Optimization and Identification in a Non-equilibrium Dynamic Game

In this paper, we consider optimization and identification problems in a non-equilibrium dynamic game. To be precise, we consider infinitely repeated games between a human and a machine based on the standard prisoners' dilemma model. The machine's strategy is assumed to be fixed with k-step memory, which may be unknown to the human. By analyzing the state transfer graph, it will be shown that the optimal strategy that maximizes the human's averaged payoff is actually periodic after finite steps. This can help us to find the optimal strategy in a feasible way. Moreover, when k = 1, the human will not lose to the machine while optimizing his averaged payoff; but when k ¿ 2, he may indeed lose if he focuses on optimizing his own payoff only. Identifiability problem will also be investigated when the machine's strategy is unknown to the human.