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On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games

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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.

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Authors and Affiliations

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

    Aixin Liu, Haitao Li, Ping Li & Xinrong Yang

Authors
  1. Aixin Liu
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  2. Haitao Li
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  3. Ping Li
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  4. Xinrong Yang
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Corresponding author

Correspondence to Haitao Li.

Additional information

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, A., Li, H., Li, P. et al. On Basis and Pure Nash Equilibrium of Finite Pure Harmonic Games. J Syst Sci Complex 35, 1415–1428 (2022). https://doi.org/10.1007/s11424-022-0032-0

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  • DOI: https://doi.org/10.1007/s11424-022-0032-0

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