On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games  

作　　者：LIU Aixin LI Haitao LI Ping YANG Xinrong 

机构地区：[1]School of Mathematics and Statistics,Shandong Normal University,Jinan,250014,China

出　　处：《Journal of Systems Science & Complexity》2022年第4期1415-1428,共14页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant No.62073202;the Young Experts of Taishan Scholar Project under Grant No.tsqn201909076。

摘　　要：This paper investigates the basis and pure Nash equilibrium of finite pure harmonic games(FPHGs) based on the vector space structure. First, a new criterion is proposed for the construction of pure harmonic subspace, based on which, a more concise basis is constructed for the pure harmonic subspace. Second, based on the new basis of FPHGs and auxiliary harmonic vector, a more easily verifiable criterion is presented for the existence of pure Nash equilibrium in basis FPHGs. Third,by constructing a pure Nash equilibrium cubic matrix, the verification of pure Nash equilibrium in three-player FPHGs is given.

关 键 词：Auxiliary harmonic vector finite pure harmonic games semi-tensor product of matrices vector space structure 

分 类 号：O225[理学—运筹学与控制论]