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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.

Suggested Citation

  • Kominers, Scott Duke, 2010. "Matching with preferences over colleagues solves classical matching," Games and Economic Behavior, Elsevier, vol. 68(2), pages 773-780, March.
  • Handle: RePEc:eee:gamebe:v:68:y:2010:i:2:p:773-780

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    References listed on IDEAS

    1. Michael Schwarz & M. Bumin Yenmez, 2009. "Median Stable Matching," NBER Working Papers 14689, National Bureau of Economic Research, Inc.
    2. 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.
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    4. 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.
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    6. Dinko Dimitrov & Emiliya Lazarova, 2008. "Coalitional Matchings," Working Papers 2008.45, Fondazione Eni Enrico Mattei.
    7. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    8. 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.
    9. Pablo Revilla, 2004. "Many-to-one Matching When Colleagues Matter," Economic Working Papers at Centro de Estudios Andaluces E2004/85, Centro de Estudios Andaluces.
    10. 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.
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    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. Adachi, Hiroyuki, 2000. "On a characterization of stable matchings," Economics Letters, Elsevier, vol. 68(1), pages 43-49, July.
    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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    Cited by:

    1. 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).
    2. Francis Flanagan, 2015. "Contracts vs. preferences over colleagues in matching," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 209-223, February.
    3. repec:eee:gamebe:v:107:y:2018:i:c:p:135-152 is not listed on IDEAS


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