Controllability of Non-cooperative Dynamical Games

In this paper, we consider a new class of control systems based on non-cooperative dynamical games. It involves a hierarchal decision making structure: one leader and multiple followers. Given any strategy of the leader, the followers form a non-cooperative dynamical game which may reach a Nash equilibrium. We such an equilibrium which has not be investigated before. It seems to be a new direction of dynamical games from the perspective of control and beyond the frameworks of both the traditional control theory and game theory. First, we will give the definition of the controllability, and then give some necessary and sufficient conditions of the controllability for non-cooperative linear-quadratic dynamical games.