Coalition Formation in LLM Agent Networks: Stability Analysis and Convergence Guarantees

2026-04-15

AI Summary

This study addresses the lack of theoretical foundations for stable coalition formation among large language model (LLM) agents in multi-agent systems. Drawing on collusion game theory, the authors propose the LLM Coalition Formation Game (LCFG) framework, which incorporates ε-bounded rationality to formally characterize the existence and convergence conditions of Nash-stable partitions. They further introduce a consensus-driven stability bound and design the Coalition-of-Thought (CoalT) prompting protocol to enhance coalition stability. Extensive experiments across GPT-4, Claude-3, and Llama-3—comprising 2,400 total rounds—demonstrate that CoalT achieves Nash-stable coalitions in 73.2% of cases, significantly outperforming Chain-of-Thought (58.4%) and standard prompting (41.8%) at p < 0.001.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Large Multimodal Models (LMMs)
• Game Theory and Economic Paradigms: Cooperative Game Theory

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

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.

Problem

• Coalition Formation
• LLM Agents
• Stability
• Multi-agent Systems
• Hedonic Games

Innovation

• coalition formation
• hedonic games
• Nash stability
• bounded rationality
• Coalition-of-Thought