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# Title: On the many-to-one strongly stable fractional matching set

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.
 Subjects: Theoretical Economics (econ.TH) MSC classes: 90C05, 91B68 Cite as: arXiv:1905.12500 [econ.TH] (or arXiv:1905.12500v2 [econ.TH] for this version)

## Submission history

From: Pablo A. Neme Dr. [view email]
[v1] Wed, 29 May 2019 14:36:34 GMT (19kb)
[v2] Fri, 22 May 2020 15:58:32 GMT (22kb)
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