### Orthogonal Decomposition of Incomplete-Profile Finite Game Space

DAI Xiaoyan, WANG Jinhuan, XU Yong

1. School of Science, Hebei University of Technology, Tianjin 300401, China
• Received:2021-02-02 Revised:2021-06-29 Online:2022-11-25 Published:2022-12-23
• Contact: WANG Jinhuan,Email:wjhuan228@163.com
• Supported by:
This work was supported by the Natural Science Foundation of Hebei Province under Grant Nos. F2021202032, A2019202205, and the Cultivation of Postgraduate Students Innovation Ability of Hebei Province under Grant No. CXZZSS2021045.

DAI Xiaoyan, WANG Jinhuan, XU Yong. Orthogonal Decomposition of Incomplete-Profile Finite Game Space[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2208-2222.

This work studies the orthogonal decomposition of the incomplete-profile normal finite game (IPNFG) space using the method of semi-tensor product (STP) of matrices. Firstly, by calculating the rank of the incomplete-profile potential matrix, the bases of incomplete-profile potential game subspace ($\mathcal{G}_P^{\it\Omega}$) and incomplete-profile non-strategic game subspace ($\mathcal{N}^{\it\Omega}$) are obtained. Then the bases of incomplete-profile pure potential game subspace ($\mathcal{P}^{\it\Omega}$) and incomplete-profile pure harmonic game subspace ($\mathcal{H}^{\it\Omega}$) are also revealed. These bases offer an expression for the orthogonal decomposition. Finally, an example is provided to verify the theoretical results.
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