Hedonic games and matching problems

JUAN C. CESCO

Mendoza

Congreso; LVIII Reunión de Comunicaciones Científicas; 2008

Unión MAtemática Argentina

We consider the existence problem of stable matchings in the setting of many-to-one matching problems. Unlike other approaches which use algorithmic techniques to provide sufficient and necessary and sufficient conditions to guarantee the existence of stable matchings, we adopt a game theoretic point of view. We first associate, with each many-to-one matching problem, a hedonic game to take advantage of recent results guaranteeing the existence of core-partitions for that class of games, to build up our conditions. The main result states that a many-to-one matching problem, with no restrictions on individual preferences, has stable* matchings if and only if a related hedonic game is pivotally balanced. In the case that the preferences in the matching problem are substitutable, the notions of stability and stability* coincide.