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Hedonic games related to many-to-one matching problems

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  • Juan Cesco

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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

Suggested Citation

  • Juan Cesco, 2012. "Hedonic games related to many-to-one matching problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 737-749, October.
  • Handle: RePEc:spr:sochwe:v:39:y:2012:i:4:p:737-749
    DOI: 10.1007/s00355-011-0559-9
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    References listed on IDEAS

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    1. Dinko Dimitrov & Emiliya Lazarova, 2008. "Coalitional Matchings," Working Papers 2008.45, Fondazione Eni Enrico Mattei.
    2. Echenique, Federico & Oviedo, Jorge, 2004. "Core many-to-one matchings by fixed-point methods," Journal of Economic Theory, Elsevier, vol. 115(2), pages 358-376, April.
    3. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    4. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    5. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    6. repec:dau:papers:123456789/87 is not listed on IDEAS
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    Cited by:

    1. Ana Mauleon & Nils Roehl & Vincent Vannetelbosch, 2014. "Constitutions and Social Networks," Working Papers Dissertations 02, Paderborn University, Faculty of Business Administration and Economics.
    2. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2018. "Constitutions and groups," Games and Economic Behavior, Elsevier, vol. 107(C), pages 135-152.

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