Semi-tensor product approach for partially symmetric games

Abstract

In this paper, a criterion for the partially symmetric game (PSG) is derived by using the semi-tensor product approach. The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated. The testing equations with the minimum number are concretely determined, and the computational complexity is analysed. Finally, two examples are displayed to show the theoretical results.

Keywords:

• Partially symmetric game
• semi-tensor product of matrices
• adjacent transpositions

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research was funded by the National Natural Science Foundation of China under Grants 61673012 and 11971240, respectively.

Notes on contributors

Lei Wang

Lei Wang received the B.Sc. degree in Mathematics from Henan University, Kaifeng, China, in 2018. She is currently pursuing her Ph.D. degree at the School of Mathematical Sciences, Nanjing Normal University, Nanjing, China. Her research interests include control theory of Boolean control networks and game theory.

Jiandong Zhu

Jiandong Zhu received the B.Sc. degree from Xuzhou Normal University, Xuzhou, China, in 1996, the M.Sc. and Ph.D. degrees from Shandong University, Jinan, China, in 1999 and 2002, respectively. Currently, he is a Professor at the School of Mathematical Sciences, Nanjing Normal University. He was a Postdoctoral Research Associate at Southeast University, Nanjing, China, from 2002 to 2004, a Visiting Academic at RMIT University, Melbourne, Australia, from 2010 to 2011, and a Visiting Scholar at the University of Texas at San Antonio, USA, from 2016 to 2017. His research interests include Boolean control networks, multi-agent systems and the stability of nonlinear systems.