Pareto stability in two-sided many-to-many matching with weak preferences

Abstract

This paper studies the two-sided matching problem with multi-unit capacities and weak preferences on both sides. The simultaneous presence of these two features complicates the problem greatly, because either can make a stable matching not necessarily Pareto efficient. To ensure both fairness and efficiency, a natural solution is Pareto stability, which requires both pairwise stability and Pareto efficiency. We introduce a computationally efficient algorithm to construct a Pareto stable matching. This result immediately implies the existence of a Pareto stable matching in the general many-to-many matching problem with weak preferences.