We study a two-player dynamic Stackelberg game where the follower's intention is unknown to the leader. Classical formulations of the Stackelberg equilibrium (SE) assume that the follower's best response (BR) function is known to the leader. However, this is not always true in practice. We study a setting in which the leader receives updated beliefs about the follower BR before the end of the game, such that the update prompts the leader and subsequently the follower to re-optimize their strategies. We characterize the optimality guarantees of the SE solutions under this belief update for both open loop and feedback information structures. Interestingly, we prove that in general, assuming an incorrect follower's BR may lead to a lower leader cost over the entire game than knowing the true follower's BR. We support these results with numerical examples in a linear quadratic (LQ) Stackelberg game, and use Monte Carlo simulations to show that the instances of incorrect BR achieving lower leader costs are non-trivial in collision avoidance LQ Stackelberg games.

翻译：本文研究一个两方动态斯塔克尔伯格博弈，其中跟随者的意图对领导者而言是未知的。斯塔克尔伯格均衡（SE）的经典公式假设跟随者的最佳响应（BR）函数为领导者所知。然而，这在实践中并非总是成立。我们研究一种场景，其中领导者在博弈结束前会接收到关于跟随者最佳响应的更新信念，这种更新促使领导者及随后的跟随者重新优化其策略。我们刻画了在这种信念更新下，针对开环和反馈信息结构，斯塔克尔伯格均衡解的最优性保证。有趣的是，我们证明在一般情况下，假设错误的跟随者最佳响应可能导致领导者在整个博弈中的成本低于了解真实跟随者最佳响应的情况。我们通过线性二次型（LQ）斯塔克尔伯格博弈中的数值算例支撑这些结果，并采用蒙特卡洛模拟表明，在避碰型LQ斯塔克尔伯格博弈中，错误最佳响应实现更低领导者成本的实例并非微不足道。