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

TL;DR

This paper introduces LLM-Stackelberg games, a novel framework integrating large language models into strategic decision-making, capturing bounded rationality and uncertainty, with applications demonstrated in a spearphishing case study.

Contribution

It develops a new class of sequential decision models using LLMs, defining equilibrium concepts that incorporate reasoning, belief updates, and uncertainty in strategic interactions.

Findings

Framework captures bounded rationality and asymmetric information.

Case study demonstrates LLMs' potential in deception and cybersecurity.

Provides a foundation for modeling decision-making in adversarial settings.

Abstract

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.