# Competition and Cooperation of LLM Agents in Games

arXiv: https://arxiv.org/abs/2604.00487 · HTML: https://mlsanity.com/paper/2604.00487/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 1 Apr 2026.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 13 of 13)

- [Understanding the planning of LLM agents: A survey](https://mlsanity.com/paper/2402.02716/) (2024)
- [SMART-LLM: Smart Multi-Agent Robot Task Planning using Large Language Models](https://mlsanity.com/paper/2309.10062/) (2023)
- [Algorithmic Collusion by Large Language Models](https://mlsanity.com/paper/2404.00806/) (2024)
- [Game-theoretic LLM: Agent Workflow for Negotiation Games](https://mlsanity.com/paper/2411.05990/) (2024)
- [Enhancing LLMs for Power System Simulations: A Feedback-driven Multi-agent Framework](https://mlsanity.com/paper/2411.16707/) (2024)
- [Grid-Agent: An LLM-Powered Multi-Agent System for Power Grid Control](https://mlsanity.com/paper/2508.05702/) (2025)
- [FAIRGAME: a Framework for AI Agents Bias Recognition using Game Theory](https://mlsanity.com/paper/2504.14325/) (2025)
- [The Effect of State Representation on LLM Agent Behavior in Dynamic Routing Games](https://mlsanity.com/paper/2506.15624/) (2025)
- [Multi-Agent Reinforcement Learning in Cournot Games](https://mlsanity.com/paper/2009.06224/) (2020)
- [Behavioral Generative Agents for Energy Operations](https://mlsanity.com/paper/2506.12664/) (2025)
- [Competition and Coalition Formation of Renewable Power Producers](https://mlsanity.com/paper/1502.00679/) (2015)
- [Behavioral Generative Agents for Power Dispatch and Auction](https://mlsanity.com/paper/2603.08477/) (2026)
- [Reasonably reasoning AI agents can avoid game-theoretic failures in zero-shot, provably](https://mlsanity.com/paper/2603.18563/) (2026)

## Built on by (most cited first, 3 of 3)

- [Humans Are More Diverse: Frontier LLMs Show Extreme Policies in Idealised AI Development Races](https://mlsanity.com/paper/2608.01193/) (2026)
- [RestoreBench: Can AI Agents Restore Power Flow Convergence?](https://mlsanity.com/paper/2609.00384/) (2026)
- [Correct Answers, Invalid Traces: What Verifiable Grade-School Math Reveals About Chain-of-Thought Traces](https://mlsanity.com/paper/2609.38107/) (2026)

## Abstract (arXiv)

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.