IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2103.03418.html
   My bibliography  Save this paper

Stable matching: an integer programming approach

Author

Listed:
  • Chao Huang

Abstract

This paper develops an integer programming approach to two-sided many-to-one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that stable matchings exist in a discrete matching market when firms' preference profile satisfies a total unimodularity condition that is compatible with various forms of complementarities. We provide a class of firms' preference profiles that satisfy this condition.

Suggested Citation

  • Chao Huang, 2021. "Stable matching: an integer programming approach," Papers 2103.03418, arXiv.org, revised Apr 2022.
    • Handle: RePEc:arx:papers:2103.03418
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2103.03418
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Klaus, Bettina & Klijn, Flip, 2005. "Stable matchings and preferences of couples," Journal of Economic Theory, Elsevier, vol. 121(1), pages 75-106, March.
    2. Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, vol. 59(1), pages 46-71, April.
    3. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    4. Danilov, Vladimir & Koshevoy, Gleb & Murota, Kazuo, 2001. "Discrete convexity and equilibria in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 41(3), pages 251-273, May.
    5. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
    6. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    7. Yeon‐Koo Che & Jinwoo Kim & Fuhito Kojima, 2019. "Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 87(1), pages 65-110, January.
    8. Bettina Klaus & Flip Klijn & Toshifumi Nakamura, 2005. "Corrigendum: Stable Matchings and Preferences of Couples," Working Papers 261, Barcelona School of Economics.
    9. Parag A. Pathak & Alvin E. Roth, 2013. "Matching with Couples: Stability and Incentives in Large Markets," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(4), pages 1585-1632.
    10. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    11. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    12. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    13. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
    14. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    15. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    16. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    17. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    18. , M. & , Glen & White, Alexander, 2013. "Walrasian equilibrium in large, quasi-linear markets," Theoretical Economics, Econometric Society, vol. 8(2), May.
    19. Ning Sun & Zaifu Yang, 2009. "A Double-Track Adjustment Process for Discrete Markets With Substitutes and Complements," Econometrica, Econometric Society, vol. 77(3), pages 933-952, May.
    20. Marek Pycia, 2012. "Stability and Preference Alignment in Matching and Coalition Formation," Econometrica, Econometric Society, vol. 80(1), pages 323-362, January.
    21. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    22. Thành Nguyen & Rakesh Vohra, 2018. "Near-Feasible Stable Matchings with Couples," American Economic Review, American Economic Association, vol. 108(11), pages 3154-3169, November.
    23. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    24. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
    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. Chao Huang, 2022. "Two-sided matching with firms' complementary preferences," Papers 2205.05599, arXiv.org, revised May 2022.
    2. Chao Huang, 2021. "Unidirectional substitutes and complements," Papers 2108.12572, arXiv.org.
    3. Chao Huang, 2022. "Firm-worker hypergraphs," Papers 2211.06887, arXiv.org, revised Nov 2023.

    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. Chao Huang, 2022. "Firm-worker hypergraphs," Papers 2211.06887, arXiv.org, revised Nov 2023.
    2. Chao Huang, 2021. "Unidirectional substitutes and complements," Papers 2108.12572, arXiv.org.
    3. Chao Huang, 2022. "Two-sided matching with firms' complementary preferences," Papers 2205.05599, arXiv.org, revised May 2022.
    4. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    5. 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.
    6. Hatfield, John William & Kominers, Scott Duke, 2015. "Multilateral matching," Journal of Economic Theory, Elsevier, vol. 156(C), pages 175-206.
    7. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    8. Itai Ashlagi & Mark Braverman & Avinatan Hassidim, 2014. "Stability in Large Matching Markets with Complementarities," Operations Research, INFORMS, vol. 62(4), pages 713-732, August.
    9. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).
    10. Kazuo Murota, 2016. "Discrete convex analysis: A tool for economics and game theory," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 151-273, December.
    11. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    12. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    13. Huang, Chao, 2023. "Stable matching: an integer programming approach," Theoretical Economics, Econometric Society, vol. 18(1), January.
    14. Jagadeesan, Ravi & Kominers, Scott Duke & Rheingans-Yoo, Ross, 2018. "Strategy-proofness of worker-optimal matching with continuously transferable utility," Games and Economic Behavior, Elsevier, vol. 108(C), pages 287-294.
    15. Jiang, Zhishan & Tian, Guoqiang, 2013. "Matching with Couples: Stability and Algorithm," MPRA Paper 57936, University Library of Munich, Germany, revised Jul 2014.
    16. Dur, Umut Mert & Wiseman, Thomas, 2019. "School choice with neighbors," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 101-109.
    17. Alvin E. Roth, 2010. "Marketplace Institutions Related to the Timing of Transactions," NBER Working Papers 16556, National Bureau of Economic Research, Inc.
    18. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    19. Ozan Candogan & Markos Epitropou & Rakesh V. Vohra, 2021. "Competitive Equilibrium and Trading Networks: A Network Flow Approach," Operations Research, INFORMS, vol. 69(1), pages 114-147, January.
    20. Thanh Nguyen & Rakesh Vohra, 2014. "Near Feasible Stable Matchings with Complementarities," PIER Working Paper Archive 14-028, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2103.03418. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.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.
    pFad - Phonifier reborn

    Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

    Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


    Alternative Proxies:

    Alternative Proxy

    pFad Proxy

    pFad v3 Proxy

    pFad v4 Proxy