Abstract: | 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. |