In this paper, we study scalar linear quadratic differential games with state feedback information structure. We present a numerical algorithm which determines whether this game will have no, one, or multiple equilibria. Furthermore, in case there is a unique equilibrium, the algorithm provides this equilibrium. The algorithm is efficient in the sense that it is capable of handling a large number of players. The analysis is restricted to the case the involved cost depend only on the state and control variables.
- Linear quadratic differential games
- Linear feedback Nash equilibria
- Coupled algebraic Riccati equations