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

arXiv: https://arxiv.org/abs/2403.11807 · HTML: https://mlsanity.com/paper/2403.11807/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for LLM agents, one of 16 directions in LLM agents and tool use.
- Builds on 36 of its 86 references that are in the map.
- First posted on arXiv 18 Mar 2024.

## Placed in

- LLM agents and tool use / [Reinforcement learning for LLM agents](https://mlsanity.com/agents/reinforcement-learning-for-llm-agents/)

## Builds on (most cited first, 30 of 36)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Mixtral of Experts](https://mlsanity.com/paper/2401.04088/) (2024)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies](https://mlsanity.com/paper/2208.10264/) (2022)
- [Is ChatGPT a General-Purpose Natural Language Processing Task Solver?](https://mlsanity.com/paper/2302.06476/) (2023)
- [GPT-4 Is Too Smart To Be Safe: Stealthy Chat with LLMs via Cipher](https://mlsanity.com/paper/2308.06463/) (2023)
- [LegalBench: A Collaboratively Built Benchmark for Measuring Legal Reasoning in Large Language Models](https://mlsanity.com/paper/2308.11462/) (2023)
- [Large Language Models for Information Retrieval: A Survey](https://mlsanity.com/paper/2308.07107/) (2023)
- [Exploring Large Language Models for Communication Games: An Empirical Study on Werewolf](https://mlsanity.com/paper/2309.04658/) (2023)
- [Better Zero-Shot Reasoning with Role-Play Prompting](https://mlsanity.com/paper/2308.07702/) (2023)
- [Evaluating Large Language Models in Theory of Mind Tasks](https://mlsanity.com/paper/2302.02083/) (2023)
- [Playing repeated games with Large Language Models](https://mlsanity.com/paper/2305.16867/) (2023)
- [Is ChatGPT A Good Translator? Yes With GPT-4 As The Engine](https://mlsanity.com/paper/2301.08745/) (2023)
- [Language Agents with Reinforcement Learning for Strategic Play in the Werewolf Game](https://mlsanity.com/paper/2310.18940/) (2023)
- [SmartPlay: A Benchmark for LLMs as Intelligent Agents](https://mlsanity.com/paper/2310.01557/) (2023)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [Avalon's Game of Thoughts: Battle Against Deception through Recursive Contemplation](https://mlsanity.com/paper/2310.01320/) (2023)
- [Cooperation, Competition, and Maliciousness: LLM-Stakeholders Interactive Negotiation](https://mlsanity.com/paper/2309.17234/) (2023)
- [Can Large Language Models Serve as Rational Players in Game Theory? A Systematic Analysis](https://mlsanity.com/paper/2312.05488/) (2023)
- [Put Your Money Where Your Mouth Is: Evaluating Strategic Planning and Execution of LLM Agents in an Auction Arena](https://mlsanity.com/paper/2310.05746/) (2023)
- [ChatGPT or Grammarly? Evaluating ChatGPT on Grammatical Error Correction Benchmark](https://mlsanity.com/paper/2303.13648/) (2023)
- [Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4](https://mlsanity.com/paper/2309.17277/) (2023)
- [Can Large Language Model Agents Simulate Human Trust Behavior?](https://mlsanity.com/paper/2402.04559/) (2024)
- [LLM-Based Agent Society Investigation: Collaboration and Confrontation in Avalon Gameplay](https://mlsanity.com/paper/2310.14985/) (2023)
- [MAgIC: Investigation of Large Language Model Powered Multi-Agent in Cognition, Adaptability, Rationality and Collaboration](https://mlsanity.com/paper/2311.08562/) (2023)
- [Hoodwinked: Deception and Cooperation in a Text-Based Game for Language Models](https://mlsanity.com/paper/2308.01404/) (2023)
- [GameEval: Evaluating LLMs on Conversational Games](https://mlsanity.com/paper/2308.10032/) (2023)

## Built on by (most cited first, 30 of 67)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [OASIS: Open Agent Social Interaction Simulations with One Million Agents](https://mlsanity.com/paper/2411.11581/) (2024)
- [Agentic Large Language Models, a survey](https://mlsanity.com/paper/2503.23037/) (2025)
- [LLM as a Mastermind: A Survey of Strategic Reasoning with Large Language Models](https://mlsanity.com/paper/2404.01230/) (2024)
- [Embodied LLM Agents Learn to Cooperate in Organized Teams](https://mlsanity.com/paper/2403.12482/) (2024)
- [LLM-based Multi-Agent Reinforcement Learning: Current and Future Directions](https://mlsanity.com/paper/2405.11106/) (2024)
- [Unlocking the Capabilities of Thought: A Reasoning Boundary Framework to Quantify and Optimize Chain-of-Thought](https://mlsanity.com/paper/2410.05695/) (2024)
- [Game-theoretic LLM: Agent Workflow for Negotiation Games](https://mlsanity.com/paper/2411.05990/) (2024)
- [PathFinder: A Multi-Modal Multi-Agent System for Medical Diagnostic Decision-Making Applied to Histopathology](https://mlsanity.com/paper/2502.08916/) (2025)
- [Orak: A Foundational Benchmark for Training and Evaluating LLM Agents on Diverse Video Games](https://mlsanity.com/paper/2506.03610/) (2025)
- [TMGBench: A Systematic Game Benchmark for Evaluating Strategic Reasoning Abilities of LLMs](https://mlsanity.com/paper/2410.10479/) (2024)
- [SPIN-Bench: How Well Do LLMs Plan Strategically and Reason Socially?](https://mlsanity.com/paper/2503.12349/) (2025)
- [A Survey on Large Language Model-Based Social Agents in Game-Theoretic Scenarios](https://mlsanity.com/paper/2412.03920/) (2024)
- [DSGBench: A Diverse Strategic Game Benchmark for Evaluating LLM-based Agents in Complex Decision-Making Environments](https://mlsanity.com/paper/2503.06047/) (2025)
- [STRIDE: A Tool-Assisted LLM Agent Framework for Strategic and Interactive Decision-Making](https://mlsanity.com/paper/2405.16376/) (2024)
- [SelfGoal: Your Language Agents Already Know How to Achieve High-level Goals](https://mlsanity.com/paper/2406.04784/) (2024)
- [GLEE: A Unified Framework and Benchmark for Language-based Economic Environments](https://mlsanity.com/paper/2410.05254/) (2024)
- [How Well Can LLMs Echo Us? Evaluating AI Chatbots' Role-Play Ability with ECHO](https://mlsanity.com/paper/2404.13957/) (2024)
- [Toward LLM-Agent-Based Modeling of Transportation Systems: A Conceptual Framework](https://mlsanity.com/paper/2412.06681/) (2024)
- [Are Large Vision Language Models Good Game Players?](https://mlsanity.com/paper/2503.02358/) (2025)
- [GAMEBoT: Transparent Assessment of LLM Reasoning in Games](https://mlsanity.com/paper/2412.13602/) (2024)
- [LLM Strategic Reasoning: Agentic Study through Behavioral Game Theory](https://mlsanity.com/paper/2502.20432/) (2025)
- [Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontiers](https://mlsanity.com/paper/2502.09053/) (2025)
- [MobileSteward: Integrating Multiple App-Oriented Agents with Self-Evolution to Automate Cross-App Instructions](https://mlsanity.com/paper/2502.16796/) (2025)
- [Self-Resource Allocation in Multi-Agent LLM Systems](https://mlsanity.com/paper/2504.02051/) (2025)
- [A Survey on Human-Centric LLMs](https://mlsanity.com/paper/2411.14491/) (2024)
- [Shapley-Coop: Credit Assignment for Emergent Cooperation in Self-Interested LLM Agents](https://mlsanity.com/paper/2506.07388/) (2025)
- [EconEvals: Benchmarks and Litmus Tests for Economic Decision-Making by LLM Agents](https://mlsanity.com/paper/2503.18825/) (2025)
- [Towards Strategic Persuasion with Language Models](https://mlsanity.com/paper/2509.22989/) (2025)

## Abstract (arXiv)

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.