On basis and pure Nash equilibrium of finite pure harmonic games. (English) Zbl 1497.91019
Summary: 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.
Keywords:
auxiliary harmonic vector; finite pure harmonic games; semi-tensor product of matrices; vector space structureReferences:
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