The Set of Stable Matchings and the Core in a Matching Market with Ties and Matroid Constraints

TL;DR

This paper generalizes the relationship between stable matchings and the core from capacity-constrained markets to those with matroid constraints, broadening the theoretical understanding of matching markets with ties.

Contribution

It extends existing results on the core and stable matchings to markets with matroid constraints, a significant generalization over capacity constraints.

Findings

Generalization of core-stable matching relationship to matroid constraints

Proof that previous results hold under more complex constraints

Broader applicability of stable matching theory in complex markets

Abstract

In this paper, we consider a many-to-one matching market where ties in the preferences of agents are allowed. For this market with capacity constraints, Bonifacio, Juarez, Neme, and Oviedo proved some relationship between the set of stable matchings and the core. In this paper, we consider a matroid constraint that is a generalization of a capacity constraint. We prove that the results proved by Bonifacio, Juarez, Neme, and Oviedo can be generalized to this setting.