The Shapley value for directed graph games

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 induc...

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Bibliographic Details
Published in:Operations research letters 2016-01, Vol.44 (1), p.143-147
Main Authors: Khmelnitskaya, Anna, Selçuk, Özer, Talman, Dolf
Format: Article
Language:English
Subjects:
Convexity
Core
Directed graph
Dominance
Dominance structure
Games
Graph theory
Mathematical analysis
Operations research
Permutations
Players
Shapley value
TU game
Vectors (mathematics)
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Summary: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.
ISSN:0167-6377
1872-7468
DOI:10.1016/j.orl.2015.12.009