The Shapley value for directed graph games

Anna Khmelnitskaya, Ozer Selcuk, Dolf Talman

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Abstract

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 languageEnglish
Pages (from-to)143-147
JournalOperations Research Letters
Volume44
Issue number1
Early online date19 Dec 2015
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • TU game
  • Shapley value
  • directed graph
  • dominance structure
  • core
  • convexity

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