# LLM-Stackelberg Games: Conjectural Reasoning Equilibria and Their Applications to Spearphishing

arXiv: https://arxiv.org/abs/2507.09407 · HTML: https://mlsanity.com/paper/2507.09407/

## Key facts

- Cited by 3 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 6 of its 12 references that are in the map.
- First posted on arXiv 12 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, 6 of 6)

- [Next-Generation Phishing: How LLM Agents Empower Cyber Attackers](https://mlsanity.com/paper/2411.13874/) (2024)
- [Revisiting Game-Theoretic Control in Socio-Technical Networks: Emerging Design Frameworks and Contemporary Applications](https://mlsanity.com/paper/2411.01794/) (2024)
- [ADVERT: An Adaptive and Data-Driven Attention Enhancement Mechanism for Phishing Prevention](https://mlsanity.com/paper/2106.06907/) (2021)
- [Reasoning and Behavioral Equilibria in LLM-Nash Games: From Mindsets to Actions](https://mlsanity.com/paper/2507.08208/) (2025)
- [Toward a Dynamic Stackelberg Game-Theoretic Framework for Agentic AI Defense Against LLM Jailbreaking](https://mlsanity.com/paper/2507.08207/) (2025)
- [Phishing for Phools in the Internet of Things: Modeling One-to-Many Deception using Poisson Signaling Games](https://mlsanity.com/paper/1703.05234/) (2017)

## Built on by (most cited first, 3 of 3)

- [Agentic AI for Cyber Resilience: A New Security Paradigm and Its System-Theoretic Foundations](https://mlsanity.com/paper/2512.22883/) (2025)
- [The Internet of Agentic AI: Communication, Coordination, and Collective Intelligence at Scale](https://mlsanity.com/paper/2606.12835/) (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 framework of LLM-Stackelberg games, a class of sequential decision-making models that integrate large language models (LLMs) into strategic interactions between a leader and a follower. Departing from classical Stackelberg assumptions of complete information and rational agents, our formulation allows each agent to reason through structured prompts, generate probabilistic behaviors via LLMs, and adapt their strategies through internal cognition and belief updates. We define two equilibrium concepts: reasoning and behavioral equilibrium, which aligns an agent's internal prompt-based reasoning with observable behavior, and conjectural reasoning equilibrium, which accounts for epistemic uncertainty through parameterized models over an opponent's response. These layered constructs capture bounded rationality, asymmetric information, and meta-cognitive adaptation. We illustrate the framework through a spearphishing case study, where a sender and a recipient engage in a deception game using structured reasoning prompts. This example highlights the cognitive richness and adversarial potential of LLM-mediated interactions. Our results show that LLM-Stackelberg games provide a powerful paradigm for modeling decision-making in domains such as cybersecurity, misinformation, and recommendation systems.