Feedback and well-posedness of singularly perturbed Nash games

This paper discusses linear-quadratic Nash games for systems with slow and fast modes. Singular perturbation is employed to replace a Nash game played on the full model by a game played on a reduced order model. The well-posedness of different solutions corresponding to different state feedback information structures is considered. An important relation between the feedback information structure and the well-posedness of the game is found and used to conjecture special cases when the linear memoryless closed-loop solution is well-posed.