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

TL;DR

This paper introduces the LLM-Nash framework, a game-theoretic model where agents use reasoning prompts with large language models to reach behavioral equilibria, capturing bounded rationality and cognitive constraints in strategic interactions.

Contribution

The paper presents a novel game-theoretic framework modeling reasoning prompts as strategic choices, extending classical Nash concepts to LLM-based decision-making with explicit reasoning processes.

Findings

Reasoning equilibria can differ from classical Nash outcomes

Framework captures bounded rationality and cognitive constraints

Enables analysis of epistemic learning in LLM interactions

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.