We study a wireless jamming problem consisting of the competition between a legitimate receiver and a jammer, as a zero-sum game with the value to maximize/minimize being 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 an exploding strategy space, we exploit reinforcement learning to obtain efficient strategies leading 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 setups.

翻译：我们研究了一个由合法接收机和干扰机之间的竞争构成的无线干扰问题，将其建模为零和博弈，其中最大化/最小化的值为接收机侧的信道容量。现有文献中的大多数方法假设两个参与者均为固定节点。相反，我们探究了当参与者能够改变位置时（具体而言是沿线性几何移动）所发生的情况。我们首先将其构建为一个可闭式求解的静态博弈，随后将其扩展为动态博弈，并针对对手位置信息的完整性/完美性（分别对应于移动的隐蔽性/顺序性假设）考虑三种不同版本。我们首先给出静态博弈的一些理论条件，这些条件也有助于识别适用于任何场景（包括动态博弈）的优良策略。由于动态博弈虽然更符合实际，但策略空间呈爆炸式增长，我们利用强化学习来获得能够导向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进行博弈，并在实际场景中验证了我们的方法。