@article{Wang2022, 
author = {Lei Wang and Xinyun Liu and Ting Li and Jiandong Zhu},
title = {Skew-symmetric games and symmetric-based decomposition of finite games},
year = {2022},
journal = {Mathematical Modelling and Control},
volume = {2},
number = {4},
pages = {257-267},
keywords = {semi-tensor product of matrices, skew-symmetric games, asymmetric games, decomposition of finite games, adjacent transpositions},
url = {https://www.sciopen.com/article/10.3934/mmc.2022024},
doi = {10.3934/mmc.2022024},
abstract = {In this paper, skew-symmetric games and a symmetric-based decomposition of finite games are investigated. First, necessary and sufficient conditions for testing skew-symmetric games are obtained by the semi-tensor product method based on adjacent transpositions. By using the obtained conditions for skew-symmetric games, a basis of the skew-symmetric game subspace is constructed. Then, the discriminant equations for a skew-symmetric game with the minimum number are derived. Furthermore, based on the basis of the skew-symmetric game subspace and that of the symmetric game subspace, a basis of the asymmetric game subspace is constructed, which completely solves the problem of symmetric-based decomposition of finite games. Finally, an illustrative example is provided to validate the obtained theoretical results.}
}