The Uniformed Patroller Game

TL;DR

This paper studies a modified patrolling game where the attacker gains early observation of the patroller's presence, revealing that strategic timing and movement of the patroller significantly affect attack success rates.

Contribution

It introduces a new model allowing the attacker to observe the patroller and delay attacks, analyzing optimal strategies and showing how information impacts attack success.

Findings

Attacker's advantage can be up to fourfold with early observation.

Optimal attack timing is in the second period after patroller leaves.

Patroller should avoid attacking the same location consecutively.

Abstract

Patrolling Games were introduced by Alpern, Morton and Papadaki (2011) to model the adversarial problem where a mobile Patroller can thwart an attack at some location only by visiting it during the attack period, which has a prescribed integer duration m. Here, we modify the problem by allowing the Attacker to go to his planned attack location early and observe the presence or the absence there of the Patroller (who wears a uniform). To avoid being too predictable, the Patroller may sometimes remain at her base when she could have been visiting a possible attack location. The Attacker can then choose to delay attacking for some number of periods d after the Patroller leaves his planned attack location. As shown here, this extra information for the Attacker can reduce thwarted attacks by as much as a factor of four in specific models. Our main finding, is that the attack should begin in the second period the Patroller is away (d = 2) and that the Patroller should never attack the same location in consecutive periods.