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：大语言模型代理正越来越多地被部署在竞争性的多代理环境中，这引发了关于它们是否收敛于均衡以及如何表征其策略行为的根本性问题。本文研究了LLM代理在两种标准博弈——网络资源分配博弈和古诺竞争博弈中的交互行为。我们发现，与收敛于纳什均衡不同，LLM代理在提供多轮提示和非零和情境时倾向于合作。思维链分析揭示，公平性推理是这一行为的核心。我们提出一个分析框架，该框架捕捉了LLM代理跨轮次推理的动态过程，并解释了这些实验结果。