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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Acknowledgements
The authors thank two anonymous reviewers for their very constructive comments. The first author gratefully acknowledges the Faculty Scholarship provided by Southampton Business School.
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Le, P.H., Nguyen, TD. & Bektaş, T. Efficient computation of the Shapley value for large-scale linear production games. Ann Oper Res 287, 761–781 (2020). https://doi.org/10.1007/s10479-018-3047-0
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DOI: https://doi.org/10.1007/s10479-018-3047-0