In numerous industrial management situations, multiple departments or units engage in complex, multi-grade interactions that influence overall organizational decisions. This study introduces a new assessing scheme that accounts for units' activity grades within such a situation. Unlike the Shapley value and the equal allocation of nonseparable costs, this assessing scheme remains computationally linear due to its single-pass step-grade decomposition, and it preserves several useful properties under any graded coalition. By applying specific reduction and excess function, several axiomatic and dynamic results are established to characterize the scheme's consistency and stability. These theoretical findings, generated from game-theoretical analysis, offer actionable insights into key participating units, including stakeholder engagement, incentive structures, and coalition formation, thereby enhancing the strategic decision-making processes in real-world industrial management contexts.
Citation: Yu-Hsien Liao. Integrating axiomatic and dynamic mechanisms under industrial management situations: game-theoretical analysis[J]. AIMS Mathematics, 2025, 10(6): 14975-14995. doi: 10.3934/math.2025671
In numerous industrial management situations, multiple departments or units engage in complex, multi-grade interactions that influence overall organizational decisions. This study introduces a new assessing scheme that accounts for units' activity grades within such a situation. Unlike the Shapley value and the equal allocation of nonseparable costs, this assessing scheme remains computationally linear due to its single-pass step-grade decomposition, and it preserves several useful properties under any graded coalition. By applying specific reduction and excess function, several axiomatic and dynamic results are established to characterize the scheme's consistency and stability. These theoretical findings, generated from game-theoretical analysis, offer actionable insights into key participating units, including stakeholder engagement, incentive structures, and coalition formation, thereby enhancing the strategic decision-making processes in real-world industrial management contexts.
| [1] |
E. M. Bednarczuk, J. Miroforidis, P. Pyzel, A multi-criteria approach to approximate solution of multiple-choice knapsack problem, Comput. Optim. Appl., 70 (2018), 889–910. https://doi.org/10.1007/s10589-018-9988-z doi: 10.1007/s10589-018-9988-z
|
| [2] | C. Y. Cheng, E. C. Chi, K. Chen, Y. H. Liao, A power mensuration and its normalization under multicriteria situations, IAENG Int. J. Appl. Math., 50 (2020), 262–267. |
| [3] |
A. Goli, H. K. Zare, R. Tavakkoli-Moghaddam, A. Sadegheih, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: the dairy products industry, Comput. Ind. Eng., 137 (2019), 106090. https://doi.org/10.1016/j.cie.2019.106090 doi: 10.1016/j.cie.2019.106090
|
| [4] |
M. R. Guarini, F. Battisti, A. Chiovitti, A methodology for the selection of multi-criteria decision analysis methods in real estate and land management processes, Sustainability, 10 (2018), 507. https://doi.org/10.3390/su10020507 doi: 10.3390/su10020507
|
| [5] |
S. Hart, A. Mas-Colell, Potential, value and consistency, Econometrica, 57 (1989), 589–614. https://doi.org/10.2307/1911054 doi: 10.2307/1911054
|
| [6] |
Y. A. Hwang, Y. H. Liao, The consistent value of fuzzy games, Fuzzy Sets Syst., 160 (2009), 644–656. https://doi.org/10.1016/j.fss.2008.10.003 doi: 10.1016/j.fss.2008.10.003
|
| [7] |
Y. A. Hwang, Y. H. Liao, The unit-level-core for multi-choice games: the replicated core for TU games, J. Glob. Optim., 47 (2010), 161–171. https://doi.org/10.1007/s10898-009-9463-6 doi: 10.1007/s10898-009-9463-6
|
| [8] | Y. L. Hsieh, Y. H. Liao, The pseudo EANSC: axiomatization and dynamic process, MS. Thesis, National Pingtung University, 2016. |
| [9] | Y. H. Liao, The maximal equal allocation of nonseparable costs on multi-choice games, Econ. Bull., 3 (2008), 1–8. |
| [10] |
Y. H. Liao, The duplicate extension for the equal allocation of nonseparable costs, Oper. Res. Int. J., 13 (2012), 385–397. https://doi.org/10.1007/s12351-012-0127-9 doi: 10.1007/s12351-012-0127-9
|
| [11] |
M. Maschler, G. Owen, The consistent Shapley value for hyperplane games, Int. J. Game Theory, 18 (1989), 389–407. https://doi.org/10.1007/BF01358800 doi: 10.1007/BF01358800
|
| [12] |
H. Moulin, On additive methods to share joint costs, Jpn. Econ. Rev., 46 (1985), 303–332. https://doi.org/10.1111/j.1468-5876.1995.tb00024.x doi: 10.1111/j.1468-5876.1995.tb00024.x
|
| [13] | I. Mustakerov, D. Borissova, E. Bantutov, Multiple-choice decision making by multicriteria combinatorial optimization, Adv. Model. Optim., 14 (2018), 729–737. |
| [14] | A. van den Nouweland, S. Tijs, J. Potters, J. Zarzuelo, Core and related solution concepts for multi-choice games, Z. Oper. Res., 41 (1995), 289–311. |
| [15] | J. S. Ransmeier, The Tennessee Valley authority: a case study in the economics of multiple purpose stream planning, Vanderbilt University Press, 1942. |
| [16] | L. S. Shapley, A value for $n$-person games, In: H. W. Kuhn, A. W. Tucker, Contributions to the theory of games II, Princeton University Press, 1953,307–317. |
| [17] | H. C. Wei, A. T. Li, W. N. Wang, Y. H. Liao, Solutions and its axiomatic results under fuzzy behavior and multicriteria situations, IAENG Int. J. Appl. Math., 49 (2019), 612–617. |
Yu-Hsien Liao. Integrating axiomatic and dynamic mechanisms under industrial management situations: game-theoretical analysis[J]. AIMS Mathematics, 2025, 10(6): 14975-14995. doi: 10.3934/math.2025671
DownLoad: