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:游戏中的信息不对称使信息优势的玩家能够通过战略性地向其他玩家披露信息来操纵他人的信仰。 这项工作认为巴伊西亚史达克尔贝格游戏中双向信息不对称, 从混合战略承诺中抽样的领袖的已实现行动被隐藏在追随者手中。 相反, 追随者掌握着有关其报酬的私人信息。 鉴于双方的不对称信息, 产生了一个重要问题 : \ emph{ Does the lead's info优势大于追随者? } 我们在这项工作中肯定地回答了这个问题, 我们通过适当设计一个信号装置, 向追随者展示关于领袖已实现行动的部分信息, 领导者可以实现比不信号的预期更大的效用。 此外, 与以前在巴伊西亚斯史达克尔伯格游戏中使用数学编程工具的作品不同, 我们将领导人的承诺解释为对信仰空间的概率衡量。 这样一种概率语言大大简化了分析并允许间接信号计划, 导致对拟议游戏模式下的平衡进行几何测量。</s>