Pareto stable matchings under one-sided matroid constraints

The Pareto stability is one of the solution concepts in two-sided matching markets with ties. It is known that there always exists a Pareto stable matching in the many-to-many setting. In this paper, we consider the following generalization of the Pareto stable matching problem in the many-to-many setting. Each agent v of one side has a matroid defined on the set of edges incident to v, and the set of edges assigned to v must be an independent set of this matroid. By extending the algorithm of Kamiyama for the many-to-many setting, we prove that there always exists a Pareto stable matching in this setting, and a Pareto stable matching can be found in polynomial time.