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Matching with preferences over colleagues solves classical matching

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  • Kominers, Scott Duke

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Many-to-one matching Stability Matching algorithms;

References

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  1. Alvin E. Roth, 2007. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," NBER Working Papers 13225, National Bureau of Economic Research, Inc.
  2. 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.
  3. Bettina Klaus & Flip Klijn, 2006. "Median Stable Matching for College Admissions," International Journal of Game Theory, Springer, vol. 34(1), pages 1-11, April.
  4. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
  5. 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.
  6. Dinko Dimitrov & Emiliya Lazarova, 2008. "Coalitional Matchings," Working Papers 2008.45, Fondazione Eni Enrico Mattei.
  7. 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.
  8. 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.
  9. Federico Echenique & Mehmet B. Yenmez, 2005. "A Solution to Matching with Preferences over Colleagues," Working Papers 2005.120, Fondazione Eni Enrico Mattei.
  10. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
  11. Pablo Revilla, 2004. "Many-to-one Matching When Colleagues Matter," Economic Working Papers at Centro de Estudios Andaluces E2004/85, Centro de Estudios Andaluces.
  12. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
  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.
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Cited by:
  1. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers CIE 74, University of Paderborn, CIE Center for International Economics.
  2. repec:pdn:wpaper:74 is not listed on IDEAS
  3. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers Dissertations 02, University of Paderborn, Faculty of Business Administration and Economics.
  4. MAULEON, Ana & ROEHL, Nils & VANNETELBOSCH, Vincent, 2014. "Constitutions and social networks," CORE Discussion Papers 2014003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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