The Tragedy of the Commons in Multi-Population Resource Games

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.