A Hierarchical Model for Cooperative Games

  • Ulrich Faigle
  • Britta Peis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4997)


Classically, a cooperative game is given by a normalized real-valued function v on the collection of all subsets of the set N of players. Shapley has observed that the core of the game is non-empty if v is a non-negative convex (a.k.a. supermodular) set function. In particular, the Shapley value of a convex game is a member of the core. We generalize the classical model of games such that not all subsets of N need to form feasible coalitions. We introduce a model for ranking individual players which yields natural notions of Weber sets and Shapley values in a very general context. We establish Shapley’s theorem on the nonemptyness of the core of monotone convex games in this framework. The proof follows from a greedy algorithm that, in particular, generalizes Edmonds’ polymatroid greedy algorithm.


Greedy Algorithm Cooperative Game Choice Function Submodular Function Convex Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ulrich Faigle
    • 1
  • Britta Peis
    • 2
  1. 1.Zentrum für Angewandte Informatik Köln (ZAIK)KölnGermany
  2. 2.Technische Universität BerlinBerlinGermany

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