IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v118y2019icp626-647.html
   My bibliography  Save this article

A stable marriage requires communication

Author

Listed:
  • Gonczarowski, Yannai A.
  • Nisan, Noam
  • Ostrovsky, Rafail
  • Rosenbaum, Will

Abstract

In 1976, Knuth asked whether the worst-case running-time of the Gale-Shapley algorithm for the Stable Marriage Problem can be improved when non-sequential access to the input is allowed. Partial negative answers were given by Ng and Hirschberg and as part of Segal's general communication-complexity analysis. We give a far simpler, yet significantly more powerful, argument showing that Ω(n2) Boolean queries of any type are required for finding a stable — or even approximately stable — marriage. Unlike Segal's lower bound, our lower bound generalizes additionally to (A) randomized algorithms, (B) allowing arbitrary separate preprocessing of the women's and men's respective preferences profiles, (C) related problems, e.g. whether a given pair is married in every/some stable marriage, (D) whether a proposed marriage is stable or far from stable. To analyze “approximately stable” marriages, we introduce the notion of “distance to stability” and provide an efficient algorithm for its computation.

Suggested Citation

  • Gonczarowski, Yannai A. & Nisan, Noam & Ostrovsky, Rafail & Rosenbaum, Will, 2019. "A stable marriage requires communication," Games and Economic Behavior, Elsevier, vol. 118(C), pages 626-647.
    • Handle: RePEc:eee:gamebe:v:118:y:2019:i:c:p:626-647
    DOI: 10.1016/j.geb.2018.10.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825619301034
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2018.10.013?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kimmo Eriksson & Olle Häggström, 2008. "Instability of matchings in decentralized markets with various preference structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 409-420, March.
    2. Ashlagi, Itai & Gonczarowski, Yannai A., 2018. "Stable matching mechanisms are not obviously strategy-proof," Journal of Economic Theory, Elsevier, vol. 177(C), pages 405-425.
    3. Muriel Niederle & Alvin E. Roth, 2003. "Unraveling Reduces Mobility in a Labor Market: Gastroenterology with and without a Centralized Match," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1342-1352, December.
    4. Shengwu Li, 2017. "Obviously Strategy-Proof Mechanisms," American Economic Review, American Economic Association, vol. 107(11), pages 3257-3287, November.
    5. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
    6. Muriel Niederle & Alvin E. Roth, 2001. "Unraveling Reduces the Scope of an Entry Level Labor Market: Gastroenterology With and Without a Centralized Match," NBER Working Papers 8616, National Bureau of Economic Research, Inc.
    7. Guillaume R. Fréchette & Alvin E. Roth & M. Utku Ünver, 2007. "Unraveling yields inefficient matchings: evidence from post-season college football bowls," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 967-982, December.
    8. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-440, June.
    9. Segal, Ilya, 2007. "The communication requirements of social choice rules and supporting budget sets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 341-378, September.
    10. Bogomolnaia, Anna & Laslier, Jean-Francois, 2007. "Euclidean preferences," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 87-98, February.
    11. Jean-Claude Picard, 1976. "Maximal Closure of a Graph and Applications to Combinatorial Problems," Management Science, INFORMS, vol. 22(11), pages 1268-1272, July.
    12. Itai Ashlagi & Yash Kanoria & Jacob D. Leshno, 2017. "Unbalanced Random Matching Markets: The Stark Effect of Competition," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 69-98.
    13. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
    14. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    15. Li, Hao & Rosen, Sherwin, 1998. "Unraveling in Matching Markets," American Economic Review, American Economic Association, vol. 88(3), pages 371-387, June.
    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. Linda Cai & Clayton Thomas, 2019. "Representing All Stable Matchings by Walking a Maximal Chain," Papers 1910.04401, arXiv.org.
    2. Naveen Durvasula, 2022. "Utility-Based Communication Requirements for Stable Matching in Large Markets," Papers 2212.04024, arXiv.org.
    3. Tamás Fleiner & Zsuzsanna Jankó & Ildikó Schlotter & Alexander Teytelboym, 2023. "Complexity of stability in trading networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 629-648, September.
    4. Suat Evren, 2023. "Social Surplus Maximization in Sponsored Search Auctions Requires Communication," Papers 2305.07729, arXiv.org.
    5. Kenny Peng & Nikhil Garg, 2024. "Wisdom and Foolishness of Noisy Matching Markets," Papers 2402.16771, arXiv.org.

    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. Muriel Niederle & Alvin E. Roth, 2009. "The Effects of a Centralized Clearinghouse on Job Placement, Wages, and Hiring Practices," NBER Chapters, in: Studies of Labor Market Intermediation, pages 235-271, National Bureau of Economic Research, Inc.
    2. 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.
    3. Muriel Niederle & Alvin E. Roth & M. Utku Ünver, 2013. "Unraveling Results from Comparable Demand and Supply: An Experimental Investigation," Games, MDPI, vol. 4(2), pages 1-40, June.
    4. Alvin E. Roth, 2009. "What Have We Learned from Market Design?," Innovation Policy and the Economy, University of Chicago Press, vol. 9(1), pages 79-112.
    5. Marie-Pierre Dargnies & Rustamdjan Hakimov & Dorothea Kübler, 2019. "Self-Confidence and Unraveling in Matching Markets," Management Science, INFORMS, vol. 65(12), pages 5603-5618, December.
    6. Benjamin N. Roth & Ran I. Shorrer, 2021. "Making Marketplaces Safe: Dominant Individual Rationality and Applications to Market Design," Management Science, INFORMS, vol. 67(6), pages 3694-3713, June.
    7. Siqi Pan, 2018. "Exploding offers and unraveling in two-sided matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 351-373, March.
    8. Haruvy, Ernan & Roth, Alvin E. & Unver, M. Utku, 2006. "The dynamics of law clerk matching: An experimental and computational investigation of proposals for reform of the market," Journal of Economic Dynamics and Control, Elsevier, vol. 30(3), pages 457-486, March.
    9. C. Nicholas McKinney & Muriel Niederle & Alvin E. Roth, 2005. "The Collapse of a Medical Labor Clearinghouse (and Why Such Failures Are Rare)," American Economic Review, American Economic Association, vol. 95(3), pages 878-889, June.
    10. Jonathan M.V. Davis, 2017. "The Short and Long Run Impacts of Centralized Clearinghouses: Evidence from Matching Teach For America Teachers to Schools," 2017 Papers pda791, Job Market Papers.
    11. Muriel Niederle & Alvin E. Roth, 2009. "Market Culture: How Rules Governing Exploding Offers Affect Market Performance," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 199-219, August.
    12. Yann Bramoullé & Brian W. Rogers & Erdem Yenerdag, 2022. "Matching with Recall," AMSE Working Papers 2203, Aix-Marseille School of Economics, France.
    13. Yannai A. Gonczarowski & Clayton Thomas, 2022. "Structural Complexities of Matching Mechanisms," Papers 2212.08709, arXiv.org, revised Mar 2024.
    14. Halaburda, Hanna, 2010. "Unravelling in two-sided matching markets and similarity of preferences," Games and Economic Behavior, Elsevier, vol. 69(2), pages 365-393, July.
    15. Ettore Damiano & Hao Li & Wing Suen, 2005. "Unravelling of Dynamic Sorting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(4), pages 1057-1076.
    16. Fainmesser, Itay P., 2013. "Social networks and unraveling in labor markets," Journal of Economic Theory, Elsevier, vol. 148(1), pages 64-103.
    17. Muriel Niederle & Alvin E. Roth, 2004. "Market Culture: How Norms Governing Exploding Offers Affect Market Performance," Levine's Bibliography 122247000000000018, UCLA Department of Economics.
    18. Alvin E. Roth, 2007. "Repugnance as a Constraint on Markets," Journal of Economic Perspectives, American Economic Association, vol. 21(3), pages 37-58, Summer.
    19. Muriel Niederle & Alvin E. Roth, 2001. "Unraveling Reduces the Scope of an Entry Level Labor Market: Gastroenterology With and Without a Centralized Match," NBER Working Papers 8616, National Bureau of Economic Research, Inc.
    20. 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.

    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:gamebe:v:118:y:2019:i:c:p:626-647. 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/inca/622836 .

    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.