Adversarial Patrolling in a Uniform

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.