A class of differential games which admits a feedback solution with linear value functions

This paper presents a class of differential games which admits a feedback Nash equilibrium solution with linear value functions. An interesting feature is that not only may the equilibrium strategies be highly nonlinear, they may even assume a general structure instead of an explicit specification. A number of existing games are shown to be games belonging to this class of games. Two new applications – one in political support scrambling and one in common pool non-renewable resources extraction – are provided.