Balanced many-to-one matching problems with preferences over colleages

Abstract

Matching problems is a well studied class of coalitions formation models. Several core-like type solutions have been proposed for these models. However, unlike what happens in game theory, no balancedness properties have been introduced to study existence problems so far. In this paper we state a balancedness condition on a many-to-one matching problem with preferences over colleagues which turns to be a necessary and sufficient condition to guarantee the non-emptiness of the set of core matchings. We use this result to improve a recent characterization about the existence of core matchings for the classical many-to-one matching problem without preferences over colleagues. Our approach has been carried out by using some techniques and results from the theory of hedonic games, which is another class of coalitions formation models.