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arXiv · 2505.24637

Note on the size of a stable matching

Gregory Z. Gutin·Philip R. Neary·Anders Yeo
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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. We then identify the minimum number of equilibrium pairings that must be ``sacrificed'' when maximising the employment rate is the objective; if each stable matching is of size $\ceiling{\frac{n}{2}}$, then no such pairs appear when all vacancies are filled.

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Gregory Z. Gutin, Philip R. Neary, Anders Yeo. 2025-05-30. Note on the size of a stable matching. https://arxiv.org/abs/2505.24637

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