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Note On the core of a collection of coalitions


Author Info

  • Hans Reijnierse

    (Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands)

  • Jean Derks

    (Department of Mathematics, University of Maastricht, P.O.Box 616, 6200 MD Maastricht, The Netherlands)


For a collection of subsets of a finite set N we define its core to be equal to the polyhedral cone {x∈IRN: ∑i∈N xi=0 and ∑i∈Sxi\geq0 for all S∈}. This note describes several applications of this concept in the field of cooperative game theory. Especially collections are considered with core equal to {0}. This property of a one-point core is proved to be equivalent to the non-degeneracy and balancedness of . Further, the notion of exact cover is discussed and used in a second characterization of collections with core equal to {0}.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 27 (1998)
Issue (Month): 3 ()
Pages: 451-459

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Handle: RePEc:spr:jogath:v:27:y:1998:i:3:p:451-459

Note: Received May 1997/Final version May 1998
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Keywords: Core · restricted core · non-degeneracy · balancedness · exactness;


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Cited by:
  1. repec:hal:journl:halshs-00583868 is not listed on IDEAS
  2. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2007. "Balancedness Conditions for Exact Games," Research Memorandum 039, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Michel Grabisch & Lijue Xie, 2011. "The restricted core of games on distributive lattices: how to share benefits in a hierarchy," Computational Statistics, Springer, vol. 73(2), pages 189-208, April.
  4. Imma Curiel & Herbert Hamers & Stef Tijs & Jos Potters, 1997. "Restricted component additive games," Computational Statistics, Springer, vol. 45(2), pages 213-220, June.
  5. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," PSE - Labex "OSE-Ouvrir la Science Economique" hal-00803233, HAL.
  6. Csóka, Péter & Herings, P. Jean-Jacques & Kóczy, László Á., 2009. "Stable allocations of risk," Games and Economic Behavior, Elsevier, vol. 67(1), pages 266-276, September.
  7. repec:hal:journl:halshs-00423922 is not listed on IDEAS
  8. repec:hal:journl:halshs-00344802 is not listed on IDEAS
  9. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00650964, HAL.
  10. repec:hal:cesptp:hal-00803233 is not listed on IDEAS
  11. repec:hal:journl:halshs-00445171 is not listed on IDEAS
  12. Jesus Fco. Getan Olivan & Jesus Montes & Carlos Rafels Pallarola, 2006. "On the monotonic core," Working Papers in Economics 155, Universitat de Barcelona. Espai de Recerca en Economia.


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