In Monderer and Shapley (1996) (pdf) there is the following theorem.
The next theorem is well-known (and very useful).
THEOREM 4.5
Let $\Gamma$ be a game in which the strategy sets are intervals of real numbers. Suppose the payoff functions are twice continuously differentiable. Then $\Gamma$ is a potential game iff $\frac{\partial^2{u^i}}{\partial{y^i}{y^j}}=\frac{\partial^2{u^j}}{\partial{y^i}{y^j}}$ for every $i,j \in \mathbb{N}$.
Where was this from? I might be missing something but I don't see a reference. Thank you in advance for your help.
