We introduce and study coverage games - a novel framework for multi-agent planning in settings in which a system operates several agents but does not have full control on them, or interacts with an environment that consists of several agents. The game is played between a coverer, who has a set of objectives, and a disruptor. The coverer operates several agents that interact with the adversarial disruptor. The coverer wins if every objective is satisfied by at least one agent. Otherwise, the disruptor wins. Coverage games thus extend traditional two-player games with multiple objectives by allowing a (possibly dynamic) decomposition of the objectives among the different agents. They have many applications, both in settings where the system is the coverer (e.g., multi-robot surveillance, coverage in multi-threaded systems) and settings where it is the disruptor (e.g., prevention of resource exhaustion, ensuring non-congestion). We first study the theoretical properties of coverage games, including determinacy, and the ability to a priori decompose the objectives among the agents. We then study the problems of deciding whether the coverer or the disruptor wins. Besides a comprehensive analysis of the tight complexity of the problems, we consider interesting special cases, such as the one-player cases and settings with a fixed number of agents or objectives.

翻译：我们引入并研究了覆盖游戏——一种适用于多智能体规划的新颖框架，其场景为：系统操控多个智能体但无法完全控制它们，或与由多个智能体构成的环境进行交互。该游戏由覆盖者（Coverer，拥有若干目标）和破坏者（Disruptor）参与。覆盖者操控多个与对抗性破坏者交互的智能体。若每个目标至少被一个智能体满足，则覆盖者获胜；否则破坏者获胜。覆盖游戏通过允许在不同智能体之间（可能是动态地）分解目标，从而将传统双人多目标博弈进行了扩展。该框架具有广泛应用，既适用于系统作为覆盖者的场景（如多机器人监控、多线程系统中的覆盖），也适用于系统作为破坏者的场景（如防止资源耗尽、确保无拥塞）。我们首先研究了覆盖游戏的理论性质，包括确定性以及预先在智能体间分解目标的能力。随后研究了判定覆盖者或破坏者获胜的问题。除了对问题严格复杂度的全面分析外，我们还考虑了有趣的特殊情况，例如单人博弈以及固定智能体或目标数量的场景。