Game Theory Meets Large Language Models: A Systematic Survey

2025-02-13

AI Summary

The intersection of game theory and large language models (LLMs) remains underexplored, with unresolved tensions between classical equilibrium concepts and LLMs’ emergent strategic reasoning capabilities. Method: We propose a novel “modeling–evaluation–impact” interdisciplinary framework, integrating game-theoretic modeling, equilibrium analysis, and multi-agent simulation to design gamified benchmarks, enhance LLMs’ strategic reasoning, and analyze their societal implications; concurrently, we examine how LLMs’ advanced linguistic understanding challenges foundational notions such as Nash equilibrium. Contribution/Results: We introduce the first scalable, gamified evaluation suite for LLMs, deliver the field’s inaugural systematic survey, distill six core open challenges, and outline concrete research pathways. This work catalyzes a paradigm shift in game theory–AI integration, advancing both rigorous LLM assessment and theoretical extensions of equilibrium concepts.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Machine Learning: Large Multimodal Models (LMMs)
• Natural Language Processing: (Large) Language Models

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

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.

Problem

• Intersection of game theory and LLMs
• Standardized benchmarks for LLM evaluation
• Societal impacts through game modeling

Innovation

• Game theory benchmarks for LLMs
• Algorithmic enhancements via game theory
• Societal impact modeling using games