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

Author

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  • Phuoc Hoang Le

    (University of Southampton)

  • Tri-Dung Nguyen

    (University of Southampton)

  • Tolga Bektaş

    (University of Southampton)

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.

Suggested Citation

  • Phuoc Hoang Le & Tri-Dung Nguyen & Tolga Bektaş, 2020. "Efficient computation of the Shapley value for large-scale linear production games," Annals of Operations Research, Springer, vol. 287(2), pages 761-781, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-018-3047-0
    DOI: 10.1007/s10479-018-3047-0
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    References listed on IDEAS

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    1. Sheida Etemadidavan & Andrew J. Collins, 2021. "An Empirical Distribution of the Number of Subsets in the Core Partitions of Hedonic Games," SN Operations Research Forum, Springer, vol. 2(4), pages 1-20, December.

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