On potential equations of finite symmetric games

Abstract

In this paper, potential equations of finite symmetric games are proposed to verify whether a symmetric game is potential or not. Some simpler verification conditions allowing a finite symmetric game to be a potential game are presented, along with a minimum number of verification equations. The obtained verification method is extended to other types of symmetric games, such as weighted symmetric games and skew‐symmetric games. Finally, two illustrative examples are given to demonstrate the effectiveness of the theoretical results.