Stackelberg-Leontief Model for Optimal Defense of Industrial Sites

Abstract

Large industrial facilities offer attractive targets to malicious attacks by terrorists. These attacks can trigger cascading failures, capitalizing on the high levels of integration among the components of highly optimized industrial systems. Any defensive measure will generally be resource-constrained and may be difficult to conceal perfectly. In this work, a novel hybrid Stackelberg-Leontief model is developed for planning optimal defensive measures in industrial sites against targeted attacks. The core of the model represents the industrial site with a physical input-output model, which is embedded in a leader-follower game. The defender acts as the leader, who selects defensive measures to implement from a suite of options. Each selected defensive measure incurs a fixed cost regardless of whether an attack occurs or not; however, the defensive measure also mitigates the economic damage caused by any attack. The attacker acts as the follower, who selects an attack strategy based on a set of options with damage coefficients; the attacker is also resource-constrained and needs to optimize the attack while considering the defensive measures put in place. The defender anticipates the attacker’s strategic behavior in developing the defense strategy, resulting in a Stackelberg game formulated as a bilevel mixed integer linear program. The model is illustrated with a didactic case study. In both scenarios considered, the Stackelberg strategy is for the defender to protect the RO module with the attacker targeting the CHP and RO module (Scenario 1) or the CHP, Chiller, and RO module (Scenario 2). This results in the lowest possible mitigation cost (100 USD/h) and a 26 – 27 % increase in the leader’s objective relative to a no defense strategy.