In many settings of interest, a policy is set by one party, the leader, in order to influence the action of another party, the follower, where the follower's response is determined by some private information. A natural question to ask is, can the leader improve their strategy by learning about the unknown follower through repeated interactions? A well known folk theorem from dynamic pricing, a special case of this leader-follower setting, would suggest that the leader cannot learn effectively from the follower when the follower is fully strategic, leading to a large literature on learning in strategic settings that relies on limiting the strategic space of the follower in order to provide positive results. In this paper, we study dynamic Bayesian Stackelberg games, where a leader and a \emph{fully strategic} follower interact repeatedly, with the follower's type unknown. Contrary to existing results, we show that the leader can improve their utility through learning in repeated play. Using a novel average-case analysis, we demonstrate that learning is effective in these settings, without needing to weaken the follower's strategic space. Importantly, this improvement is not solely due to the leader's ability to commit, nor does learning simply substitute for communication between the parties. We provide an algorithm, based on a mixed-integer linear program, to compute the optimal leader policy in these games and develop heuristic algorithms to approximate the optimal dynamic policy more efficiently. Through simulations, we compare the efficiency and runtime of these algorithms against static policies.

翻译：在许多重要场景中，一方（领导者）通过制定策略来影响另一方（跟随者）的行动，而跟随者的响应由其私有信息决定。一个自然的问题是：领导者能否通过重复交互来学习未知的跟随者，从而改进自身策略？动态定价领域的一个著名民间定理（作为此类领导者-跟随者场景的特例）表明，当跟随者完全理性时，领导者无法从跟随者处有效学习，这催生了大量关于战略环境中学习的研究文献——这些研究通常通过限制跟随者的策略空间来获得积极结果。本文研究动态贝叶斯斯塔克尔伯格博弈，其中领导者与完全理性的跟随者进行重复交互，且跟随者类型未知。与现有结论相反，我们证明领导者可以通过重复博弈中的学习提升其效用。通过新颖的平均案例分析，我们表明在此类场景中学习是有效的，且无需弱化跟随者的策略空间。重要的是，这种改进不仅源于领导者的承诺能力，学习也并非简单地替代双方间的信息传递。我们提出一种基于混合整数线性规划的算法来计算此类博弈中的最优领导者策略，并开发启发式算法以更高效地逼近最优动态策略。通过仿真实验，我们比较了这些算法与静态策略在效率和运行时间上的表现。