Adversarial Patrolling in a Uniform

• Published in: Operations research 2022-01, Vol.70 (1), p.129-140
• Main Authors: Alpern, Steve, Chleboun, Paul, Katsikas, Stamatios, Lin, Kyle Y.
• Format: Article
• Language: English
• Subjects: Algorithms; attack duration; constant-sum game; delay; Integer programming; Military and Homeland Security; Operations research; patrolling game; Patrols; Personal profiles; Role playing; star network; Terrorism; two-person game; uniformed patroller
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.2021.2152

Many of us will have seen uniformed guards patrolling in museums, airports, and other places where thefts or attacks are possible. In other similar places, we may have been unaware of undercover agents carrying out similar patrols. The latter type of patrollers has been modeled in recent literature. However, when the patroller is visible (wears a uniform), the potential thief or terrorist may be able to spot him when he is nearby and to time his theft appropriately. For example, the thief may wait a specified time after the uniformed patroller leaves his area. In “The Uniformed Patroller Game,” Steve Alpern, Paul Chleboun, Stamatios Katsikas, and Kyle Y. Lin study the effect on the patrolling game of having a visible (uniformed) patroller. It turns out that putting a uniform on the patroller greatly reduces his effectiveness in intercepting thefts or attacks. Of course, the visibility of a uniform may act as a deterrent to having the theft take place at all. Patrolling games were introduced by Alpern, Morton, and Papadaki in 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. In this note, 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 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 some cases. Our main finding is that the attack should begin in the second period the Patroller is away and the Patroller should never visit the same location (other than her base) in consecutive periods.