  Static potential games are non-cooperative games which admit a fictitious
function, also referred to as a potential function, such that the minimizers of
this function constitute a subset (or a refinement) of the Nash equilibrium
strategies of the associated non-cooperative game. In this paper, we study a
class $N$-player non-zero sum difference games with inequality constraints
which admit a potential game structure. In particular, we provide conditions
for the existence of an optimal control problem (with inequality constraints)
such that the solution of this problem yields an open-loop Nash equilibrium
strategy of the corresponding dynamic non-cooperative game (with inequality
constraints). Further, we provide a way to construct potential functions
associated with this optimal control problem. We specialize our general results
to a linear-quadratic setting and provide a linear complementarity
problem-based approach for computing the refinements of the open-loop Nash
equilibria. We illustrate our results with an example inspired by energy
storage incentives in a smart grid.
