Explicit solutions of coupled Riccati equations occurring in Nash games-The open-loop case

The paper considers two-person open-loop Nash games being noncooperative differential games such that finding of equilibrium (Nash strategy) requires solving of a complex two-point boundary value problems. The usual approach is to iteratively solve in an approximate manner the resoluting Riccati systems. The paper proposes, for a subclass of the problem defined by proportionality of the integral state cost matrices, the explicit solutions to the coupled Riccati differential systems.