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Note on the size of a stable matching

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  • Gregory Z. Gutin
  • Philip R. Neary
  • Anders Yeo

Abstract

Consider a one-to-one two-sided matching market with workers on one side and single-position firms on the other, and suppose that the largest individually rational matching contains $n$ pairs. We show that the number of workers employed and positions filled in every stable matching is bounded from below by $\lceil\frac{n}{2}\rceil$ and we characterise the class of preferences that attain the bound.

Suggested Citation

  • Gregory Z. Gutin & Philip R. Neary & Anders Yeo, 2025. "Note on the size of a stable matching," Papers 2505.24637, arXiv.org.
    • Handle: RePEc:arx:papers:2505.24637
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    References listed on IDEAS

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    3. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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    5. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    6. Echenique,Federico & Immorlica,Nicole & Vazirani,Vijay V. (ed.), 2023. "Online and Matching-Based Market Design," Cambridge Books, Cambridge University Press, number 9781108831994, Enero-Abr.
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