The Shapley value for directed graph games

Anna Borisovna Khmelnitskaya, Özer Selcuk, Dolf Talman

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The Shapley value for directed graph (digraph) games, TU games with limited cooperation introduced by an arbitrary digraph prescribing the dominance relation among the players, is introduced. It is dened as the average of marginal contribution vectors corresponding to all permutations that do not violate the subordination of players. We assume that in order to cooperate players may join only coalitions containing no players dominating them. Properties of this solution are studied and a convexity type condition is provided that guarantees its stability with respect to an appropriately dened core concept. An axiomatization for cycle digraph games for which the digraphs are directed cycles is obtained.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages9
Publication statusPublished - Oct 2014

Publication series

NameMemorandum of the Department of Applied Mathematics
ISSN (Print)1874-4850


  • IR-92219
  • METIS-306069
  • C71
  • EWI-25167
  • directed graph
  • dominance structure
  • TU game
  • Shapley value
  • Core
  • Convexity

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