Symmetry-based decomposition of finite games

Abstract

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.

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Acknowledgements

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

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Correspondence to Fenghua He.

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Li, C., He, F., Liu, T. et al. Symmetry-based decomposition of finite games. Sci. China Inf. Sci. 62, 12207 (2019). https://doi.org/10.1007/s11432-017-9411-0

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Keywords

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