Hedonic games related to many-to-one matching problems (original) (raw)

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.

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Authors and Affiliations

1. Instituto de Matemática Aplicada San Luis (UNSL-CONICET), Av. Ejército de los Andes 950, 5700, San Luis, Argentina
   Juan Carlos Cesco
2. Departamento de Matemática (U.N. San Luis), Chacabuco y Pedernera, 5700, San Luis, Argentina
   Juan Carlos Cesco

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Correspondence toJuan Carlos Cesco.

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Cesco, J.C. Hedonic games related to many-to-one matching problems.Soc Choice Welf 39, 737–749 (2012). https://doi.org/10.1007/s00355-011-0559-9

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• Received: 26 February 2010
• Accepted: 26 May 2011
• Published: 11 June 2011
• Issue date: October 2012
• DOI: https://doi.org/10.1007/s00355-011-0559-9

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