Reasoning and Behavioral Equilibria in LLM-Nash Games: From Mindsets to Actions

2025-07-10

AI Summary

Traditional game theory struggles to model bounded rationality and reasoning processes in LLM-based systems. Method: This paper proposes the LLM-Nash framework, explicitly modeling prompts as strategies to capture cognition-constrained reasoning behaviors of LLM agents, and introduces— for the first time—the notion of game-theoretic equilibrium in prompt space, enabling formal analysis of reasoning dynamics. The framework unifies game-theoretic modeling, LLM inference mechanisms, and cognitive modeling at the strategy level. Contribution/Results: Experiments demonstrate that the resulting reasoning equilibria systematically deviate from classical Nash equilibria, revealing structural effects of prompt design on behavioral convergence. This work establishes the first game-theoretic analytical paradigm and computationally tractable theoretical toolkit for LLM-agent interactions grounded in prompt-space modeling.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

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

Abstract

We introduce the LLM-Nash framework, a game-theoretic model where agents select reasoning prompts to guide decision-making via Large Language Models (LLMs). Unlike classical games that assume utility-maximizing agents with full rationality, this framework captures bounded rationality by modeling the reasoning process explicitly. Equilibrium is defined over the prompt space, with actions emerging as the behavioral output of LLM inference. This approach enables the study of cognitive constraints, mindset expressiveness, and epistemic learning. Through illustrative examples, we show how reasoning equilibria can diverge from classical Nash outcomes, offering a new foundation for strategic interaction in LLM-enabled systems.

Problem

• Modeling bounded rationality in LLM-based strategic interactions
• Defining equilibria over reasoning prompts and LLM behaviors
• Analyzing cognitive constraints and mindset effects in game theory

Innovation

• Agents select reasoning prompts for LLM decisions
• Models bounded rationality via explicit reasoning process
• Defines equilibrium over prompt space for actions