The Shapley value for directed graph games

Anna Khmelnitskaya; Özer Selcuk; Dolf Talman

doi:10.1016/j.orl.2015.12.009

The Shapley value for directed graph games

Anna Khmelnitskaya, Özer Selcuk, Dolf Talman

Discrete Mathematics and Mathematical Programming

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

22 Citations (Scopus)

428 Downloads (Pure)

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

Keywords

Dominance structure
Directed graphs
C71
Core
Shapley value
TU game
Convexity
n/a OA procedure

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10.1016/j.orl.2015.12.009

22 Citations
1 Report

The Shapley value for directed graph games
Khmelnitskaya, A. B., Selcuk, Ö. & Talman, D., Oct 2014, Enschede: University of Twente. 9 p. (Memorandum of the Department of Applied Mathematics; no. 2038)
Research output: Book/Report › Report › Other research output

Cite this

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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.",

keywords = "Dominance structure, Directed graphs, C71, Core, Shapley value, TU game, Convexity, n/a OA procedure",

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KW - Dominance structure

KW - Directed graphs

KW - C71

KW - Core

KW - Shapley value

KW - TU game

KW - Convexity

KW - n/a OA procedure

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The Shapley value for directed graph games

Abstract

Keywords

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The Shapley value for directed graph games

Cite this