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.

翻译：大语言模型（LLM）智能体越来越多地被部署在需要策略协调的多智能体系统中。尽管近期研究分析了双人博弈中的LLM行为，但涉及$n$个智能体动态形成合作团体的联盟形成问题在理论上仍未被刻画。我们提出了首个基于享乐博弈论、具有形式化稳定性保证的LLM智能体网络联盟形成框架。我们引入了LLM联盟形成博弈（LCFG），建立了纳什稳定分区的充分条件，并证明了复杂性结果。分析表明，LLM智能体表现出以$\epsilon$-理性偏好为特征的有界理性；我们提供了确定性存在保证和一致性驱动的稳定性界，其预测与实证结果一致。在GPT-4、Claude-3和Llama-3上跨越2400轮实验的验证支持了我们的框架：在我们的"思维联盟"（CoalT）协议下，73.2%的LLM联盟达到纳什稳定性，而思维链协议下为58.4%，标准提示下为41.8%（$p < 0.001$）。我们的框架为设计稳定的多智能体LLM系统提供了理论基础。