48-52.
    5. J. P. Aubin & I. Ekeland, 1976. "Estimates of the Duality Gap in Nonconvex Optimization," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 225-245, August.
    Full references (including those not matched with items on IDEAS)

    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. Budish, Eric & Reny, Philip J., 2020. "An improved bound for the Shapley–Folkman theorem," Journal of Mathematical Economics, Elsevier, vol. 89(C), pages 48-52.
    2. S. Flåm & L. Koutsougeras, 2010. "Private information, transferable utility, and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 591-609, March.
    3. Nguyen, Thành & Peivandi, Ahmad & Vohra, Rakesh, 2016. "Assignment problems with complementarities," Journal of Economic Theory, Elsevier, vol. 165(C), pages 209-241.
    4. Echenique, Federico & Goel, Sumit & Lee, SangMok, 2024. "Stable allocations in discrete exchange economies," Journal of Economic Theory, Elsevier, vol. 222(C).
    5. Hung-po Chao, 2019. "Incentives for efficient pricing mechanism in markets with non-convexities," Journal of Regulatory Economics, Springer, vol. 56(1), pages 33-58, August.
    6. Th`anh Nguyen & Alexander Teytelboym & Shai Vardi, 2023. "Dynamic Combinatorial Assignment," Papers 2303.13967, arXiv.org.
    7. M. Ali Khan & Kali P. Rath, 2011. "The Shapley-Folkman Theorem and the Range of a Bounded Measure: An Elementary and Unified Treatment," Economics Working Paper Archive 586, The Johns Hopkins University,Department of Economics.
    8. Erlanson, Albin & Szwagrzak, Karol, 2013. "Strategy-Proof Package Assignment," Working Papers 2013:43, Lund University, Department of Economics.
    9. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202103100800001123, Iowa State University, Department of Economics.
    10. Parag A. Pathak & Alex Rees-Jones & Tayfun Sönmez, 2025. "Immigration Lottery Design: Engineered and Coincidental Consequences of H-1B Reforms," The Review of Economics and Statistics, MIT Press, vol. 107(1), pages 1-13, January.
    11. Eric Budish & Gérard P. Cachon & Judd B. Kessler & Abraham Othman, 2017. "Course Match: A Large-Scale Implementation of Approximate Competitive Equilibrium from Equal Incomes for Combinatorial Allocation," Operations Research, INFORMS, vol. 65(2), pages 314-336, April.
    12. Anna Bogomolnaia & Hervé Moulin, 2023. "Guarantees in Fair Division: General or Monotone Preferences," Mathematics of Operations Research, INFORMS, vol. 48(1), pages 160-176, February.
    13. Dur, Umut Mert & Wiseman, Thomas, 2019. "School choice with neighbors," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 101-109.
    14. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    15. Borglin, Anders & Flåm, Sjur Didrik, 2007. "Risk exchange as a market or production game," Working Papers in Economics 09/07, University of Bergen, Department of Economics.
    16. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    17. Llinares, Juan-Vicente, 1998. "Unified treatment of the problem of existence of maximal elements in binary relations: a characterization," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 285-302, April.
    18. Martin Bichler & Johannes Knörr & Felipe Maldonado, 2023. "Pricing in Nonconvex Markets: How to Price Electricity in the Presence of Demand Response," Information Systems Research, INFORMS, vol. 34(2), pages 652-675, June.
    19. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    20. Wim Ackooij & Nadia Oudjane, 2024. "On supply and network investment in power systems," 4OR, Springer, vol. 22(4), pages 465-481, December.

    More about this item

    Keywords

    Shapley–Folkman lemma; Error-estimation;

    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:eee:mateco:v:114:y:2024:i:c:s0304406824000880. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.