The Shapley value for directed graph games

A. Khmelnitskaya, Ozer Selçuk, Dolf Talman

Research output: Contribution to journalArticleScientificpeer-review

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.
LanguageEnglish
Article number1
Pages143-147
Number of pages5
JournalOperations Research Letters
Volume44
Issue number1
DOIs
StatePublished - 1 Jan 2016

Fingerprint

Shapley Value
Directed graphs
Directed Graph
Game
TU Game
Dominance Relation
Subordination
Axiomatization
Violate
Digraph
Permutation
Cycle
Shapley value
Directed graph

Keywords

  • TU game
  • Shapley value
  • Directed graph
  • Dominance structure
  • Core
  • Convexity

Cite this

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The Shapley value for directed graph games. / Khmelnitskaya, A.; Selçuk, Ozer; Talman, Dolf.

In: Operations Research Letters, Vol. 44, No. 1, 1, 01.01.2016, p. 143-147.

Research output: Contribution to journalArticleScientificpeer-review

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KW - Dominance structure

KW - Core

KW - Convexity

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