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Hedonic games related to many-to-one matching problems

Juan Cesco

Social Choice and Welfare, 2012, vol. 39, issue 4, 737-749

Abstract: We consider the existence problem of stable matchings in many-to-one matching problems. Unlike other approaches which use algorithmic techniques to give necessary and sufficient conditions, 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. Copyright Springer-Verlag 2012

Date: 2012
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DOI: 10.1007/s00355-011-0559-9

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