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

Abstract

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.