Least squares prenucleolus and nucleolus solution of multi-objective cooperative games
JIANG Binqian1, LI Dengfeng2, LIN Pingping1
1. School of Economics and Management, Fuzhou University, Fuzhou 350108, China; 2. School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 611731, China
Abstract：In the real life, there exist many complicated game situations with the unequal coalitions and more than one relevant or irrelevant objections. First of all, this paper constructs the multi-objective cooperative games with comprehensive weights, and those weights are associated with coalitions and objections. Then the least squares prenucleolus model and the least squares nucleolus model of the multi-objective cooperative games are proposed with hybrid objections, including the irrelevant objections and relevant objections. Second, the methods of least squares prenucleolus and the algorithm of least squares nucleolus in the classical cooperative games are extended to the multi-objective cooperative games. Using Lagrange multiplier method and pseudo-inverse theory, we have the explicit expression of the least squares prenucleolus of the multi-objective cooperative games and an algorithm for least squares nucleolus of the multi-objective cooperative games, and also prove the validity of the algorithm by properties of convex function. Finally, the correctness and effectiveness of the proposed models are verified though an numerical example of water resources allocation, and the advantages of the proposed models are reflected by comparison.
江彬倩, 李登峰, 林萍萍. 多目标合作博弈最小二乘预核仁与核仁解[J]. 系统工程理论与实践, 2020, 40(3): 691-702.
JIANG Binqian, LI Dengfeng, LIN Pingping. Least squares prenucleolus and nucleolus solution of multi-objective cooperative games. Systems Engineering - Theory & Practice, 2020, 40(3): 691-702.
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2020, Vol. 40 
