Game Theory Meets Large Language Models: A Systematic Survey

Game theory establishes a fundamental framework for analyzing strategic interactions among rational decision-makers. The rapid advancement of large language models (LLMs) has sparked extensive research exploring the intersection of these two fields. Specifically, game-theoretic methods are being applied to evaluate and enhance LLM capabilities, while LLMs themselves are reshaping classic game models. This paper presents a comprehensive survey of the intersection of these fields, exploring a bidirectional relationship from three perspectives: (1) Establishing standardized game-based benchmarks for evaluating LLM behavior; (2) Leveraging game-theoretic methods to improve LLM performance through algorithmic innovations; (3) Characterizing the societal impacts of LLMs through game modeling. Among these three aspects, we also highlight how the equilibrium analysis for traditional game models is impacted by LLMs' advanced language understanding, which in turn extends the study of game theory. Finally, we identify key challenges and future research directions, assessing their feasibility based on the current state of the field. By bridging theoretical rigor with emerging AI capabilities, this survey aims to foster interdisciplinary collaboration and drive progress in this evolving research area.