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.