# TMGBench: A Systematic Game Benchmark for Evaluating Strategic Reasoning Abilities of LLMs

arXiv: https://arxiv.org/abs/2410.10479 · HTML: https://mlsanity.com/paper/2410.10479/

## Key facts

- Cited by 24 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 32 of its 56 references that are in the map.
- First posted on arXiv 14 Oct 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 32)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Inner Monologue: Embodied Reasoning through Planning with Language Models](https://mlsanity.com/paper/2207.05608/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Using Large Language Models to Simulate Multiple Humans and Replicate Human Subject Studies](https://mlsanity.com/paper/2208.10264/) (2022)
- [Recent Advances in Natural Language Processing via Large Pre-Trained Language Models: A Survey](https://mlsanity.com/paper/2111.01243/) (2021)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [Large Language Models Fail on Trivial Alterations to Theory-of-Mind Tasks](https://mlsanity.com/paper/2302.08399/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Large Language Models as Commonsense Knowledge for Large-Scale Task Planning](https://mlsanity.com/paper/2305.14078/) (2023)
- [Playing repeated games with Large Language Models](https://mlsanity.com/paper/2305.16867/) (2023)
- [ART: Automatic multi-step reasoning and tool-use for large language models](https://mlsanity.com/paper/2303.09014/) (2023)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [LLM as a Mastermind: A Survey of Strategic Reasoning with Large Language Models](https://mlsanity.com/paper/2404.01230/) (2024)
- [Can Large Language Models Serve as Rational Players in Game Theory? A Systematic Analysis](https://mlsanity.com/paper/2312.05488/) (2023)
- [Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4](https://mlsanity.com/paper/2309.17277/) (2023)
- [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)
- [Strategic Reasoning with Language Models](https://mlsanity.com/paper/2305.19165/) (2023)
- [MAgIC: Investigation of Large Language Model Powered Multi-Agent in Cognition, Adaptability, Rationality and Collaboration](https://mlsanity.com/paper/2311.08562/) (2023)
- [Knowledge Mechanisms in Large Language Models: A Survey and Perspective](https://mlsanity.com/paper/2407.15017/) (2024)
- [Boosting Logical Reasoning in Large Language Models through a New Framework: The Graph of Thought](https://mlsanity.com/paper/2308.08614/) (2023)
- [InterIntent: Investigating Social Intelligence of LLMs via Intention Understanding in an Interactive Game Context](https://mlsanity.com/paper/2406.12203/) (2024)
- [Beyond Static Datasets: A Deep Interaction Approach to LLM Evaluation](https://mlsanity.com/paper/2309.04369/) (2023)
- [The Machine Psychology of Cooperation: Can GPT models operationalise prompts for altruism, cooperation, competitiveness and selfishness in economic games?](https://mlsanity.com/paper/2305.07970/) (2023)
- [Evaluating and Enhancing LLMs Agent based on Theory of Mind in Guandan: A Multi-Player Cooperative Game under Imperfect Information](https://mlsanity.com/paper/2408.02559/) (2024)
- [GLEE: A Unified Framework and Benchmark for Language-based Economic Environments](https://mlsanity.com/paper/2410.05254/) (2024)

## Built on by (most cited first, 24 of 24)

- [Agentic Large Language Models, a survey](https://mlsanity.com/paper/2503.23037/) (2025)
- [Game Theory Meets Large Language Models: A Systematic Survey with Taxonomy and New Frontiers](https://mlsanity.com/paper/2502.09053/) (2025)
- [The Effect of State Representation on LLM Agent Behavior in Dynamic Routing Games](https://mlsanity.com/paper/2506.15624/) (2025)
- [PLANET: A Collection of Benchmarks for Evaluating LLMs' Planning Capabilities](https://mlsanity.com/paper/2504.14773/) (2025)
- [Communication Enables Cooperation in LLM Agents: A Comparison with Curriculum-Based Approaches](https://mlsanity.com/paper/2510.05748/) (2025)
- [Towards properly implementing Theory of Mind in AI systems: An account of four misconceptions](https://mlsanity.com/paper/2503.16468/) (2025)
- [Agents Require Metacognitive and Strategic Reasoning to Succeed in the Coming Labor Markets](https://mlsanity.com/paper/2505.20120/) (2025)
- [Shall We Play a Game? Language Models for Open-ended Wargames](https://mlsanity.com/paper/2509.17192/) (2025)
- [Socially-Weighted Alignment: A Game-Theoretic Framework for Multi-Agent LLM Systems](https://mlsanity.com/paper/2602.14471/) (2026)
- [CivBench: Progress-Based Evaluation for LLMs' Strategic Decision-Making in Civilization V](https://mlsanity.com/paper/2604.07733/) (2026)
- [CHBench: A Cognitive Hierarchy Benchmark for Evaluating Strategic Reasoning Capability of LLMs](https://mlsanity.com/paper/2508.11944/) (2025)
- [Evaluating Counterfactual Strategic Reasoning in Large Language Models](https://mlsanity.com/paper/2603.19167/) (2026)
- [HCAG: Hierarchical Abstraction and Retrieval-Augmented Generation on Theoretical Repositories with LLMs](https://mlsanity.com/paper/2603.20299/) (2026)
- [WARBENCH: A Comprehensive Benchmark for Evaluating LLMs in Military Decision-Making](https://mlsanity.com/paper/2603.21280/) (2026)
- [Evaluating Large Language Models in a Complex Hidden Role Game](https://mlsanity.com/paper/2605.22826/) (2026)
- [AIDG: A Formal Decomposition of Information Extraction and Containment Asymmetries in Multi-Turn LLM Dialogue](https://mlsanity.com/paper/2602.17443/) (2026)
- [On Emotion-Sensitive Decision Making of Small Language Model Agents](https://mlsanity.com/paper/2604.06562/) (2026)
- [Explicit Trait Inference for Multi-Agent Coordination](https://mlsanity.com/paper/2604.19278/) (2026)
- [Equilibrium Residuals Expose Three Regimes of Matrix-Game Strategic Reasoning in Language Models](https://mlsanity.com/paper/2605.10410/) (2026)
- [Can Agents Deceive? Evaluating Reasoning and Deception in ParliamentBench using a Social Deduction Game](https://mlsanity.com/paper/2607.28146/) (2026)
- [AI Alignment through a Game-theoretic Lens: A Survey](https://mlsanity.com/paper/2608.27910/) (2026)
- [Benchmarking large language model agent societies against human behavioural distributions](https://mlsanity.com/paper/2608.28182/) (2026)
- [Do LLMs Understand Sequential Structure? A Controlled Study of Inference and Generation](https://mlsanity.com/paper/2610.04977/) (2026)
- [Choosing LLMs for Strategic Agent Interactions](https://mlsanity.com/paper/2610.18354/) (2026)

## Abstract (arXiv)

The rapid advancement of large language models has accelerated their application in reasoning, with strategic reasoning drawing increasing attention. To evaluate the strategic reasoning capabilities of LLMs, game theory, with its concise structure, has become the preferred approach for many researchers. However, current research typically focuses on a limited selection of games, resulting in low coverage of game types. Additionally, classic game scenarios carry risks of data leakage, and the benchmarks used often lack extensibility, rendering them inadequate for evaluating state-of-the-art models. To address these challenges, we propose TMGBench, characterized by comprehensive game type coverage, diverse scenarios and flexible game organization. Specifically, we incorporate all 144 game types summarized by the Robinson-Goforth topology of 2x2 games, constructed as classic games in our benchmark; we also synthetize diverse, higher-quality game scenarios for each classic game, which we refer to as story-based games. Lastly, to provide a sustainable evaluation framework adaptable to increasingly powerful LLMs, we treat the aforementioned games as atomic units and organize them into more complex forms through sequential, parallel, and nested structures. We conducted a comprehensive evaluation of mainstream LLMs, covering tests on rational reasoning, reasoning robustness, Theory-of-Mind capabilities, and reasoning in complex game forms. The results revealed LLMs still have flaws in the accuracy and consistency of strategic reasoning processes, and their levels of mastery over Theory-of-Mind also vary. Additionally, SOTA models like o3-mini, Qwen3 and deepseek-reasoner, were also evaluated across the sequential, parallel, and nested game structures while the results highlighted the challenges posed by TMGBench.