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

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.