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...

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Bibliographic Details
Published in:Annals of operations research 2020-04, Vol.287 (2), p.761-781
Main Authors: Le, Phuoc Hoang, Nguyen, Tri-Dung, Bektaş, Tolga
Format: Article
Language:English
Subjects:
Analysis
Business and Management
Combinatorics
Computational efficiency
Economic models
Game theory
Linear programming
Methods
Operations research
Operations Research/Decision Theory
Production management
S.I.: Game theory and optimization
Sensitivity analysis
Studies
Technology application
Theory of Computation
Value (Economics)
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Summary: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.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-018-3047-0