With the tool of semi-tensor product of matrices, an algorithm is proposed to verify whether a finite game is a weighted potential game (WPG) without pre-knowledge on its weights. Then the algorithm is applied to find the closest WPG for a given finite game. In the light of evolutionary equivalence between finite games with respect to certain strategy updating rules, the concept and criterion of near weighted potential games (NWPGs) are given. Based on this, a method is proposed for replacing PGs by WPGs or NWPGs in game theoretic control, which improved the applicability of PG-based optimization. 

　　Publication: 

　　Automatica, Volume 141, July 2022, 110303 

　　Author: 

　　Daizhan Cheng 

　　Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China 

　　Email: dcheng@iss.ac.cn 

　　Zhengping Ji 

　　Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China 

　　School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, PR China