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泄露来操控其他参与者的信念。本研究考虑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采样得到的实际行动对追随者隐藏，而追随者则持有其自身收益的私有信息。在双方信息不对称的背景下，一个关键问题随之产生：**领导者的信息优势能否胜过追随者？** 我们对此问题给出肯定回答，证明通过合理设计向追随者部分披露领导者实际行动的信号装置，领导者可获得比无信号情形更高的期望效用。此外，与以往利用数学规划工具研究贝叶斯斯塔克尔伯格博弈的工作不同，本文将领导者的承诺解释为信念空间上的概率测度。这种概率论语言大幅简化了分析过程，并通过引入间接信号机制，为所提博弈模型下的均衡提供了几何刻画。