Strategy detection of noncooperative dynamic games

This paper is a continuation of [4,13], and considers a different fundamental problem that is called strategy detection. Specifically, we consider an infinitely repetitive noncooperative game between a human and a machine, where the machine updates its strategy according to the previous strategies and payoffs of the machine and the human, the update rule of the machine is known to the human, but the strategies played by the machine are unknown to the human. We formulate the process of obtaining the strategy of the machine by observing its payoffs as the strategy detection problem. By defining a graph called weighted pair graph, and using the theories of finite automata and formal languages, we give an equivalent condition for the existence of the solution to the problem, and design algorithms for finding the solution and detecting the strategy of the machine.