The structure of finite games with symmetric potential functions is investigated in this paper. First, by constructing a basis of symmetric functions, a necessary and sufficient condition is presented to verify whether a finite game has symmetric potential functions. Then, a basis of the subspace of finite games with symmetric potential functions is provided. Next, the symmetric potential game is studied. By proving the symmetry of the potential function, a linear system is also presented for the verification of symmetric potential games, as well as a basis. Finally, as an application of the obtained results, the optimization of quasi-symmetric spatial games is considered. A sufficient condition for the utility design is given to turn the spatial game into a weighted potential game with the preassigned objective function as the potential function.

Publication:

SCIENCE CHINA-INFORMATION SCIENCES

http://dx.doi.org/10.1007/s11432-025-4831-x

Author:

Xinrong YANG

Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author

email: xinrongyang2019@163.com

Xiaodong LU

School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education, Beijing 100083, China

Corresponding author

email: luxiaodong@ustb.edu.cn