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Continuity of stable marriage correspondences

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  • Will Sandholtz
  • Andrew Tai

Abstract

We study a continuum version of the stable marriage problem, in which each agent has a variable mass to be paired to the opposite side. An agent's mass is interpretable as the divisible time of a single atomistic agent, or as a mass of infinitesimal agents of a particular type. Our object of interest is the mapping between the vector of masses to the set of stable matches. As in the canonical stable marriage model, the set of stable matches can be multi-valued, so this mapping is a correspondence. This correspondence is continuous if and only if the stable match is unique, implying that small changes in the masses may cause discontinuous jumps in the set of stable matches.

Suggested Citation

  • Will Sandholtz & Andrew Tai, 2026. "Continuity of stable marriage correspondences," Papers 2610.17460, arXiv.org.
    • Handle: RePEc:arx:papers:2610.17460
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    References listed on IDEAS

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    1. Michael Greinecker & Christopher Kah, 2021. "Pairwise Stable Matching in Large Economies," Econometrica, Econometric Society, vol. 89(6), pages 2929-2974, November.
    2. Itai Ashlagi & Yash Kanoria & Jacob D. Leshno, 2017. "Unbalanced Random Matching Markets: The Stark Effect of Competition," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 69-98.
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    6. Hiller, Victor & Wu, Jiabin & Zhang, Hanzhe, 2023. "Marital preferences and stable matching in cultural evolution," Journal of Economic Theory, Elsevier, vol. 210(C).
    7. Mourad Baïou & Michel Balinski, 2002. "Erratum: The Stable Allocation (or Ordinal Transportation) Problem," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 662-680, November.
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