Strategic allocation and dynamic rescue for multi-defender stackelberg security games with infectious attacks

Abstract

Interconnected systems can suffer infectious attacks, where the compromise of one node exposes neighboring nodes and may trigger cascading loss. Existing Stackelberg and network-defense models usually address only part of this setting: a centralized defender, independent targets, or no post-attack resource transfer. This paper studies an observable pure-strategy setting in which multiple heterogeneous defenders independently allocate limited resources before an attacker selects a target. A publicly announced response rule fixed before deployment then reallocates transferable surplus after the target is observed. We formulate the resulting allocation game by backward induction: rescue is target-contingent for every allocation–target pair, the attacker anticipates that response when choosing a target, and defenders anticipate both continuation stages when choosing their allocations. We give a necessary-and-sufficient equilibrium characterization and sufficient conditions for pure-strategy existence, and use a centralized MILP only as an aggregate minimax benchmark. The optimal rescue problem is NP-hard even with fixed initial allocation and target. We therefore propose a two-stage heuristic aimed at the (ϵ,ξ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\epsilon ,\xi )$$\end{document}-SNE conditions: equilibrium-guided initial allocation followed by feasible node-level greedy rescue. Experiments on three simulated and three real-world networks show lower aggregate loss than the tested baselines on all six datasets, at the cost of additional runtime. On the tested power-law instances, the method remains close to the centralized MILP lower-bound benchmark.