Mixed Strategies for Security Games with General Defending Requirements

TL;DR

This paper explores mixed strategies in security games with targets having different defending requirements, establishing NP-hardness for optimal solutions and proposing an efficient approximation algorithm with practical effectiveness.

Contribution

It introduces the first study of mixed strategies for security games with non-uniform defending requirements and develops a close-to-optimal algorithm for such complex scenarios.

Findings

NP-hardness of computing optimal mixed strategies with general defending requirements

Proposed an efficient Patching algorithm for near-optimal mixed strategies

Experimental validation on large real-world datasets shows effectiveness

Abstract

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 attack by the attacker. While allowing targets to have different values, classic settings often assume uniform requirements to defend 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 the security games in which the targets can have different defending requirements. In contrast to the case of uniform defending requirement, 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 that strong upper and lower bounds for the optimal mixed strategy defending result can be derived. We propose an efficient close-to-optimal Patching algorithm that computes mixed strategies that use only few pure strategies. We also study the setting when the game is played on a network and resource sharing is enabled between neighboring targets. Our experimental results demonstrate the effectiveness of our algorithm in several large real-world datasets.