Note on the size of a stable matching

Gregory Z. Gutin, Philip R. Neary and 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.

Date: 2025-05
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