Self-optimizing behaviors can lead to outcomes where collective benefits are ultimately destroyed, a well-known phenomenon known as the ``tragedy of the commons". These scenarios are widely studied using game-theoretic approaches to analyze strategic agent decision-making. In this paper, we examine this phenomenon in a bi-level decision-making hierarchy, where low-level agents belong to multiple distinct populations, and high-level agents make decisions that impact the choices of the local populations they represent. We study strategic interactions in a context where the populations benefit from a common environmental resource that degrades with higher extractive efforts made by high-level agents. We characterize a unique symmetric Nash equilibrium in the high-level game, and investigate its consequences on the common resource. While the equilibrium resource level degrades as the number of populations grows large, there are instances where it does not become depleted. We identify such regions, as well as the regions where the resource does deplete.

翻译：自优化行为可能导致集体利益最终被破坏的结果，这一众所周知的现象被称为“公地悲剧”。这类场景通常采用博弈论方法来分析智能体的战略决策。本文在一个双层决策层级中研究这一现象，其中底层智能体属于多个不同的群体，而高层智能体做出的决策会影响其所代表的本地群体的选择。我们研究的战略互动情境是：各群体从共享的环境资源中获益，而该资源会随着高层智能体提高开采力度而退化。我们刻画了高层博弈中一个独特的对称纳什均衡，并研究了其对公共资源的影响。虽然均衡资源水平会随着群体数量增加而退化，但在某些情况下资源并不会枯竭。我们识别了这类区域，以及资源确实会枯竭的区域。