# GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations

arXiv: https://arxiv.org/abs/2402.12348 · HTML: https://mlsanity.com/paper/2402.12348/

## Key facts

- Cited by 120 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 41 of its 64 references that are in the map.
- First posted on arXiv 19 Feb 2024.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 30 of 41)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [CAMEL: Communicative Agents for "Mind" Exploration of Large Language Model Society](https://mlsanity.com/paper/2303.17760/) (2023)
- [WebShop: Towards Scalable Real-World Web Interaction with Grounded Language Agents](https://mlsanity.com/paper/2207.01206/) (2022)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate](https://mlsanity.com/paper/2305.19118/) (2023)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [DeepSeek LLM: Scaling Open-Source Language Models with Longtermism](https://mlsanity.com/paper/2401.02954/) (2024)
- [MineDojo: Building Open-Ended Embodied Agents with Internet-Scale Knowledge](https://mlsanity.com/paper/2206.08853/) (2022)
- [A Survey on Large Language Model (LLM) Security and Privacy: The Good, the Bad, and the Ugly](https://mlsanity.com/paper/2312.02003/) (2023)
- [ScienceWorld: Is your Agent Smarter than a 5th Grader?](https://mlsanity.com/paper/2203.07540/) (2022)
- [TextWorld: A Learning Environment for Text-based Games](https://mlsanity.com/paper/1806.11532/) (2018)
- [ReConcile: Round-Table Conference Improves Reasoning via Consensus among Diverse LLMs](https://mlsanity.com/paper/2309.13007/) (2023)
- [MINT: Evaluating LLMs in Multi-turn Interaction with Tools and Language Feedback](https://mlsanity.com/paper/2309.10691/) (2023)
- [Is Reinforcement Learning (Not) for Natural Language Processing: Benchmarks, Baselines, and Building Blocks for Natural Language Policy Optimization](https://mlsanity.com/paper/2210.01241/) (2022)
- [Exploring Large Language Models for Communication Games: An Empirical Study on Werewolf](https://mlsanity.com/paper/2309.04658/) (2023)
- [Playing repeated games with Large Language Models](https://mlsanity.com/paper/2305.16867/) (2023)
- [OpenSpiel: A Framework for Reinforcement Learning in Games](https://mlsanity.com/paper/1908.09453/) (2019)
- [Do the Rewards Justify the Means? Measuring Trade-Offs Between Rewards and Ethical Behavior in the MACHIAVELLI Benchmark](https://mlsanity.com/paper/2304.03279/) (2023)
- [Interactive Fiction Games: A Colossal Adventure](https://mlsanity.com/paper/1909.05398/) (2019)

## Built on by (most cited first, 30 of 120)

- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [Cooperate or Collapse: Emergence of Sustainable Cooperation in a Society of LLM Agents](https://mlsanity.com/paper/2404.16698/) (2024)
- [Emergent social conventions and collective bias in LLM populations](https://mlsanity.com/paper/2410.08948/) (2024)
- [Agentic Large Language Models, a survey](https://mlsanity.com/paper/2503.23037/) (2025)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [LLM as a Mastermind: A Survey of Strategic Reasoning with Large Language Models](https://mlsanity.com/paper/2404.01230/) (2024)
- [GameBench: Evaluating Strategic Reasoning Abilities of LLM Agents](https://mlsanity.com/paper/2406.06613/) (2024)
- [AutoHarness: improving LLM agents by automatically synthesizing a code harness](https://mlsanity.com/paper/2603.03329/) (2026)
- [How Far Are We on the Decision-Making of LLMs? Evaluating LLMs' Gaming Ability in Multi-Agent Environments](https://mlsanity.com/paper/2403.11807/) (2024)
- [ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees](https://mlsanity.com/paper/2407.00499/) (2024)
- [Nicer Than Humans: How do Large Language Models Behave in the Prisoner's Dilemma?](https://mlsanity.com/paper/2406.13605/) (2024)
- [Game-theoretic LLM: Agent Workflow for Negotiation Games](https://mlsanity.com/paper/2411.05990/) (2024)
- [A Survey of Uncertainty Estimation in LLMs: Theory Meets Practice](https://mlsanity.com/paper/2410.15326/) (2024)
- [UProp: Investigating the Uncertainty Propagation of LLMs in Multi-Step Agentic Decision-Making](https://mlsanity.com/paper/2506.17419/) (2025)
- [Moral Alignment for LLM Agents](https://mlsanity.com/paper/2410.01639/) (2024)
- [Parameters vs. Context: Fine-Grained Control of Knowledge Reliance in Language Models](https://mlsanity.com/paper/2503.15888/) (2025)
- [G1: Bootstrapping Perception and Reasoning Abilities of Vision-Language Model via Reinforcement Learning](https://mlsanity.com/paper/2505.13426/) (2025)
- [TextArena](https://mlsanity.com/paper/2504.11442/) (2025)
- [Estimating LLM Uncertainty with Evidence](https://mlsanity.com/paper/2502.00290/) (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)
- [CoT-UQ: Improving Response-wise Uncertainty Quantification in LLMs with Chain-of-Thought](https://mlsanity.com/paper/2502.17214/) (2025)
- [DSGBench: A Diverse Strategic Game Benchmark for Evaluating LLM-based Agents in Complex Decision-Making Environments](https://mlsanity.com/paper/2503.06047/) (2025)
- [LLMs with Personalities in Multi-issue Negotiation Games](https://mlsanity.com/paper/2405.05248/) (2024)
- [Evaluating Large Language Models with Grid-Based Game Competitions: An Extensible LLM Benchmark and Leaderboard](https://mlsanity.com/paper/2407.07796/) (2024)
- [GLEE: A Unified Framework and Benchmark for Language-based Economic Environments](https://mlsanity.com/paper/2410.05254/) (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)
- [Self-Improvements in Modern Agentic Systems: A Survey](https://mlsanity.com/paper/2607.13104/) (2026)

## Abstract (arXiv)

As Large Language Models (LLMs) are integrated into critical real-world applications, their strategic and logical reasoning abilities are increasingly crucial. This paper evaluates LLMs' reasoning abilities in competitive environments through game-theoretic tasks, e.g., board and card games that require pure logic and strategic reasoning to compete with opponents. We first propose GTBench, a language-driven environment composing 10 widely recognized tasks, across a comprehensive game taxonomy: complete versus incomplete information, dynamic versus static, and probabilistic versus deterministic scenarios. Then, we (1) Characterize the game-theoretic reasoning of LLMs; and (2) Perform LLM-vs.-LLM competitions as reasoning evaluation. We observe that (1) LLMs have distinct behaviors regarding various gaming scenarios; for example, LLMs fail in complete and deterministic games yet they are competitive in probabilistic gaming scenarios; (2) Most open-source LLMs, e.g., CodeLlama-34b-Instruct and Llama-2-70b-chat, are less competitive than commercial LLMs, e.g., GPT-4, in complex games, yet the recently released Llama-3-70b-Instruct makes up for this shortcoming. In addition, code-pretraining greatly benefits strategic reasoning, while advanced reasoning methods such as Chain-of-Thought (CoT) and Tree-of-Thought (ToT) do not always help. We further characterize the game-theoretic properties of LLMs, such as equilibrium and Pareto Efficiency in repeated games. Detailed error profiles are provided for a better understanding of LLMs' behavior. We hope our research provides standardized protocols and serves as a foundation to spur further explorations in the strategic reasoning of LLMs.