Observability of non-cooperative adaptive games

Controlling complex systems to desired states is a very important issue in science and engineering. In the paper, we consider a new class of control systems based on non-cooperative adaptive games which can give some light on this kind of complex systems. It involves a hierarchal decision making structure: one leader and multiple followers. Given any strategy of the leader, the followers can form a non-cooperative adaptive game which may reach a Nash equilibrium. We can study the leader's observability of such an equilibrium which has not be investigated before. It seems to be a new direction of adaptive games from the perspective of control and beyond the frameworks of both the traditional control theory and game theory. More importantly, the resulting adaptive profile is shown to have some nice stability and convergence properties, for example, an asymptotic Nash equilibrium can be reached.