A characterization of a strong stable fractional matching

NEME, PABLO A.; JORGE OVIEDO

LI Reunión Anual, Asociación Argentina de Econimía Politica

Asociacion Argentina de Econimia Politica

Lugar: Tucuman; Año: 2016 vol. 2019

In the study of stable fractional matching as a not necessarily integer solution of a linearprogram, Roth, Rothblum and Vande Vate (1993) observe that for this fractional matching, can bea blocking pair. Those fractional matching that are not blocked, they called strong stable fractionalmatchings. In this paper we give a characterization of this matchings. This characterization usesthe concept of cyclic matching. We will see that the set of all strong stable fractional matching is aunion of some convex sets. Each one of this convex sets are generated by a stable matching and itscyclic matchings. We present an algorithm that computes the set of matchings necessary in orderto generate the above mentioned convex sets. We also show that the set of strong stable fractionalmatchings have a lattice structure.