We study a wireless jamming problem consisting of the competition between a legitimate receiver and a jammer, as a zero-sum game where the value to maximize/minimize is the channel capacity at the receiver's side. Most of the approaches found in the literature consider the two players to be stationary nodes. Instead, we investigate what happens when they can change location, specifically moving along a linear geometry. We frame this at first as a static game, which can be solved in closed form, and subsequently we extend it to a dynamic game under three different versions for what concerns completeness/perfection of mutual information about the adversary's position, corresponding to different assumptions of concealment/sequentiality of the moves, respectively. We first provide some theoretical conditions that hold for the static game and also help identify good strategies valid under any setup, including dynamic games. Since dynamic games, although more realistic, are characterized by a significantly expanded strategy space, we exploit reinforcement learning to obtain efficient strategies that lead to equilibrium outcomes. We show how theoretical findings can be used to train smart agents to play the game and validate our approach in practical settings.

翻译：我们研究了一个由合法接收者与干扰者之间的竞争构成的无线干扰问题，将其建模为零和博弈，其中博弈值（需最大化/最小化）为接收端的信道容量。已有文献中的大多数方法均假设双方为固定节点。与此相反，我们探究了当双方可以改变位置（具体而言是沿线性几何路径移动）时的情形。我们首先将该问题框架化为一个可求解闭式解的静态博弈，随后将其扩展为动态博弈，并考虑了关于对手位置信息完备性/完美性的三种不同版本，分别对应移动隐蔽性/顺序性的不同假设。我们首先给出了静态博弈成立的一些理论条件，这些条件也有助于识别在任何场景（包括动态博弈）下均有效的优质策略。由于动态博弈虽更贴近现实，但其策略空间显著扩大，我们利用强化学习来获取可实现均衡结果的高效策略。我们展示了如何利用理论发现来训练智能体参与博弈，并在实际场景中验证了所提方法的有效性。