Static potential games are non-cooperative games that admit a fictitious function, also referred to as a potential function, such that the optimizers of this function constitute a subset or a refinement of the Nash equilibria of the associated non-cooperative game. In this work, we study a class of N-player non-zero sum difference games with inequality constraints that admit a potential game structure, with an open-loop information structure. We introduce the notion of an open-loop potential difference game and provide the conditions under which a class of non-zero sum difference games, with inequality constraints, admit an open-loop potential game structure. When the potential functions are not specified apriori, we provide a method of constructing the dynamic potential functions from the players’ objective functions using the theory of conservative vector fields. We specialize the obtained results to a linear quadratic setting, and characterize a class of linear-quadratic potential difference games with inequality constraints. Additionally, we provide a linear complementarity problem based approach for computing a refinement of open-loop Nash equilibria. We illustrate our results with an example inspired by energy storage incentives in a smart grid. Finally, we attempt to extend our results to non-zero sum difference games with feedback information structure.