On the many-to-one strongly stable fractional matching set

Pablo Neme and Jorge Oviedo

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Abstract: For a many-to-one matching market where firms have strict and $\boldsymbol{q}$-responsive preferences, we give a characterization of the set of strongly stable fractional matchings as the union of the convex hull of all connected sets of stable matchings. Also, we prove that a strongly stable fractional matching is represented as a convex combination of stable matchings that are ordered in the common preferences of all firms.

Date: 2019-05, Revised 2020-05
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