In this paper, we consider the design of equilibrium linear feedback control policies in an uncertain process (e.g., an economy) affected by either one or more players. We consider a process which nominal (commonly believed) development in time is described by a linear system. Assuming every player is risk averse and has his own expectation about a worst-case development of the nominal process we model this problem using a linear quadratic differential game framework. Conditions under which equilibrium policies exist are studied. Assuming players have an infinite planning horizon, we provide a complete description in case the system is scalar, whereas for the multi-variable case, we provide existence results for some important classes of systems.