IDEAS home Printed from
   My bibliography  Save this article

A unifying model for matrix-based pairing situations


  • Tejada, O.
  • Borm, P.
  • Lohmann, E.


We present a unifying framework for transferable utility coalitional games that are derived from a non-negative matrix in which every entry represents the value obtained by combining the corresponding row and column. We assume that every row and every column is associated with a player, and that every player is associated with at most one row and at most one column. The instances arising from this framework are called pairing games, and they encompass assignment games and permutation games as two polar cases. We show that the core of a pairing game is always non-empty by proving that the set of pairing games coincides with the set of permutation games. Then we exploit the wide range of situations comprised in our framework to investigate the relationship between pairing games that have different player sets, but are defined by the same underlying matrix. We show that the core and the set of extreme core allocations are immune to the merging of a row player with a column player. Moreover, the core is also immune to the reverse manipulation, i.e., to the splitting of a player into a row player and a column player. Other common solution concepts fail to be either merging-proof or splitting-proof in general.

Suggested Citation

  • Tejada, O. & Borm, P. & Lohmann, E., 2014. "A unifying model for matrix-based pairing situations," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 55-61.
  • Handle: RePEc:eee:matsoc:v:72:y:2014:i:c:p:55-61
    DOI: 10.1016/j.mathsocsci.2014.09.003

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Curiel, I. & Tijs, S.H., 1986. "Assignment games and permutation games," Other publications TiSEM c9a47c3b-28d3-4874-b0a2-f, Tilburg University, School of Economics and Management.
    2. Solymosi, Tamas & Raghavan, T. E. S. & Tijs, Stef, 2005. "Computing the nucleolus of cyclic permutation games," European Journal of Operational Research, Elsevier, vol. 162(1), pages 270-280, April.
    3. Quint, Thomas, 1996. "On One-Sided versus Two-Sided Matching Games," Games and Economic Behavior, Elsevier, vol. 16(1), pages 124-134, September.
    4. Martínez-de-Albéniz, F. Javier & Núñez, Marina & Rafels, Carles, 2011. "Assignment markets with the same core," Games and Economic Behavior, Elsevier, vol. 73(2), pages 553-563.
    5. O. Tejada and M. Alvarez-Mozos, 2012. "Vertical Syndication-Proof Competitive Prices in Multilateral Markets," Working Papers in Economics 283, Universitat de Barcelona. Espai de Recerca en Economia.
    6. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    7. Tijs, S.H. & Parthasarathy, T. & Potters, J.A.M. & Rajendra Prasad, V., 1984. "Permutation games : Another class of totally balanced games," Other publications TiSEM a7edfa18-6224-4be3-b677-5, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Saadia El Obadi & Silvia Miquel, 2019. "Assignment Games with a Central Player," Group Decision and Negotiation, Springer, vol. 28(6), pages 1129-1148, December.

    More about this item


    Access and download statistics


    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:eee:matsoc:v:72:y:2014:i:c:p:55-61. 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: (Haili He). General contact details of provider: .

    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.