On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games

被引：1

作者：

Liu Aixin ^{[1
]}

Li Haitao ^{[1
]}

Li Ping ^{[1
]}

Yang Xinrong ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2022年 / 35卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Auxiliary harmonic vector; finite pure harmonic games; semi-tensor product of matrices; vector space structure; STABILIZATION; DECOMPOSITION;

D O I：

10.1007/s11424-022-0032-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：1415 / 1428

页数：14

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