IDEAS home Printed from https://ideas.repec.org/p/fem/femwpa/2011.41.html
   My bibliography  Save this paper

A Measure to Compare Matchings in Marriage Markets

Author

Listed:
  • Florian M. Biermann

    (The Hebrew University of Jerusalem)

Abstract

In matching markets the number of blocking pairs is often used as a criterion to compare matchings. We argue that this criterion is lacking an economic interpretation: In many circumstances it will neither reflect the expected extent of partner changes, nor will it capture the satisfaction of the players with the matching. As an alternative, we set up two principles which single out a particularly “disruptive” subcollection of blocking pairs. We propose to take the cardinality of that subset as a measure to compare matchings. This cardinality has an economic interpretation: the subset is a justified objection against the given matching according to a bargaining set characterization of the set of stable matchings. We prove multiple properties relevant for a workable measure of comparison.

Suggested Citation

  • Florian M. Biermann, 2011. "A Measure to Compare Matchings in Marriage Markets," Working Papers 2011.41, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2011.41
    as

    Download full text from publisher

    File URL: https://feem-media.s3.eu-central-1.amazonaws.com/wp-content/uploads/NDL2011-041.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Alvin E Roth & Muriel Niederle, 2007. "Making Markets Thick: Designing Rules for Offers and Acceptances," Levine's Bibliography 843644000000000142, UCLA Department of Economics.
    2. 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.
    3. 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.
    4. Klijn, Flip & Masso, Jordi, 2003. "Weak stability and a bargaining set for the marriage model," Games and Economic Behavior, Elsevier, vol. 42(1), pages 91-100, January.
    5. Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
    6. Blum, Yosef & Rothblum, Uriel G., 2002. ""Timing Is Everything" and Marital Bliss," Journal of Economic Theory, Elsevier, vol. 103(2), pages 429-443, April.
    7. Ehlers, Lars, 2007. "Von Neumann-Morgenstern stable sets in matching problems," Journal of Economic Theory, Elsevier, vol. 134(1), pages 537-547, May.
    8. Bettina Klaus & Flip Klijn & Markus Walzl, 2011. "Farsighted Stability for Roommate Markets," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 921-933, December.
    9. Roth, Alvin E & Xing, Xiaolin, 1997. "Turnaround Time and Bottlenecks in Market Clearing: Decentralized Matching in the Market for Clinical Psychologists," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 284-329, April.
    10. 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.
    11. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    12. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
    13. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667, Elsevier.
    14. Bettina Klaus & Flip Klijn, 2010. "Smith and Rawls share a room: stability and medians," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 647-667, October.
    15. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
    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. Péter Biró & Flip Klijn, 2013. "Matching With Couples: A Multidisciplinary Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-18.
    2. Peter Biro & Elena Iñarra & Elena Molis, 2014. "A new solution for the roommate problem. The Q-stable matchings," ThE Papers 14/04, Department of Economic Theory and Economic History of the University of Granada..
    3. repec:ehu:ikerla:13424 is not listed 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. Atay, Ata & Mauleon, Ana & Vannetelbosch, Vincent, 2021. "A bargaining set for roommate problems," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    2. Hirata, Daisuke & Kasuya, Yusuke & Tomoeda, Kentaro, 2021. "Stability against robust deviations in the roommate problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 474-498.
    3. Jiang, Zhishan & Tian, Guoqiang, 2013. "Matching with Couples: Stability and Algorithm," MPRA Paper 57936, University Library of Munich, Germany, revised Jul 2014.
    4. , & , J. & ,, 2011. "Von Neumann-Morgenstern farsightedly stable sets in two-sided matching," Theoretical Economics, Econometric Society, vol. 6(3), September.
    5. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    6. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    7. 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.
    8. Jean-Jacques Herings, P. & Mauleon, Ana & Vannetelbosch, Vincent, 2017. "Stable sets in matching problems with coalitional sovereignty and path dominance," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 14-19.
    9. 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.
    10. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.
    11. Jens Gudmundsson, 2014. "Sequences in Pairing Problems: A new approach to reconcile stability with strategy-proofness for elementary matching problems," 2014 Papers pgu351, Job Market Papers.
    12. Lahiri, S., 2004. "Stable outcomes for contract choice problems," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 15(4), pages 409-418.
    13. Morimitsu Kurino, 2020. "Credibility, efficiency, and stability: a theory of dynamic matching markets," The Japanese Economic Review, Springer, vol. 71(1), pages 135-165, January.
    14. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
    15. 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.
    16. 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.
    17. Burak Can & Bettina Klaus, 2013. "Consistency and population sensitivity properties in marriage and roommate markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 835-862, October.
    18. Damiano, Ettore & Lam, Ricky, 2005. "Stability in dynamic matching markets," Games and Economic Behavior, Elsevier, vol. 52(1), pages 34-53, July.
    19. Sun, Ning & Trockel, Walter & Yang, Zaifu, 2008. "Competitive outcomes and endogenous coalition formation in an n-person game," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 853-860, July.
    20. Bettina Klaus & Flip Klijn & Markus Walzl, 2011. "Farsighted Stability for Roommate Markets," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 13(6), pages 921-933, December.

    More about this item

    Keywords

    Stable Marriage Problem; Matching; Blocking Pair; Instability; Matching Comparison; Decentralized Market; Bargaining Set;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General

    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:fem:femwpa:2011.41. 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: Alberto Prina Cerai The email address of this maintainer does not seem to be valid anymore. Please ask Alberto Prina Cerai to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/feemmit.html .

    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.