On the Structure of Feedback Potential Difference Games

Abstract

A static potential game is a non-cooperative game for which there exists a fictitious function, also referred to as a potential function, whose optimizers provide a Nash equilibrium of the associated non-cooperative game. In this paper, we study non-zero-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 non-cooperative game. We specialize the obtained results to 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.