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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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  • 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

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    Cited by:

    1. MAULEON, Ana & ROEHL, Nils & VANNETELBOSCH, Vincent, 2014. "Constitutions and social networks," LIDAM Discussion Papers CORE 2014003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Eduardo Duque & Juan S. Pereyra & Juan Pablo Torres-Martinez, 2024. "Local Non-Bossiness and Preferences Over Colleagues," Working Papers wp559, University of Chile, Department of Economics.
    3. Peng, Zixuan & Shan, Wenxuan & Zhu, Xiaoning & Yu, Bin, 2022. "Many-to-one stable matching for taxi-sharing service with selfish players," Transportation Research Part A: Policy and Practice, Elsevier, vol. 160(C), pages 255-279.
    4. Piazza, Adriana & Torres-Martínez, Juan Pablo, 2024. "Coalitional stability in matching problems with externalities and random preferences," Games and Economic Behavior, Elsevier, vol. 143(C), pages 321-339.
    5. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2018. "Constitutions and groups," Games and Economic Behavior, Elsevier, vol. 107(C), pages 135-152.
    6. Chao Huang, 2023. "Concave many-to-one matching," Papers 2309.04181, arXiv.org.
    7. repec:ris:msuecw:2018_013 is not listed on IDEAS
    8. 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.

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