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Efficient computation of the Shapley value for large-scale linear production games

Efficient computation of the Shapley value for large-scale linear production games
Efficient computation of the Shapley value for large-scale linear production games
The linear production game is concerned with allocating the total payoff of an enterprise among the owners of the resources in a fair way. With cooperative game theory providing a mathematical framework for sharing the benefit of the cooperation, the Shapley value is one of the widely used solution concepts as a fair measurement in this area. Finding the exact Shapley value for linear production games is, however, challenging when the number of players exceeds 30. This paper describes the use of linear programming sensitivity analysis for a more efficient computation of the Shapley value. The paper also proposes a stratified sampling technique to estimate the Shapley value for large-scale linear production games. Computational results show the effectiveness of the proposed methods compared to others.
Le, Phuoc Hoang
70c6e39a-4046-48e4-94f0-eab08c73882b
Nguyen, Tri-Dung
a6aa7081-6bf7-488a-b72f-510328958a8e
Bektas, Tolga
0db10084-e51c-41e5-a3c6-417e0d08dac9
Le, Phuoc Hoang
70c6e39a-4046-48e4-94f0-eab08c73882b
Nguyen, Tri-Dung
a6aa7081-6bf7-488a-b72f-510328958a8e
Bektas, Tolga
0db10084-e51c-41e5-a3c6-417e0d08dac9

Le, Phuoc Hoang, Nguyen, Tri-Dung and Bektas, Tolga (2018) Efficient computation of the Shapley value for large-scale linear production games. Annals of Operations Research. (doi:10.1007/s10479-018-3047-0).

Record type: Article

Abstract

The linear production game is concerned with allocating the total payoff of an enterprise among the owners of the resources in a fair way. With cooperative game theory providing a mathematical framework for sharing the benefit of the cooperation, the Shapley value is one of the widely used solution concepts as a fair measurement in this area. Finding the exact Shapley value for linear production games is, however, challenging when the number of players exceeds 30. This paper describes the use of linear programming sensitivity analysis for a more efficient computation of the Shapley value. The paper also proposes a stratified sampling technique to estimate the Shapley value for large-scale linear production games. Computational results show the effectiveness of the proposed methods compared to others.

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Accepted/In Press date: 1 September 2018
e-pub ahead of print date: 20 September 2018
Published date: September 2018

Identifiers

Local EPrints ID: 425036
URI: http://eprints.soton.ac.uk/id/eprint/425036
PURE UUID: d09eccd3-ca60-43ab-b6d9-2abf971b0d32
ORCID for Tri-Dung Nguyen: ORCID iD orcid.org/0000-0002-4158-9099
ORCID for Tolga Bektas: ORCID iD orcid.org/0000-0003-0634-144X

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Date deposited: 09 Oct 2018 16:30
Last modified: 18 Feb 2021 17:16

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