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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. 

Abstract The EngageAI Institute focuses on AI‐driven narrative‐centered learning environments that create engaging story‐based problem‐solving experiences to support collaborative learning. The institute's research has three complementary strands. First, the institute creates narrative‐centered learning environments that generate interactive story‐based problem scenarios to elicit rich communication, encourage coordination, and spark collaborative creativity. Second, the institute creates virtual embodied conversational agent technologies with multiple modalities for communication (speech, facial expression, gesture, gaze, and posture) to support student learning. Embodied conversational agents are driven by advances in natural language understanding, natural language generation, and computer vision. Third, the institute is creating an innovative multimodal learning analytics framework that analyzes parallel streams of multimodal data derived from students’ conversations, gaze, facial expressions, gesture, and posture as they interact with each other, with teachers, and with embodied conversational agents. Woven throughout the institute's activities is a strong focus on ethics, with an emphasis on creating AI‐augmented learning that is deeply informed by considerations of fairness, accountability, transparency, trust, and privacy. The institute emphasizes broad participation and diverse perspectives to ensure that advances in AI‐augmented learning address inequities in STEM. The institute brings together a multistate network of universities, diverse K‐12 school systems, science museums, and nonprofit partners. Key to all of these endeavors is an emphasis on diversity, equity, and inclusion.