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

Jen-tse Huang, Eric John Li+8 more|arXiv (Cornell University)|Mar 18, 2024

Franchising Strategies and Performance8 citations

TL;DR

The paper introduces γ-Bench, a multi-player, multi-round evaluation framework using eight classic game theory games to assess LLM decision-making, robustness, generalizability, and improvement strategies across several models.

ABSTRACT

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($γ$)-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. $γ$-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 at https://github.com/CUHK-ARISE/GAMABench.

Motivation & Objective

• Assess LLMs' decision-making using game theory in multi-agent environments.
• Quantify robustness, generalizability, and enhancement strategies for LLMs in multi-player games.
• Provide a publicly available benchmark and analysis across models (GPT-3.5, GPT-4, Gemini Pro).

Proposed method

• Define a γ-Bench framework with eight classical multi-agent games categorized as cooperative, betraying, and sequential.
• Implement a scoring scheme to quantify performance in each game (per-game and aggregate scores).
• Evaluate LLMs and humans in multi-agent, multi-round settings, including robustness checks (restarts, temperature, prompts).
• Investigate effects of Chain-of-Thought prompts and instructional prompts on decision-making performance.
• Compare multiple LLMs (GPT-3.5 variants, GPT-4, Gemini Pro) and report leaderboard-style results.

Experimental results

Research questions

• RQ1 How do LLMs perform in cooperative, betraying, and sequential multi-agent games relative to Nash equilibria and social welfare?
• RQ2 What is the robustness of LLM decisions across runs, temperatures, and prompt templates?
• RQ3 Can reasoning enhancements (e.g., Chain-of-Thought) or incentives improve LLM decision-making in these game settings?
• RQ4 How well do LLMs generalize across different game settings and rounds, and how do different models rank on γ-Bench?

Key findings

• GPT-4 generally outperforms other models on γ-Bench with a leaderboard score of 72.5.
• GPT-3.5 (0613, 1106, 0125) shows improved intelligence across iterations, but generalizability remains limited.
• Cooperative games show potential for spontaneous cooperation in LLMs without explicit communication.
• Performance varies by game type; robustness is high for most games but lower in certain sequential games.
• Chain-of-Thought prompts can enhance performance in some tasks, notably in Guess 2/3 of the Average.