On the computation of mixed strategies for security games with general defending requirements

The Stackelberg security game is played between a defender and an attacker, where the defender needs to allocate a limited amount of resources to multiple targets in order to minimize the loss due to adversarial attacks by the attacker. While allowing targets to have different values, classic settings often assume uniform requirements for defending the targets. This enables existing results that study mixed strategies (randomized allocation algorithms) to adopt a compact representation of the mixed strategies. In this work, we initiate the study of mixed strategies for security games in which the targets can have different defending requirements. In contrast to the case of uniform defending requirements, for which an optimal mixed strategy can be computed efficiently, we show that computing the optimal mixed strategy is NP-hard for the general defending requirements setting. However, we show strong upper and lower bounds for the optimal mixed strategy defending result. Additionally, we extend our analysis to study uniform attack settings on these security games. We propose an efficient close-to-optimal Patching algorithm that computes mixed strategies using only a few pure strategies. Furthermore, we study the setting when the game is played on a network and resource sharing is enabled between neighboring targets. We show the effectiveness of our algorithm in various large real-world datasets, addressing both uniform and general defending requirements. © 2025 Elsevier B.V.