IDEAS home Printed from https://ideas.repec.org/p/has/discpr/1142.html
   My bibliography  Save this paper

Computing Solutions for Matching Games

Author

Listed:
  • Peter Biro

    () (Institute of Economics - Hungarian Academy of Sciences)

  • Walter Kern

    () (Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O.Box 217, NL-7500 AE Enschede)

  • Daniel Paulusma

    () (Department of Computer Science, University of Durham Science Laboratories, South Road, Durham DH1 3EY, England)

Abstract

A matching game is a cooperative game (N; v) defined on a graph G = (N;E) with an edge weighting w : E ! R+. The player set is N and the value of a coalition S N is de ned as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm+n2 log n) algorithm that tests if the core of a matching game defined on a weighted graph with n vertices and m edges is nonempty and that computes a core member if the core is nonempty. This algorithm improves previous work based on the ellipsoid method and can also be used to compute stable solutions for instances of the stable roommates problem with payments. Second we show that the nucleolus of an n-player matching game with a nonempty core can be computed in O(n4) time. This generalizes the corresponding result of Solymosi and Raghavan for assignment games. Third we prove that is NP-hard to determine an imputation with minimum number of blocking pairs, even for matching games with unit edge weights, whereas the problem of determining an imputation with minimum total blocking value is shown to be polynomial-time solvable for general matching games.

Suggested Citation

  • Peter Biro & Walter Kern & Daniel Paulusma, 2011. "Computing Solutions for Matching Games," IEHAS Discussion Papers 1142, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  • Handle: RePEc:has:discpr:1142
    as

    Download full text from publisher

    File URL: http://econ.core.hu/file/download/mtdp/MTDP1142.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. M. L. Balinski, 1965. "Integer Programming: Methods, Uses, Computations," Management Science, INFORMS, pages 253-313.
    2. Jeroen Kuipers & Ulrich Faigle & Walter Kern, 2001. "On the computation of the nucleolus of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 79-98.
    3. Johan Karlander & Kimmo Eriksson, 2001. "Stable outcomes of the roommate game with transferable utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 555-569.
    4. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
    5. Bettina Klaus & Alexandru Nichifor, 2010. "Consistency in one-sided assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 415-433, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peter Biro & Matthijs Bomhoff & Walter Kern & Petr A. Golovach & Daniel Paulusma, 2012. "Solutions for the Stable Roommates Problem with Payments," IEHAS Discussion Papers 1211, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    2. Peter Biro & Walter Kern & Daniel Paulusma & Peter Wojuteczky, 2015. "The Stable Fixtures Problem with Payments," IEHAS Discussion Papers 1545, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    3. repec:jmi:articl:jmi-v2i1a4 is not listed on IDEAS
    4. F.Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2015. "Insights into the nucleolus of the assignment game," UB Economics Working Papers 2015/333, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.

    More about this item

    Keywords

    matching game; nucleolus; cooperative game theory;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:has:discpr:1142. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Adrienn Foldi). General contact details of provider: http://edirc.repec.org/data/iehashu.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.