IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v54y2014icp63-73.html
   My bibliography  Save this article

A many-to-many ‘rural hospital theorem’

Author

Listed:
  • Klijn, Flip
  • Yazıcı, Ayşe

Abstract

We show that the full version of the so-called ‘rural hospital theorem’ generalizes to many-to-many matching problems where agents on both sides of the problem have substitutable and weakly separable preferences. We reinforce our result by showing that when agents’ preferences satisfy substitutability, the domain of weakly separable preferences is also maximal for the rural hospital theorem to hold.

Suggested Citation

  • Klijn, Flip & Yazıcı, Ayşe, 2014. "A many-to-many ‘rural hospital theorem’," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 63-73.
  • Handle: RePEc:eee:mateco:v:54:y:2014:i:c:p:63-73
    DOI: 10.1016/j.jmateco.2014.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S030440681400113X
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Joana Pais, 2008. "Random matching in the college admissions problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 99-116, April.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Fuhito Kojima, 2012. "The “rural hospital theorem” revisited," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 67-76, March.
    7. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    8. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    9. John William Hatfield & Scott Duke Kominers, 2012. "Matching in Networks with Bilateral Contracts," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 176-208, February.
    10. 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.
    11. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
    12. 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.
    13. 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.
    14. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
    15. 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.
    16. Ruth Martínez & Jordi Massó & Alejdanro Neme & Jorge Oviedo, 2004. "On group strategy-proof mechanisms for a many-to-one matching model," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 115-128, January.
    17. Ruth Mart?ez & Jordi MassóAuthor-Name: Alejandro Neme & Jorge Oviedo, "undated". "An Algorithm To Compute The Set Of Many-To-Many Stable Matchings," UFAE and IAE Working Papers 457.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    18. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    19. Orhan Ayg?n & Tayfun S?nmez, 2013. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 103(5), pages 2050-2051, August.
    20. Ahmet Alkan, 2001. "original papers : On preferences over subsets and the lattice structure of stable matchings," Review of Economic Design, Springer;Society for Economic Design, vol. 6(1), pages 99-111.
    21. 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.
    22. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    23. Ahmet Alkan, 2002. "A class of multipartner matching markets with a strong lattice structure," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(4), pages 737-746.
    24. Jinpeng Ma, 2002. "original papers : Stable matchings and the small core in Nash equilibrium in the college admissions problem," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 117-134.
    25. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    26. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    27. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2000. "Single Agents and the Set of Many-to-One Stable Matchings," Journal of Economic Theory, Elsevier, vol. 91(1), pages 91-105, March.
    28. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 473-488, March.
    29. Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.
    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. 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.
    2. 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.
    3. Bettina Klaus & David F. Manlove & Francesca Rossi, 2014. "Matching under Preferences," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 14.07, Université de Lausanne, Faculté des HEC, DEEP.
    4. Jaramillo, Paula & Kayı, Çaǧatay & Klijn, Flip, 2013. "Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare," Games and Economic Behavior, Elsevier, vol. 82(C), pages 693-701.

    More about this item

    Keywords

    Matching; Many-to-many; Stability; Rural hospital theorem;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D60 - Microeconomics - - Welfare Economics - - - General

    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:mateco:v:54:y:2014:i:c:p:63-73. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.