Active Inverse Methods in Stackelberg Games with Bounded Rationality

Inverse game theory is utilized to infer the cost functions of all players based on game outcomes. However, existing inverse game theory methods do not consider the learner as an active participant in the game, which could significantly enhance the learning process. In this paper, we extend inverse game theory to active inverse methods. For Stackelberg games with bounded rationality, the leader, acting as a learner, actively chooses actions to better understand the follower's cost functions. First, we develop a method of active learning by leveraging Fisher information to maximize information gain about the unknown parameters and prove the consistency and asymptotic normality. Additionally, when leaders consider its cost, we develop a method of active inverse game to balance exploration and exploitation, and prove the consistency and asymptotic Stackelberg equilibrium with quadratic cost functions. Finally, we verify the properties of these methods through simulations in the quadratic case and demonstrate that the active inverse game method can achieve Stackelberg equilibrium more quickly through active exploration.