In this note we consider linear stationary feedback Nash equilibria of the scalar linear-quadratic differential game. The planning horizon considered is assumed to be infinite. We present both necessary and sufficient conditions on the system parameters for the existence of a unique solution of the associated algebraic Riccati equations (ARE) that stabilizes the closed-loop system. For the case of more solutions, singleton-valued refinements of the equilibrium concept are studied.
['Jacob Engwerda']
Feedback Nash equilibria in the scalar infinite horizon LQ-Game