论文标题
$ 2 \ times 2 $零和零游戏，带有承诺和嘈杂的观察
$2 \times 2$ Zero-Sum Games with Commitments and Noisy Observations
论文作者
论文摘要
在本文中，根据以下假设研究了$ 2 \ times2 $零和游戏的游戏：$（1）$一位玩家（领导者）致力于通过对给定概率度量采样（策略）来选择其动作； $（2）$领导者宣布了行动，其对手（追随者）通过二进制频道观察到了行动； $（3）$追随者根据领导者战略的知识和对领导者行动的嘈杂观察而选择其策略。在这些条件下，平衡始终存在。有趣的是，即使受到噪音的影响，观察领导者的作用也被证明对跟随者是有益的或无关紧要的。更具体地说，该游戏均衡的收益在纯粹的策略中受到Stackelberg平衡（SE）的回报。并在NASH平衡处的收益下降，这在混合策略中等同于SE。在本文中，出现了在平衡处的必要条件，以等于其等于其下限的收益。还出现了足够的条件，以平衡的收益等于其上限。
In this paper, $2\times2$ zero-sum games are studied under the following assumptions: $(1)$ One of the players (the leader) commits to choose its actions by sampling a given probability measure (strategy); $(2)$ The leader announces its action, which is observed by its opponent (the follower) through a binary channel; and $(3)$ the follower chooses its strategy based on the knowledge of the leader's strategy and the noisy observation of the leader's action. Under these conditions, the equilibrium is shown to always exist. Interestingly, even subject to noise, observing the actions of the leader is shown to be either beneficial or immaterial for the follower. More specifically, the payoff at the equilibrium of this game is upper bounded by the payoff at the Stackelberg equilibrium (SE) in pure strategies; and lower bounded by the payoff at the Nash equilibrium, which is equivalent to the SE in mixed strategies.Finally, necessary and sufficient conditions for observing the payoff at equilibrium to be equal to its lower bound are presented. Sufficient conditions for the payoff at equilibrium to be equal to its upper bound are also presented.
