On the Core of a Set of Coalitions

  • Hans Reijnierse
  • Jean Derks
Conference paper


A restricted cooperative game (N,Ω,v) is a triple consisting of a (finite) player set N, a collection Ω of subsets of N and a function v : Ω\{φ} → ℝ. We assume that N ∈ Ω. If Ω equals 2 N , we get a regular cooperative game. The interest in subcollections of the power set of N is inspired by the fact that in case of restricted communication possibilities the regular model of a cooperative game is not realistic.


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  1. Derks J.J.M., The Core of the restricted null game, Mimeo RL Maastricht, March 1992.Google Scholar
  2. Weyl, H., The elementary theory of convex polyhedra, Contributions to the Theory of Games (Annals of Mathematic Studies No. 24), edited by H.W. Kuhn and A.W. Tucker, Princeton University Press, Princeton, pp. 3–18, 1950.Google Scholar
  3. Klee, V., Some characterizations of convex polyhedra (Acta. Mathematica, 102), edited by Almqvist & Wiksells Boktryckeri, Uppsala 1959.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Hans Reijnierse
    • 1
  • Jean Derks
    • 2
  1. 1.Department of MathematicsUniversity of NijmegenNijmegenNetherlands
  2. 2.Dept. of MathematicsRijksuniversiteit LimburgMaastrichtNetherlands

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