Large language model (LLM) agents are increasingly deployed in competitive multi-agent settings, raising fundamental questions about whether they converge to equilibria and how their strategic behavior can be characterized. In this paper, we study LLM agent interactions in two standard games: a network resource allocation game and a Cournot competition game. Rather than converging to Nash equilibria, we find that LLM agents tend to cooperate when given multi-round prompts and non-zero-sum context. Chain-of-thought analysis reveals that fairness reasoning is central to this behavior. We propose an analytical framework that captures the dynamics of LLM agent reasoning across rounds and explains these experimental findings.

翻译：大语言模型智能体越来越多地被部署在竞争性多智能体环境中，这引发了关于它们是否会收敛到均衡状态以及其策略行为如何被表征的基本问题。本文研究了两种标准博弈中LLM智能体的交互：一种网络资源分配博弈和一种古诺竞争博弈。我们发现，当给予多轮提示和非零和背景时，LLM智能体并未收敛到纳什均衡，而是倾向于合作。思维链分析表明，公平性推理是这一行为的核心。我们提出了一个分析框架，该框架捕捉了LLM智能体在多轮推理中的动态过程，并对这些实验发现进行了解释。