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Matching with preferences over colleagues solves classical matching

  • Kominers, Scott Duke

In this note, we demonstrate that the problem of "many-to-one matching with (strict) preferences over colleagues" is actually more difficult than the classical many-to-one matching problem, "matching without preferences over colleagues." We give an explicit reduction of any problem of the latter type to a problem of the former type. This construction leads to the first algorithm which finds all stable matchings in the setting of "matching without preferences over colleagues," for any set of preferences. Our construction directly extends to generalized matching settings.

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File URL: http://www.sciencedirect.com/science/article/B6WFW-4XDCHP1-2/2/93d8bc7bf48938ab933149d4d676508d
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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 68 (2010)
Issue (Month): 2 (March)
Pages: 773-780

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Handle: RePEc:eee:gamebe:v:68:y:2010:i:2:p:773-780
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Pablo Revilla, 2004. "Many-to-one Matching When Colleagues Matter," Economic Working Papers at Centro de Estudios Andaluces E2004/85, Centro de Estudios Andaluces.
  2. Michael Schwarz & M. Bumin Yenmez, 2009. "Median Stable Matching," NBER Working Papers 14689, National Bureau of Economic Research, Inc.
  3. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
  4. Alvin E. Roth, 2007. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," NBER Working Papers 13225, National Bureau of Economic Research, Inc.
  5. Bettina Klaus & Flip Klijn, 2004. "Median Stable Matching for College Admission," UFAE and IAE Working Papers 632.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 16 Feb 2006.
  6. 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.
  7. Echenique, Federico & Yenmez, Mehmet B., 2005. "A Solution to Matching with Preferences over Colleagues," Working Papers 1226, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. 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.
  9. Dutta, Bhaskar & Masso, Jordi, 1997. "Stability of Matchings When Individuals Have Preferences over Colleagues," Journal of Economic Theory, Elsevier, vol. 75(2), pages 464-475, August.
  10. Dinko Dimitrov & Emiliya Lazarova, 2008. "Coalitional Matchings," Working Papers 2008.45, Fondazione Eni Enrico Mattei.
  11. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
  12. 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.
  13. Clark Simon, 2006. "The Uniqueness of Stable Matchings," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-28, December.
  14. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
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