Simplification of Shapley value for cooperative games via minimum carrier

作     者：Haitao Li Shuling Wang Aixin Liu Meixia Xia Haitao Li;Shuling Wang;Aixin Liu;Meixia Xia

作者机构：School of Mathematics and StatisticsShandong Normal UniversityJinan250014ShandongChina 

出 版 物：《Control Theory and Technology》 (控制理论与技术（英文版）)

年 卷 期：2021年第19卷第2期

页      面：157-169页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(No.62073202,No.61873150) the Young Experts of Taishan Scholar Project(No.tsqn201909076) the Natural Science Fund for Distinguished Young Scholars of Shandong Province(No.JQ201613) 

主　　题：Shapley value Cooperative game Carrier Algebraic form Semi-tensor product of matrices 

摘      要：Shapley value is one of the most fundamental concepts in cooperative *** paper investigates the calculation of the Shapley value for cooperative games and establishes a new formula via ***,a necessary and sufficient condition is presented for the verification of carrier,based on which an algorithm is worked out to find the unique minimum ***,by virtue of the properties of minimum carrier,it is proved that the profit allocated to dummy players(players which do not belong to the minimum carrier)is zero,and the profit allocated to players in minimum carrier is only determined by the minimum ***,a new formula of the Shapley value is presented,which greatly reduces the computational complexity of the original formula,and shows that the Shapley value only depends on the minimum ***,based on the semi-tensor product(STP)of matrices,the obtained new formula is converted into an equivalent algebraic form,which makes the new formula convenient for calculation via MATLAB.