首次为大模型代理联盟提供稳定性理论保障，让协作更可靠。
Coalition Formation in LLM Agent Networks: Stability Analysis and Convergence Guarantees
- 用博弈论建模大模型动态组队，定义联盟稳定性的数学条件。
- 实验显示新协议下73.2%的联盟达稳定状态，显著优于传统方法。
- 适合研究多智能体系统、大模型协作与博弈理论的开发者参考。
大型语言模型（LLM）代理在需要战略协调的多智能体系统中日益普及。尽管已有研究分析了双智能体博弈中的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仍缺乏理论刻画。本文首次将联盟形成建立在基于偏好型博弈理论的框架上，并给出形式化的稳定性保证。提出LLM联盟形成游戏（LCFG），确立纳什稳定划分的充分条件，并证明复杂度结果。分析发现LLM代理表现出由ε-理性偏好刻画的有限理性；我们既提供确定性存在性保证，也给出基于一致性的稳定性边界，其预测与实证结果一致。在GPT-4、Claude-3和Llama-3上进行的2,400轮实验验证了该框架：采用我们提出的思维联盟（CoalT）协议时，73.2%的联盟达到纳什稳定，显著高于链式思维（58.4%）和标准提示（41.8%）（p < 0.001）。本框架为设计稳定多智能体LLM系统提供了理论基础。
原文摘要 · Abstract (English)
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.
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