An example of a game which is at the same time zero-sum and potential.

Consider the **zero-sum** $2\times 2$ game with payoff bimatrix given by

Itâ€™s easy to check that the game is **potential** with potential function

and that $(\text{down}, \text{left})$ with outcome $(3, -3)$ is strict Nash. Since the game has non-trivial unilateral deviations it is not strategically equivalent to the zero-game, thus showing that the spaces of zero-sum and potential games intersect non-trivially, even after quotienting away strategical equivalence.

The image below shows the response graph of the game and some trajectories of replicator dynamics converging to the strict Nash equilibrium.