IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v74y2012i2p588-600.html
   My bibliography  Save this article

On the invariance of the set of Core matchings with respect to preference profiles

Author

Listed:
  • Martínez, Ruth
  • Massó, Jordi
  • Neme, Alejandro
  • Oviedo, Jorge

Abstract

We consider the general many-to-one matching model with ordinal preferences and give a procedure to partition the set of preference profiles into subsets with the property that all preference profiles in the same subset have the same Core. We also show how to identify a profile of (incomplete) binary relations containing the minimal information needed to generate as strict extensions all the (complete) preference profiles with the same Core. This is important for applications since it reduces the amount of information that agents have to reveal about their preference relations to centralized Core matching mechanisms; moreover, this reduction is maximal.

Suggested Citation

  • Martínez, Ruth & Massó, Jordi & Neme, Alejandro & Oviedo, Jorge, 2012. "On the invariance of the set of Core matchings with respect to preference profiles," Games and Economic Behavior, Elsevier, vol. 74(2), pages 588-600.
  • Handle: RePEc:eee:gamebe:v:74:y:2012:i:2:p:588-600
    DOI: 10.1016/j.geb.2011.08.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825611001394
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2011.08.011?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. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, September.
    2. Paul Milgrom, 2009. "Assignment Messages and Exchanges," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 95-113, August.
    3. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    4. Federico Echenique, 2008. "What Matchings Can Be Stable? The Testable Implications of Matching Theory," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 757-768, August.
    5. Ruth Martínez & Jordi Massó & Alejandro Neme & Jorge Oviedo, 2008. "On the invariance of the set of stable matchings with respect to substitutable preference profiles," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 497-518, March.
    6. 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.
    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. Guillaume Haeringer & Vincent Iehlé, 2014. "Two-sided matching with one-sided preferences," Working Papers halshs-00980794, HAL.
    2. Guillaume Haeringer & Vincent Iehlé, 2019. "Two-Sided Matching with (Almost) One-Sided Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 155-190, August.
    3. Schlegel, Jan Christoph, 2015. "Contracts versus salaries in matching: A general result," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 552-573.
    4. Guillaume Haeringer & Vincent Iehlé, 2019. "Two-Sided Matching with (Almost) One-Sided Preferences," American Economic Journal: Microeconomics, American Economic Association, vol. 11(3), pages 155-190, August.
    5. Alva, Samson, 2018. "WARP and combinatorial choice," Journal of Economic Theory, Elsevier, vol. 173(C), pages 320-333.
    6. Jan Christoph Schlegel, 2014. "Contracts versus Salaries in Matching: A General Result. N.B.: This paper replaces Nr 13.09 "Contracts versus Salaries in Matching: Comment", (June 2013)," Cahiers de Recherches Economiques du Département d'économie 14.05, Université de Lausanne, Faculté des HEC, Département d’économie.

    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 & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
    2. Dimitrov, Dinko & Lazarova, Emiliya A., 2008. "Coalitional Matchings," Coalition Theory Network Working Papers 37523, Fondazione Eni Enrico Mattei (FEEM).
    3. 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.
    4. Konishi, Hideo & Unver, M. Utku, 2006. "Credible group stability in many-to-many matching problems," Journal of Economic Theory, Elsevier, vol. 129(1), pages 57-80, July.
    5. Milgrom, Paul, 2010. "Simplified mechanisms with an application to sponsored-search auctions," Games and Economic Behavior, Elsevier, vol. 70(1), pages 62-70, September.
    6. 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.
    7. Kamada, Yuichiro & Kojima, Fuhito, 2018. "Stability and strategy-proofness for matching with constraints: a necessary and sufficient condition," Theoretical Economics, Econometric Society, vol. 13(2), May.
    8. Echenique, Federico, 2007. "Counting combinatorial choice rules," Games and Economic Behavior, Elsevier, vol. 58(2), pages 231-245, February.
    9. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
    10. Ma, Jinpeng, 2001. "Job Matching and Coalition Formation with Utility or Disutility of Co-workers," Games and Economic Behavior, Elsevier, vol. 34(1), pages 83-103, January.
    11. repec:ebl:ecbull:v:3:y:2004:i:45:p:1-11 is not listed on IDEAS
    12. Bando, Keisuke, 2014. "A modified deferred acceptance algorithm for many-to-one matching markets with externalities among firms," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 173-181.
    13. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    14. 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.
    15. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    16. Danilov, Vladimir I. & Karzanov, Alexander V., 2023. "Stable and meta-stable contract networks," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    17. Kovalenkov, A. & Holtz Wooders, M., 1997. "Epsilon Cores of Games and Economies With Limited Side Payments," UFAE and IAE Working Papers 392.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    18. A Bhattacharya & H Newhouse, 2010. "Allocative Efficiency and an Incentive Scheme for Research," Discussion Papers 10/02, Department of Economics, University of York.
    19. Alexander Kovalenkov & Myrna Wooders, 2005. "Laws of scarcity for a finite game - exact bounds on estimations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 383-396, August.
    20. Westkamp, Alexander, 2010. "Market Structure and Matching with Contracts," Bonn Econ Discussion Papers 02/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    21. Bettina Klaus & Flip Klijn, 2006. "Median Stable Matching for College Admissions," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 1-11, April.

    More about this item

    Keywords

    Matching; Core;

    JEL classification:

    • 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:74:y:2012:i:2:p:588-600. 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.