This paper studies an instance of zero-sum games in which one player (the leader) commits to its opponent (the follower) to choose its actions by sampling a given probability measure (strategy). The actions of the leader are observed by the follower as the output of an arbitrary channel. In response to that, the follower chooses its action based on its current information, that is, the leader's commitment and the corresponding noisy observation of its action. Within this context, the equilibrium of the game with noisy action observability is shown to always exist and the necessary conditions for its uniqueness are identified. Interestingly, the noisy observations have important impact on the cardinality of the follower's set of best responses. Under particular conditions, such a set of best responses is proved to be a singleton almost surely. The proposed model captures any channel noise with a density with respect to the Lebesgue measure. As an example, the case in which the channel is described by a Gaussian probability measure is investigated.

翻译：本文研究一类零和博弈，其中一方（领导者）通过对给定概率测度（策略）进行抽样来承诺其对手（追随者）选择其行动。领导者的行动被追随者观测为任意信道的输出。作为响应，追随者基于其当前信息（即领导者的承诺及相应的含噪观测）选择其行动。在此背景下，本文证明具有含噪行动可观测性的博弈均衡始终存在，并确定了其唯一性的必要条件。有趣的是，含噪观测对追随者最佳响应集合的基数有重要影响。在特定条件下，该最佳响应集合几乎必然为单元素集。所提模型可刻画任意相对于勒贝格测度具有密度的信道噪声。作为示例，研究了信道由高斯概率测度描述的情形。