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Reconsidering the existence of stable solutions in three-sided matching problems with mixed preferences

Author

Listed:
  • Jorge Arenas

    (University of Chile)

  • Juan Pablo Torres-Martínez

    (University of Chile)

Abstract

We reexamine the existence of stable solutions in a class of three-sided matching problems previously studied by Zhang and Zhong (J Comb Optim 42:928–245, 2021). The sets of participants are U, V, and W. Agents in U have strict preferences defined on V, agents in V have strict preferences defined on W, and agents in W have strict preferences defined on $$U\times V$$ U × V . In this framework, we show that a weakly stable matching may not exist.

Suggested Citation

  • Jorge Arenas & Juan Pablo Torres-Martínez, 2023. "Reconsidering the existence of stable solutions in three-sided matching problems with mixed preferences," Journal of Combinatorial Optimization, Springer, vol. 45(2), pages 1-8, March.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:2:d:10.1007_s10878-023-00990-2
    DOI: 10.1007/s10878-023-00990-2
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    References listed on IDEAS

    as
    1. Eriksson, Kimmo & Sjostrand, Jonas & Strimling, Pontus, 2006. "Three-dimensional stable matching with cyclic preferences," Mathematical Social Sciences, Elsevier, vol. 52(1), pages 77-87, July.
    2. Feng Zhang & Liwei Zhong, 2021. "Three-sided matching problem with mixed preferences," Journal of Combinatorial Optimization, Springer, vol. 42(4), pages 928-936, November.
    3. Feng Zhang & Jing Li & Junxiang Fan & Huili Shen & Jian Shen & Hua Yu, 2019. "Three-dimensional stable matching with hybrid preferences," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 330-336, January.
    4. Danilov, V. I., 2003. "Existence of stable matchings in some three-sided systems," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 145-148, October.
    5. Liwei Zhong & Yanqin Bai, 2019. "Three-sided stable matching problem with two of them as cooperative partners," Journal of Combinatorial Optimization, Springer, vol. 37(1), pages 286-292, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Matching markets; Stability; Mixed preferences;
    All these keywords.

    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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