Large Language Models (LLMs) have significantly advanced natural language processing, demonstrating exceptional reasoning, tool usage, and memory capabilities. As their applications expand into multi-agent environments, there arises a need for a comprehensive evaluation framework that captures LLMs’ reasoning, planning, collaboration, and other social abilities. This work introduces a novel competition-based benchmark framework specifically designed to assess LLMs within multi-agent settings, providing quantitative metrics to evaluate their judgment, reasoning, deception, self-awareness, cooperation, coordination, and rationality.We utilize two social deduction games alongside three game-theory scenarios to create diverse environments.Our frame is fortified with the probabilistic graphic modeling (PGM) method, enhancing the LLMs’ capabilities in navigating complex social and cognitive dimensions. We evaluate seven LLMs, quantitatively highlighting a significant capability gap of over threefold between the strongest, GPT o1, and the weakest, Llama-2-70B. It also confirms that our PGM enhancement boosts the abilities of all selected models by an average of 37%. Our data and code can be found here https://github.com/cathyxl/MAgIC.