Symmetry-based decomposition of finite games

  • Changxi Li
  • Fenghua HeEmail author
  • Ting Liu
  • Daizhan Cheng
Research Paper


The symmetry-based decompositions of finite games are investigated. First, the vector space of finite games is decomposed into a symmetric subspace and an orthogonal complement of the symmetric subspace. The bases of the symmetric subspace and those of its orthogonal complement are presented. Second, the potential-based orthogonal decompositions of two-player symmetric/antisymmetric games are presented. The bases and dimensions of all dual decomposed subspaces are revealed. Finally, some properties of these decomposed subspaces are obtained.


potential game symmetric game decomposition Nash equilibrium semi-tensor product of matrices 



This work was supported by National Natural Science Foundation of China (Grant Nos. 61473099, 61273013, 61333001).


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Changxi Li
    • 1
  • Fenghua He
    • 1
    Email author
  • Ting Liu
    • 2
  • Daizhan Cheng
    • 2
  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.Key Laboratory of Systems and Control, Academy of Mathematics and Systems SciencesChinese Academy of SciencesBeijingChina

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