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The stability of many-to-many matching with max–min preferences

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  • Jiao, Zhenhua
  • Tian, Guoqiang

Abstract

This paper investigates the two-sided many-to-many matching problem, where every agent has max–min preference. The equivalence between the pairwise-stability and the setwise-stability is obtained. It is shown that the pairwise-stability implies the strong corewise-stability and the former may be strictly stronger than the latter. We also show that the strong core may be a proper subset of the core. The deferred acceptance algorithm yields a pairwise-stable matching. Thus the set of stable matchings (in all four senses) is non-empty.

Suggested Citation

  • Jiao, Zhenhua & Tian, Guoqiang, 2015. "The stability of many-to-many matching with max–min preferences," Economics Letters, Elsevier, vol. 129(C), pages 52-56.
    • Handle: RePEc:eee:ecolet:v:129:y:2015:i:c:p:52-56
    DOI: 10.1016/j.econlet.2015.02.009
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    References listed on IDEAS

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    1. 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.
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    6. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
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    Cited by:

    1. Jiao, Zhenhua & Tian, Guoqiang, 2017. "The Blocking Lemma and strategy-proofness in many-to-many matchings," Games and Economic Behavior, Elsevier, vol. 102(C), pages 44-55.

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    More about this item

    Keywords

    Many-to-many matching; Pairwise-stability; Core; Setwise-stability; Max–min preferences;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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