---
title: "Beyond Homogeneous Adversaries: Stackelberg Security Games with Mixed Quantal Response"
authors:
  - "Hoang Giang Pham"
  - "Tien Mai"
  - "Thuy Anh Ta"
  - "Minh Hoàng Hà"
doi: "10.24963/ijcai.2026/392"
url: "https://ijcai.org/proceedings/2026/392"
pdf: "https://ijcai.org/proceedings/2026/0392.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "3523-3531"
track: "Main Track"
keywords:
  - "Game Theory and Economic Paradigms: Noncooperative games"
---

# Beyond Homogeneous Adversaries: Stackelberg Security Games with Mixed Quantal Response

Hoang Giang Pham, Tien Mai, Thuy Anh Ta, Minh Hoàng Hà

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 3523-3531. DOI: [10.24963/ijcai.2026/392](https://doi.org/10.24963/ijcai.2026/392)

## 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.