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Matching Couples with Scarf's Algorithm

  • Peter Biro

    ()

    (Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences)

  • Tamas Fleiner

    ()

    (Department of Computer Science and Information Theory, Budapest University of Technology and Economics)

  • Rob Irving

    ()

    (School of Computing Science, University of Glasgow)

Scarf's algorithm [18] provides fractional core elements for NTU-games. Bir¢ and Fleiner [3] showed that Scarf's algorithm can be extended for capacitated NTU-games. In this setting agents can be involved in more than one coalition at a time, cooperations may be performed with different intensities up to some limits, and the contribution of the agents can also differ in a coalition. The fractional stable solutions for the above model, produced by the extended Scarf algorithm, are called stable allocations. In this paper we apply this solution concept for the Hospitals Residents problem with Couples (HRC). This is one of the most important general stable matching problems due to its relevant applications, also well-known to be NP-hard. We show that if a stable allocation yielded by the Scarf algorithm turns outto be integral then it provides a stable matching for an instance of HRC, so this method can be used as a heuristic. In an experimental study, we compare this method with other heuristics constructed for HRC that are applied in practice in the American and Scottish resident allocation programs, respectively. Our main finding is that the Scarf algorithm outperforms all the other known heuristics when the proportion of couples is high.

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Paper provided by Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 1330.

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Length: 13 pages
Date of creation: Sep 2013
Date of revision:
Handle: RePEc:has:discpr:1330
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  1. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
  2. Peter Biro & Sofya Kiselgof, 2013. "College admissions with stable score-limits," IEHAS Discussion Papers 1306, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  3. Peter Biro & Flip Klijn, 2011. "Matching with Couples: a Multidisciplinary Survey," IEHAS Discussion Papers 1139, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  4. Klaus Bettina & Klijn Flip & Nakamura Toshifumi, 2007. "Corrigendum: Stable Matchings and Preferences of Couples," Research Memorandum 025, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Roth, Alvin, 2008. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," Scholarly Articles 2579651, Harvard University Department of Economics.
  6. Peter Biro & Tamas Fleiner, 2012. "Fractional solutions for capacitated NTU-games, with applications to stable matchings," IEHAS Discussion Papers 1234, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  7. Bettina Klaus & Flip Klijn, 2004. "Stable Matchings and Preferences of Couples," Working Papers 117, Barcelona Graduate School of Economics.
  8. Bettina Klaus & Flip Klijn, 2002. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," UFAE and IAE Working Papers 552.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 01 Oct 2005.
  9. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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