Open-loop Nash equilibrium in games with time-varying delays

We consider a game with non-linear time-varying delays in states and in strategies for which we formulate a new sufficient optimality conditions of dual programming type for the existence of the open-loop Nash equilibria. Moreover, we propose an algorithm to construct open-loop Nash equilibria which are verified by the proven theorem. The proposed result we apply to model of active vehicle suspensions in which time-varying delay is well documented. Illustrative simulations show how the differential game tool can be usefull in construction of safer and more comfortable cars and how Nash equilibria should be adjusted to include time-varying delays in information transmission.