A concept of nucleolus for uncertain coalitional game with application to profit allocation. (English) Zbl 1533.91028
Summary: Uncertain coalitional game is a type of coalitional games where the transferable payoffs are assumed to be uncertain variables. As solutions of uncertain coalitional game, uncertain core, uncertain Shapley value, and uncertain stable set have been offered. This article further presents a new thought of uncertain nucleolus as another solution to the uncertain coalitional game. Meantime, this paper proves that uncertain nucleolus is nonempty and singleton and proves that uncertain nucleolus is a subset of the uncertain core if the uncertain core is nonempty. Finally, an uncertain nucleolus is applied to resolve a profit allocation problem.
MSC:
| 91A12 | Cooperative games |
| 91B32 | Resource and cost allocation (including fair division, apportionment, etc.) |
References:
| [1] | Amin, S. H.; Zhang, G.; Eldali, M. N., A review of closed-loop supply chain models, J. Data, Inf. Manage., 2, 4, 279-307 (2020) |
| [2] | An, X.; Wang, X.; Hu, H.; Pang, S., Optimal allocation of regional water resources under water saving management contract, J. Data Inf. Manage., 3, 4, 281-296 (2021) |
| [3] | Aumann, R. J.; Maschler, M., The bargaining set for cooperative games, Adv. Game Theory, 52, 443-476 (1964) · Zbl 0132.14003 |
| [4] | Bernardi, G.; Freixas, J., The Shapley value analyzed under the Felsenthal and Machover bargaining model, Public Choice, 176, 557-565 (2018) |
| [5] | Blau, R. A., Random-payoff two-person zero-sum games, Oper. Res., 22, 6, 1243-1251 (1974) · Zbl 0306.90087 |
| [6] | Cassidy, R. G.; Field, C. A.; Kirby, M. J.L., Solution of a satisficing model for random payoff games, Manage. Sci., 19, 3, 266-271 (1972) · Zbl 0262.90073 |
| [7] | Charnes, A. C.; Kirby, M.; Raike, W., Zero-zero chance-constrained games, Theory Probab. Appl., 13, 4, 663-681 (1968) · Zbl 0209.52008 |
| [8] | Chu, H. J.; Hsieh, J. G.; Hsia, K. H.; Chen, L. W., Fuzzy differential game of guarding a movable territory, Inform. Sci., 91, 1-2, 113-131 (1996) · Zbl 0885.90130 |
| [9] | Dai, B.; Yang, X.; Liu, X., Shapley value of uncertain coalitional game based on Hurwicz criterion with application to water resource allocation, Group Decis. Negot., 31, 1, 241-260 (2022) |
| [10] | Davis, M.; Maschler, M., Existence of stable payoff configurations for cooperative games, Bull. Am. Math. Soc., 69, 106-108 (1963) · Zbl 0114.12501 |
| [11] | Davis, M.; Maschler, M., The kernel of a cooperative game, Nav. Res. Log., 12, 3, 223-259 (1965) · Zbl 0204.20202 |
| [12] | Dey, A.; Zaman, K., A robust optimization approach for solving two-person games under interval uncertainty, Comput. Oper. Res., 119, Article 104937 pp. (2020) · Zbl 1458.91010 |
| [13] | Freixas, J., The Banzhaf value for cooperative and simple multichoice games, Group Decis. Negot., 29, 61-74 (2020) |
| [14] | Gao, J., Credibilistic game with fuzzy information, J. Uncertain Syst., 1, 1, 74-80 (2007) |
| [15] | Gao, J., Uncertain bimatrix game with application, Fuzzy Optim. Decis. Making, 12, 1, 65-78 (2013) · Zbl 1411.91015 |
| [16] | Gao, J.; Liu, B., Fuzzy multilevel programming with a hybrid intelligent algorithm, Compu. Math. Appl., 49, 9-10, 1539-1548 (2005) · Zbl 1138.90508 |
| [17] | Gao, J.; Liu, Z. Q.; Shen, P., On characterization of credibilistic equilibria of fuzzy-payoff two-player zero-sum game, Soft Comput., 13, 2, 127-132 (2009) · Zbl 1156.91305 |
| [18] | Gao, J.; Yang, X., Credibilistic bimatrix game with asymmetric information: bayesian optimistic equilibrium strategy, Inter. J. Uncertain. Fuzz., 21, suppl.01, 89-100 (2013) · Zbl 1322.91004 |
| [19] | Gao, J.; Yang, X.; Liu, D., Uncertain Shapley value of coalitional game with application to supply chain alliance, Appl. Soft Comput., 56, 551-556 (2017) |
| [20] | Gao, J.; Yu, Y., Credibilistic extensive game with fuzzy payoffs, Soft Comput., 17, 4, 557-567 (2013) · Zbl 1264.91019 |
| [21] | Gao, J.; Zhang, Z. Q.; Shen, P., Coalitional game with fuzzy payoffs and credibilistic Shapley value, Iran. J. Fuzzy Syst., 8, 4, 107-117 (2011) · Zbl 1260.91017 |
| [22] | Gillies, D. B., Solutions to general non-zero-sum games, Ann. Math. Study, 40, 47-85 (1959) · Zbl 0085.13106 |
| [23] | Li, Y.; Liu, Y., A risk-averse multi-item inventory problem with uncertain demand, J. Data, Inf. Manage., 1, 3, 77-90 (2019) |
| [24] | Li, Z.; Zhang, H., Game analysis of new product promotion and improvement between manufacturer and retailer, J. Syst. Eng., 36, 2, 213-226 (2021) · Zbl 1488.91059 |
| [25] | Liang, R.; Yu, Y.; Gao, J.; Liu, Z. Q., N-person credibilistic strategic game, Front. Comput. Sci. Chi., 4, 2, 212-219 (2010) · Zbl 1267.91010 |
| [26] | Liu, B., Uncertainty Theory (2007), Springer-Verlag: Springer-Verlag Berlin · Zbl 1141.28001 |
| [27] | Liu, B., Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty (2010), Springer-Verlag: Springer-Verlag Berlin |
| [28] | Liu, Y.; Liu, G., Stable set of uncertain coalitional game with application to electricity suppliers problem, Soft Comput., 22, 17, 5719-5724 (2018) · Zbl 1398.91041 |
| [29] | Miranda, E.; Troffaes, M. C.M.; Destercke, S., A geometric and game-theoretic study of the conjunction of possibility measures, Inform. Sci., 298, 373-389 (2015) · Zbl 1360.68845 |
| [30] | Rao, W.; Duan, Z.; Zhu, Q., A cost allocation method for balancing the satisfaction of cooperative distribution sub-alliances, J. Syst. Eng., 36, 4, 476-494 (2021) |
| [31] | Neumann, von J., O. Morgenstern, The Theory of Games in Economic Behavior (1944), Wiley: Wiley New York · Zbl 0063.05930 |
| [32] | Schmeidler, D., The nucleolus of a characteristic function game, SIMA J. Appl. Math., 17, 6, 1163-1170 (1969) · Zbl 0191.49502 |
| [33] | Shi, X.; Wang, H., Research on product selection and joint replenishment decision based on inventory capacity limitation, J. Syst. Eng., 36, 2, 264-278 (2021) · Zbl 1488.90092 |
| [34] | Shapley, L. S.; Shubik, M., A method for evaluating the distribution of power in committee system, Am Polit. Sci. Rev., 48, 3, 787-792 (1954) |
| [35] | Shapley, L. S.; Shubik, M., On the core of an economic system with externalities, Am. Econ. Assoc., 59, 4, 678-684 (1969) |
| [36] | Shen, P.; Gao, J., Coalitional game with fuzzy payoffs and credibilistic core, Soft Comput., 15, 4, 781-786 (2011) · Zbl 1243.91008 |
| [37] | Wang, C.; Tang, W.; Zhao, R., Static Bayesian games with finite fuzzy types and the existence of equilibrium, Inform. Sci., 178, 24, 4688-4698 (2008) · Zbl 1156.91317 |
| [38] | Wang, Y.; Luo, S.; Gao, J., Uncertain extensive game with application to resource allocation of national security, J. Amb. Intel. Hum. Comp., 8, 5, 797-808 (2017) |
| [39] | Yang, X.; Gao, J., Uncertain differential games with application to capitalism, J. Uncertain Anal. Appl., 1, article 17 (2013) |
| [40] | Yang, X.; Gao, J., Uncertain core for coalitional game with uncertain payoffs, J. Uncertain Syst., 8, 1, 13-21 (2014) |
| [41] | Yang, X.; Gao, J., Linear-quadratic uncertain differential game with application to resource extraction problem, IEEE Trans Fuzzy Syst., 24, 4, 819-826 (2016) |
| [42] | Yang, X.; Gao, J., Bayesian equilibria for uncertain bimatrix game with asymmetric information, J. Intell. Manuf., 28, 3, 515-525 (2017) |
| [43] | Yao, K.; Li, X., Uncertain alternating renewal process and its application, IEEE Trans Fuzzy Syst., 20, 6, 1154-1160 (2012) |
| [44] | Zhang, X.; Li, X., A semantic study of the first-order predicate logic with uncertainty involved, Fuzzy Optim. Decis. Making, 13, 4, 357-367 (2014) · Zbl 1428.03052 |
| [45] | Zhang, Y.; Gao, J.; Li, X.; Yang, X., Two-person cooperative uncertain differential game with transferable payoffs, Fuzzy Optim. Decis. Making, 20, 4, 567-594 (2021) · Zbl 1482.91034 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
