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

arXiv: https://arxiv.org/abs/2507.08208 · HTML: https://mlsanity.com/paper/2507.08208/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 4 of its 10 references that are in the map.
- First posted on arXiv 10 Jul 2025.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)

## Builds on (most cited first, 4 of 4)

- [Hypothetical Minds: Scaffolding Theory of Mind for Multi-Agent Tasks with Large Language Models](https://mlsanity.com/paper/2407.07086/) (2024)
- [Exploring Prosocial Irrationality for LLM Agents: A Social Cognition View](https://mlsanity.com/paper/2405.14744/) (2024)
- [On the Price of Transparency: A Comparison between Overt Persuasion and Covert Signaling](https://mlsanity.com/paper/2304.00096/) (2023)
- [Neurosymbolic Meta-Reinforcement Lookahead Learning Achieves Safe Self-Driving in Non-Stationary Environments](https://mlsanity.com/paper/2309.02328/) (2023)

## Built on by (most cited first, 6 of 6)

- [The Five Ws of Multi-Agent Communication: Who Talks to Whom, When, What, and Why -- A Survey from MARL to Emergent Language and LLMs](https://mlsanity.com/paper/2602.11583/) (2026)
- [Agentic AI for Cyber Resilience: A New Security Paradigm and Its System-Theoretic Foundations](https://mlsanity.com/paper/2512.22883/) (2025)
- [LLM-Stackelberg Games: Conjectural Reasoning Equilibria and Their Applications to Spearphishing](https://mlsanity.com/paper/2507.09407/) (2025)
- [Game-Theoretic Lens on LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2601.15047/) (2026)
- [LLM Active Alignment: A Nash Equilibrium Perspective](https://mlsanity.com/paper/2602.06836/) (2026)
- [LLM Semantic Signaling Game and Mechanism Design: Systematic Blindness, Awareness Shaping, and Mindset Dynamics](https://mlsanity.com/paper/2606.29113/) (2026)

## Abstract (arXiv)

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.