On the Structure of Feedback Potential Difference Games

A static potential game is a noncooperative game for which there exists a fictitious function, also referred to as a potential function, whose optimizers provide a Nash equilibrium of the associated noncooperative game. In this article, we study nonzero-sum finite-horizon difference games with feedback information structure, which admit a potential game structure. We provide conditions for the existence of an optimal control problem such that the optimal solution of this problem provides a feedback Nash equilibrium of the corresponding noncooperative game. We specialize the obtained results in a linear-quadratic setting so as to obtain these verifiable existence conditions in terms of the problem data. Finally, we illustrate our results using a network flow control problem.