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Instability in Stable Marriage Problem: Matching Unequally Numbered Men and Women

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  • Gui-Yuan Shi
  • Yi-Xiu Kong
  • Bo-Lun Chen
  • Guang-Hui Yuan
  • Rui-Jie Wu

Abstract

The goal of the stable marriage problem is to match by pair two sets composed by the same number of elements. Due to its widespread applications in the real world, especially the unique importance to the centralized matchmaker, a very large number of questions have been extensively studied in this field. This article considers a generalized form of the stable marriage problem, where different numbers of men and women need to be matched pairwise and the emergence of single men or women is inevitable. Theoretical analysis and numerical simulations confirm that even a small deviation on the number of men and women from the equality condition can have a large impact on the matching solution of the Gale-Shapley algorithm. These results provide insights to many of the real-world applications when matching two sides with an unequal number.

Suggested Citation

  • Gui-Yuan Shi & Yi-Xiu Kong & Bo-Lun Chen & Guang-Hui Yuan & Rui-Jie Wu, 2018. "Instability in Stable Marriage Problem: Matching Unequally Numbered Men and Women," Complexity, Hindawi, vol. 2018, pages 1-5, September.
    • Handle: RePEc:hin:complx:7409397
    DOI: 10.1155/2018/7409397
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    References listed on IDEAS

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    1. Paolo Laureti Yi-Cheng Zhang, 2003. "Matching games with partial information," Game Theory and Information 0307002, University Library of Munich, Germany.
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    Cited by:

    1. Enrico Maria Fenoaltea & Izat B. Baybusinov & Jianyang Zhao & Lei Zhou & Yi-Cheng Zhang, 2021. "The Stable Marriage Problem: an Interdisciplinary Review from the Physicist's Perspective," Papers 2103.11458, arXiv.org.
    2. Yi-Xiu Kong & Guang-Hui Yuan & Lei Zhou & Rui-Jie Wu & Gui-Yuan Shi, 2018. "Competition May Increase Social Utility in Bipartite Matching Problem," Complexity, Hindawi, vol. 2018, pages 1-7, November.

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