Coalition Formation in LLM Agent Networks: Stability Analysis and Convergence Guarantees
For researchers and engineers building multi-agent LLM systems, this provides theoretical foundations and practical protocols for achieving stable cooperative groups.
This paper introduces the first theoretical framework for coalition formation in LLM agent networks, grounded in hedonic game theory. It proves stability guarantees and shows that a proposed Coalition-of-Thought protocol achieves 73.2% Nash stability, significantly outperforming baselines.
Large Language Model (LLM) agents are increasingly deployed in multi-agent systems requiring strategic coordination. While recent work has analyzed LLM behavior in two-player games, coalition formation, where $n$ agents dynamically form cooperative groups, remains theoretically uncharacterized. We present the first framework grounding coalition formation in LLM agent networks in hedonic game theory with formal stability guarantees. We introduce the LLM Coalition Formation Game (LCFG), establish sufficient conditions for Nash-stable partitions, and prove complexity results. Our analysis reveals that LLM agents exhibit bounded rationality characterized by $ε$-rational preferences; we provide both deterministic existence guarantees and consistency-driven stability bounds whose predictions are consistent with empirical outcomes. Experiments with GPT-4, Claude-3, and Llama-3 across 2,400 episodes validate our framework: LLM coalitions achieve Nash stability in 73.2% of cases under our Coalition-of-Thought (CoalT) protocol, compared to 58.4% under chain-of-thought and 41.8% under standard prompting ($p < 0.001$). Our framework provides theoretical foundations for designing stable multi-agent LLM systems.