Towards a theory of game-based non-equilibrium control systems

This paper considers optimization problems for a new kind of control systems based on non-equilibrium dynamic games. To be precise, the authors consider the infinitely repeated games between a human and a machine based on the generic 2×2 game with fixed machine strategy of finite k-step memory. By introducing and analyzing the state transfer graphes (STG), it will be shown that the system state will become periodic after finite steps under the optimal strategy that maximizes the human’s averaged payoff, which helps us to ease the task of finding the optimal strategy considerably. Moreover, the question whether the optimizer will win or lose is investigated and some interesting phenomena are found, e.g., for the standard Prisoner’s Dilemma game, the human will not lose to the machine while optimizing her own averaged payoff when k = 1; however, when k ≥ 2, she may indeed lose if she focuses on optimizing her own payoff only. The robustness of the optimal strategy and identification problem are also considered. It appears that both the framework and the results are beyond those in the classical control theory and the traditional game theory.