Competition and Cooperation of LLM Agents in Games

2026-04-01

AI Summary

This study investigates whether large language model (LLM) agents converge to Nash equilibria and what strategic mechanisms govern their behavior in competitive multi-agent environments. By deploying LLM agents in two non-zero-sum games—network resource allocation and Cournot competition—and integrating multi-round interactions, chain-of-thought prompting, and game-theoretic modeling, the research finds that LLM agents consistently exhibit a propensity toward cooperation rather than Nash equilibrium play. The paper identifies fairness-based reasoning as the core mechanism driving this cooperative tendency and introduces an analytical framework that effectively captures the dynamics of LLMs’ inter-temporal strategic reasoning, thereby explaining their strategy evolution across repeated interactions.

Abstract

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.

Problem

• LLM agents
• competition
• cooperation
• Nash equilibrium
• multi-agent games

Innovation

• LLM agents
• cooperation
• fairness reasoning
• multi-round interaction
• non-zero-sum games