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Hedonic games related to many-to-one matching problems

  • Juan Cesco

    ()

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

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File URL: http://hdl.handle.net/10.1007/s00355-011-0559-9
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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 39 (2012)
Issue (Month): 4 (October)
Pages: 737-749

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Handle: RePEc:spr:sochwe:v:39:y:2012:i:4:p:737-749
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  1. Federico Echenique & Jorge Oviedo, 2003. "Core Many-to-one Matchings by Fixed-point Methods," Game Theory and Information 0302001, EconWPA.
  2. Dinko Dimitrov & Emiliya Lazarova, 2008. "Coalitional Matchings," Working Papers 2008.45, Fondazione Eni Enrico Mattei.
  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. Suryapratim Banerjee & Hideo Konishi & Tayfun Sonmez, 1999. "Core in a Simple Coalition Formation Game," Boston College Working Papers in Economics 449, Boston College Department of Economics.
  5. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
  6. Iehlé, Vincent, 2007. "The Core-Partition of Hedonic Games," Economics Papers from University Paris Dauphine 123456789/87, Paris Dauphine University.
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