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Matching with Couples: Stability and Algorithm

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  • Jiang, Zhishan
  • Tian, Guoqiang

Abstract

This paper defines a notion of semi-stability for matching problem with couples, which is a natural generalization of, and further identical to, the conventional stability for matching without couples. It is shown that there always exists a semi-stable matching for couples markets with strict preferences, and the set of semi-stable matchings can be partitioned into subsets, each of which forms a distributive lattice. We further prove that a semi-stable matching is stable when couples play reservation strategies. This result perfectly explains the puzzle of NRMP even for finite markets. Moreover, we define a notion of asymptotic stability and present sufficient conditions for a sequential couples market to be asymptotically stable. Another remarkable contribution is that we develop a new algorithm, called Persistent Improvement Algorithm, for finding semi-stable matchings, which is also more efficient than the Gale-Shapley algorithm for finding stable matchings for singles markets. Lastly, this paper investigates the welfare property and incentive issues of semi-stable mechanisms.

Suggested Citation

  • Jiang, Zhishan & Tian, Guoqiang, 2013. "Matching with Couples: Stability and Algorithm," MPRA Paper 57936, University Library of Munich, Germany, revised Jul 2014.
    • Handle: RePEc:pra:mprapa:57936
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    File URL: https://mpra.ub.uni-muenchen.de/57936/1/MPRA_paper_57936.pdf
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    References listed on IDEAS

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    Cited by:

    1. Rouzbeh Ghouchani & Szilvia Pápai, 2022. "Preference aggregation for couples," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 889-923, November.

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    More about this item

    Keywords

    Matching with couples; stability; semi-stability; asymptotic stability; algorithm;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • J41 - Labor and Demographic Economics - - Particular Labor Markets - - - Labor Contracts

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