On potential equations of finite games

In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time. Compared with the existing results, a reduced-complexity testing condition is derived. Some connections between the potential equations and the existing characterizations of potential games are established. It is revealed that a finite game is potential if and only if its every bi-matrix sub-game is potential.