A fixed-point approach to stable matchings and some applications

A fixed-point approach to stable matchings and some applications

0.00 Avg rating0 Votes
Article ID: iaor2004672
Country: United States
Volume: 28
Issue: 1
Start Page Number: 103
End Page Number: 126
Publication Date: Feb 2003
Journal: Mathematics of Operations Research
Authors:
Keywords: matching
Abstract:

We describe a fixed-point based approach to the theory of bipartite stable matchings. By this, we provide a common framework that links together seemingly distant results, like the stable marriage theorem of Gale and Shapley, the Mendelsoln–Dulmage theorem, the Kundu–Lawler theorem, Tarski's fixed-point theorem, the Cantor–Bernstein theorem, Pym's linking theorem, or the monochromatic path theorem of Sands et al. In this framework, we formulate a matroid-generalization of the stable marriage theorem and study the lattice structure of generalized stable matchings. Based on the theory of lattice polyhedra and blocking polyhedra, we extend results of Vande Vate and Rothblum on the bipartite stable matching polytope.

Reviews

Required fields are marked *. Your email address will not be published.