N -Person Linear-Quadratic Differential Games with Constraints
Richard C. Scalzo · SIAM Journal on Control · 1974
Since 1970, it has been known that open loop Nash equilibrium points exist for N-person differential games when there are integral bounds on the control functions. These results were obtained using various fixed-point theorems, and required that the duration of the game be “small”. In this paper it is assumed that the controls are constrained to take values in compact, convex subsets of $R^{q_i} $. A fixed-point theorem due to Tychonov is used, and as a result there are no restrictions on the duration of the game.