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) TU games with limited cooperation induced by a digraph prescribing the dominance relation among the players is introduced. It is defined as the average of the marginal contribution vectors corresponding to all permutations which do not violate the induced subordination of players. We study properties of this solution and its core stability. For digraph games with the digraphs being directed cycles an axiomatization of the solution is obtained.
Original languageUndefined
Pages (from-to)143-147
Number of pages5
JournalOperations research letters
Issue number1
Publication statusPublished - Jan 2016


  • dominance structure
  • directed graph
  • EWI-26852
  • C71
  • IR-99669
  • Core
  • Shapley value
  • TU game
  • METIS-316839
  • Convexity

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