Parameter Identification for Fictitious Play Algorithm in Repeated Games

In the previous works [1] and [2], we solved the optimal strategy of the human player against a machine player who makes decisions based on Fictitious Play in infinitely repeated \(2 \times 2\) games, in which the information is assumed to be complete and perfect. In this paper, we consider the problem of identification when the human player does not know the initial assessment of the machine player. In this scenario, we propose an identification algorithm for the human player and prove that the process of identification will end successfully in a finite time if the machine’s payoff parameter is rational. When the machine’s payoff parameter is irrational, the identification process will not end, which implies some advantage for the algorithm with irrational parameters.