A Stochastic Surveillance Stackelberg Game: Co-Optimizing Defense Placement and Patrol Strategy

TL;DR

This paper develops a game-theoretic framework for optimizing stochastic patrol routes and defense placements against an omniscient adversary, accounting for heterogeneous defenses and providing efficient computation methods.

Contribution

It introduces a novel model combining patrol routing and defense placement with heterogeneous defenses, and proposes efficient algorithms for strategy computation.

Findings

Strategies outperform baseline approaches in simulations

Heterogeneous defenses improve overall security effectiveness

New algorithms enable scalable strategy computation

Abstract

Stochastic patrol routing is known to be advantageous in adversarial settings; however, the optimal choice of stochastic routing strategy is dependent on a model of the adversary. We adopt a worst-case omniscient adversary model from the literature and extend the formulation to accommodate heterogeneous defenses at the various nodes of the graph. Introducing this heterogeneity leads to interesting new patrol strategies. We identify efficient methods for computing these strategies in certain classes of graphs. We assess the effectiveness of these strategies via comparison to an upper bound on the value of the game. Finally, we leverage the heterogeneous defense formulation to develop novel defense placement algorithms that complement the patrol strategies.