Beyond Homogeneous Adversaries: Stackelberg Security Games with Mixed Quantal Response

Abstract

The quantal response (QR) model is widely used in Stackelberg security games (SSGs) to capture boundedly rational adversaries. Existing work on SSGs under QR, however, almost exclusively assumes a homogeneous attacker population, ignoring heterogeneity in attacker preferences and rationality. We study SSG with mixed quantal response attackers, where the follower population consists of multiple discrete attacker types, each following a type-specific QR model. The defender allocates limited resources across targets, while an attacker drawn from this heterogeneous population observes the defender’s strategy and attacks a single target. This results in a highly non-convex equilibrium computation problem. We develop a polynomial-time approximation scheme (PTAS) for this setting when the number of attacker types is bounded, based on an exponential cone programming formulation combined with a carefully designed Branch-and-Bound procedure. Experiments demonstrate that our approach outperforms standard gradient-based methods and that explicitly modeling attacker heterogeneity yields significant gains over traditional SSG models with a single QR attacker.