A New Class of Control Systems Based on Non-equilibrium Games

In this paper, a new class of control systems based on non-equilibrium dynamic games is introduced. Specifically, we consider optimization and identification problems modeled by an infinitely repeated 2×2 generic games between a human and a machine, where the machine takes a fixed and k-step-memory strategy while the human is more intelligent in the sense that she can optimize her strategy. This framework is beyond the frameworks of both the traditional control theory and game theory. By using the concept of state transfer graphs, the optimal strategy of the human will be characterized and the win-lose situation will be discussed. These are carried out for three typical games, i.e., the Prisoner’s Dilemma game, the Snowdrift game and the Battle-of-sex game, but with different win-loss results. The problem of strategy identification will also be investigated.