How Far Are We on the Decision-Making of LLMs? Evaluating LLMs' Gaming Ability in Multi-Agent Environments

Decision-making is a complex process requiring diverse abilities, making it an excellent framework for evaluating Large Language Models (LLMs). Researchers have examined LLMs' decision-making through the lens of Game Theory. However, existing evaluation mainly focus on two-player scenarios where an LLM competes against another. Additionally, previous benchmarks suffer from test set leakage due to their static design. We introduce GAMA($\gamma$)-Bench, a new framework for evaluating LLMs' Gaming Ability in Multi-Agent environments. It includes eight classical game theory scenarios and a dynamic scoring scheme specially designed to quantitatively assess LLMs' performance. $\gamma$-Bench allows flexible game settings and adapts the scoring system to different game parameters, enabling comprehensive evaluation of robustness, generalizability, and strategies for improvement. Our results indicate that GPT-3.5 demonstrates strong robustness but limited generalizability, which can be enhanced using methods like Chain-of-Thought. We also evaluate 13 LLMs from 6 model families, including GPT-3.5, GPT-4, Gemini, LLaMA-3.1, Mixtral, and Qwen-2. Gemini-1.5-Pro outperforms others, scoring of $69.8$ out of $100$, followed by LLaMA-3.1-70B ($65.9$) and Mixtral-8x22B ($62.4$). Our code and experimental results are publicly available atthis https URL.

@article{huang2025_2403.11807,
  title={ How Far Are We on the Decision-Making of LLMs? Evaluating LLMs' Gaming Ability in Multi-Agent Environments },
  author={ Jen-tse Huang and Eric John Li and Man Ho Lam and Tian Liang and Wenxuan Wang and Youliang Yuan and Wenxiang Jiao and Xing Wang and Zhaopeng Tu and Michael R. Lyu },
  journal={arXiv preprint arXiv:2403.11807},
  year={ 2025 }
}