IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v101y2017icp63-77.html
   My bibliography  Save this article

Ordinal and cardinal solution concepts for two-sided matching

Author

Listed:
  • Echenique, Federico
  • Galichon, Alfred

Abstract

We characterize solutions for two-sided matching, both in the transferable- and in the nontransferable-utility frameworks, using a cardinal formulation. Our approach makes the comparison of the matching models with and without transfers particularly transparent. We introduce the concept of a no-trade stable matching to study the role of transfers in matching. A no-trade stable matching is one in which the availability of transfers does not affect the outcome.

Suggested Citation

  • Echenique, Federico & Galichon, Alfred, 2017. "Ordinal and cardinal solution concepts for two-sided matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 63-77.
    • Handle: RePEc:eee:gamebe:v:101:y:2017:i:c:p:63-77
    DOI: 10.1016/j.geb.2015.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825615001323
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2015.10.002?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. 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.
    2. A. Fostel & H. Scarf & M. Todd, 2004. "Two new proofs of Afriat’s theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 211-219, July.
    3. Federico Echenique, 2012. "Contracts versus Salaries in Matching," American Economic Review, American Economic Association, vol. 102(1), pages 594-601, February.
    4. 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.
    5. repec:dau:papers:123456789/10574 is not listed on IDEAS
    6. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0o6ctj2 is not listed on IDEAS
    7. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    8. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    9. 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.
    10. Ivar Ekeland & Alfred Galichon, 2013. "The housing problem and revealed preference theory: duality and an application," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 425-441, November.
    11. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, January.
    12. 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.
    13. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0o6ctj2 is not listed on IDEAS
    14. Crawford, Vincent P., 2005. "The Flexible-Salary Match: A Proposal to Increase the Salary Flexibility of the National Resident Matching Program," University of California at San Diego, Economics Working Paper Series qt2gw114b2, Department of Economics, UC San Diego.
    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. Doğan, Battal & Yıldız, Kemal, 2016. "Efficiency and stability of probabilistic assignments in marriage problems," Games and Economic Behavior, Elsevier, vol. 95(C), pages 47-58.

    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. Echenique, Federico & Galichon, Alfred, 2017. "Ordinal and cardinal solution concepts for two-sided matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 63-77.
    2. repec:hal:spmain:info:hdl:2441/t2p3rkl1d8gqrqvgeigklj2qg is not listed on IDEAS
    3. repec:hal:spmain:info:hdl:2441/5k6c74nfqf91aa74v72q2ca5tm is not listed on IDEAS
    4. Schlegel, Jan Christoph, 2020. "Equivalent choice functions and stable mechanisms," Games and Economic Behavior, Elsevier, vol. 123(C), pages 41-53.
    5. Kadam, Sangram Vilasrao, 2017. "Unilateral substitutability implies substitutable completability in many-to-one matching with contracts," Games and Economic Behavior, Elsevier, vol. 102(C), pages 56-68.
    6. Echenique, Federico & Galichon, Alfred, 2017. "Ordinal and cardinal solution concepts for two-sided matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 63-77.
    7. Assaf Romm, 2014. "Implications of capacity reduction and entry in many-to-one stable matching," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 851-875, December.
    8. 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.
    9. Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
    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. Hirata, Daisuke & Kasuya, Yusuke, 2017. "On stable and strategy-proof rules in matching markets with contracts," Journal of Economic Theory, Elsevier, vol. 168(C), pages 27-43.
    12. Kominers, Scott Duke, 2012. "On the correspondence of contracts to salaries in (many-to-many) matching," Games and Economic Behavior, Elsevier, vol. 75(2), pages 984-989.
    13. 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.
    14. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    15. 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.
    16. Marco LiCalzi, 2022. "Bipartite choices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(2), pages 551-568, December.
    17. 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.
    18. Hirata, Daisuke & Kasuya, Yusuke, 2014. "Cumulative offer process is order-independent," Economics Letters, Elsevier, vol. 124(1), pages 37-40.
    19. Alvin E. Roth, 2010. "Marketplace Institutions Related to the Timing of Transactions," NBER Working Papers 16556, National Bureau of Economic Research, Inc.
    20. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.
    21. 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.
    22. Claus-Jochen Haake & Bettina Klaus, 2010. "Stability and Nash implementation in matching markets with couples," Theory and Decision, Springer, vol. 69(4), pages 537-554, October.

    More about this item

    Keywords

    Market design; Matching theory; National resident matching program;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    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:gamebe:v:101:y:2017:i:c:p:63-77. 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.