Bosses, Kings, and the Commons: Cooperation Under Power Asymmetry in LLM Societies

Communities can sustainably manage shared resources (e.g., fisheries, forests, and water systems) through locally governed institutions with clearly defined resource and user boundaries, a central finding of Ostrom's theory of self-governance. However, these systems are typically studied under symmetric appropriators (users with comparable rights, access, and influence over the shared resource), whereas real-world settings often involve asymmetric power, where a subset of individuals or institutions exercises disproportionate control over resource extraction and governance outcomes. Large Language Models (LLMs) are increasingly proposed as agents for studying such collective decision-making and resource allocation problems in synthetic governance environments, yet existing evaluations largely ignore power asymmetry, leaving the behavior of LLM societies under unequal power poorly understood. We introduce Sovereignty over the Commons Simulation (SovSim), a generative multi-agent simulation framework that incorporates an agent with asymmetric power (boss or king) into a society of agents with symmetric power (workers or peasants), where all agents extract from a shared resource (commons), collectively determining its sustainability over time. Across six state-of-the-art models, we find that introducing asymmetric power leads to severe breakdowns in cooperation and sustainability, with up to an 86.7% degradation in survival rate relative to symmetric settings.