Information asymmetry in games enables players with the information advantage to manipulate others' beliefs by strategically revealing information to other players. This work considers a double-sided information asymmetry in a Bayesian Stackelberg game, where the leader's realized action, sampled from the mixed strategy commitment, is hidden from the follower. In contrast, the follower holds private information about his payoff. Given asymmetric information on both sides, an important question arises: \emph{Does the leader's information advantage outweigh the follower's?} We answer this question affirmatively in this work, where we demonstrate that by adequately designing a signaling device that reveals partial information regarding the leader's realized action to the follower, the leader can achieve a higher expected utility than that without signaling. Moreover, unlike previous works on the Bayesian Stackelberg game where mathematical programming tools are utilized, we interpret the leader's commitment as a probability measure over the belief space. Such a probabilistic language greatly simplifies the analysis and allows an indirect signaling scheme, leading to a geometric characterization of the equilibrium under the proposed game model.

翻译：博弈中的信息不对称使得拥有信息优势的参与者能够通过策略性信息揭示来操控其他参与者的信念。本文研究贝叶斯斯塔克尔伯格博弈中的双重信息不对称情形：领导者从混合策略承诺中抽样的实际行动对追随者隐藏，而追随者则掌握关于其收益的私有信息。在双方均存在不对称信息的情况下，一个重要问题随之产生：\emph{领导者的信息优势是否胜过追随者？} 本文给出肯定回答，证明通过适当设计向追随者部分揭示领导者实际行动信息的信号装置，领导者能够获得比无信号时更高的期望效用。此外，不同于以往利用数学规划工具分析贝叶斯斯塔克尔伯格博弈的研究，我们将领导者的承诺解释为信念空间上的概率测度。这种概率化语言极大简化了分析过程，并使得间接信号方案成为可能，最终给出了所提博弈模型下均衡的几何刻画。