On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games

doi:10.1007/s11424-022-0032-0

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (4): 1415-1428.DOI: 10.1007/s11424-022-0032-0

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On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games

LIU Aixin, LI Haitao, LI Ping, YANG Xinrong

School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

Received:2020-02-22 Revised:2021-04-21 Online:2022-08-25 Published:2022-08-02
Contact: LI Haitao,Email:haitaoli09@gmail.com
Supported by:
The paper was supported by the National Natural Science Foundation of China under Grant No. 62073202, and the Young Experts of Taishan Scholar Project under Grant No. tsqn201909076.

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LIU Aixin, LI Haitao, LI Ping, YANG Xinrong. On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games[J]. Journal of Systems Science and Complexity, 2022, 35(4): 1415-1428.

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.

Key words: Auxiliary harmonic vector, finite pure harmonic games, semi-tensor product of matrices, vector space structure

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