The Shapley value for directed graph games

A. Khmelnitskaya; Ozer Selçuk; Dolf Talman

doi:doi:10.1016/j.orl.2015.12.009

The Shapley value for directed graph games

A. Khmelnitskaya, Ozer Selçuk, Dolf Talman

Research output: Contribution to journal › Article › Scientific › peer-review

22 Citations (Scopus)

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 language	English
Article number	1
Pages (from-to)	143-147
Number of pages	5
Journal	Operations Research Letters
Volume	44
Issue number	1
DOIs	https://doi.org/doi:10.1016/j.orl.2015.12.009
Publication status	Published - 1 Jan 2016

Keywords

TU game
Shapley value
Directed graph
Dominance structure
Core
Convexity

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doi:10.1016/j.orl.2015.12.009

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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.",

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AB - 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.

KW - TU game

KW - Shapley value

KW - Directed graph

KW - Dominance structure

KW - Core

KW - Convexity

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DO - doi:10.1016/j.orl.2015.12.009

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JO - Operations Research Letters

JF - Operations Research Letters

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The Shapley value for directed graph games

Abstract

Keywords

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