An improved algorithm for detecting potential games

This note presents a simple necessary and sufficient condition for a game to be a potential game. My condition improves on the well-known condition in Monderer and Shapley (Games Econ Behav 14:124-143, 1996) in the sense that it leads to a significant reduction in the computational burden in determining whether a given game is a potential game. It also provides a logical connection between finite and continuous potential games, as it can be understood as a faithful translation of one type of characterization for a continuous potential game.