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Solutions for the Stable Roommates Problem with Payments

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Author Info

  • Peter Biro

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

  • Matthijs Bomhoff

    ()
    (Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente)

  • Walter Kern

    ()
    (Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente)

  • Petr A. Golovach

    ()
    (School of Engineering and Computing Sciences, Durham University, Science Laboratories)

  • Daniel Paulusma

    ()
    (School of Engineering and Computing Sciences, Durham University, Science Laboratories)

Abstract

The stable roommates problem with payments has as input a graph G(E,V) with an edge weighting w:E_ùR+ and the problem is to find a stable solution. A solution is a matching M with a vector p.RV that satisfies pu+pv=w(uv) for all uv.M and pu=0 for all u unmatched in M. A solution is stable if it prevents blocking pairs, i.e., pairs of adjacent vertices u and v with pu+pv

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Bibliographic Info

Paper provided by Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 1211.

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Length: 18 pages
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:has:discpr:1211

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Related research

Keywords: roommates problem; matching game; cooperative game theory;

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References

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  1. Johan Karlander & Kimmo Eriksson, 2001. "Stable outcomes of the roommate game with transferable utility," International Journal of Game Theory, Springer, vol. 29(4), pages 555-569.
  2. Effrosyni Diamantoudi & Eiichi Miyagawa & Licun Xue, 2002. "Random paths to stability in the roommate problem," Discussion Papers 0102-65, Columbia University, Department of Economics.
  3. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
  4. Péter Biró & Walter Kern & Daniël Paulusma, 2012. "Computing solutions for matching games," International Journal of Game Theory, Springer, vol. 41(1), pages 75-90, February.
  5. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-80, November.
  6. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2011. "On the number of blocks required to access the coalition structure core," MPRA Paper 29755, University Library of Munich, Germany.
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Cited by:
  1. Bary S.R. Pradelski, 2014. "Evolutionary Dynamics and Fast Convergence in the Assignment Game," Economics Series Working Papers 700, University of Oxford, Department of Economics.
  2. Newton, Jonathan & Sawa, Ryoji, 2013. "A one-shot deviation principle for stability in matching problems," Working Papers 2013-09, University of Sydney, School of Economics, revised Mar 2014.
  3. Bettina Klaus & Frédéric Payot, 2013. "Paths to Stability in the Assignment Problem," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 13.14, Université de Lausanne, Faculté des HEC, DEEP.

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