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A necessary and sufficient condition for uniqueness consistency in the stable marriage matching problem

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  • Karpov, Alexander

Abstract

The paper develops a new extension of the sequential preference condition, which leads to unique stable matching in all subpopulations, obtained by consistent restrictions of the marriage matching problem. Under the new condition, the Gale–Shapley algorithm is stable, consistent, strategy-proof, Pareto optimal for men, and Pareto optimal for women.

Suggested Citation

  • Karpov, Alexander, 2019. "A necessary and sufficient condition for uniqueness consistency in the stable marriage matching problem," Economics Letters, Elsevier, vol. 178(C), pages 63-65.
    • Handle: RePEc:eee:ecolet:v:178:y:2019:i:c:p:63-65
    DOI: 10.1016/j.econlet.2019.02.022
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    References listed on IDEAS

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    1. Romero-Medina, Antonio & Triossi, Matteo, 2013. "Acyclicity and singleton cores in matching markets," Economics Letters, Elsevier, vol. 118(1), pages 237-239.
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    5. Jaeok Park, 2017. "Competitive equilibrium and singleton cores in generalized matching problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 487-509, May.
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    7. Sang-Chul Suh & Quan Wen, 2008. "Subgame perfect implementation of stable matchings in marriage problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(1), pages 163-174, June.
    8. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    9. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," NBER Working Papers 14840, National Bureau of Economic Research, Inc.
    10. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    11. Salonen, Hannu & Salonen, Mikko A.A., 2018. "Mutually best matches," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 42-50.
    12. Wu, Qinggong, 2015. "A finite decentralized marriage market with bilateral search," Journal of Economic Theory, Elsevier, vol. 160(C), pages 216-242.
    13. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
    14. Vinay Ramani & K. S. Mallikarjuna Rao, 2018. "Paths to stability and uniqueness in two-sided matching markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1137-1150, November.
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    Cited by:

    1. Meisner, Vincent & von Wangenheim, Jonas, 2019. "School Choice and Loss Aversion," Rationality and Competition Discussion Paper Series 208, CRC TRR 190 Rationality and Competition.
    2. Vincent Iehlé & Julien Jacqmin, 2023. "SIGEM : analyse de la procédure d’affectation dans les grandes écoles de management," Revue économique, Presses de Sciences-Po, vol. 74(2), pages 139-168.
    3. Bnaya Dreyfuss & Ofer Glicksohn & Ori Heffetz & Assaf Romm, 2022. "Deferred Acceptance with News Utility," NBER Working Papers 30635, National Bureau of Economic Research, Inc.

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    More about this item

    Keywords

    Market partition paradox; Stability; Consistency; Interrupter;
    All these keywords.

    JEL classification:

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

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