A defender dispatches patrollers to circumambulate a perimeter to guard
against potential attacks. The defender decides on the time points to dispatch
patrollers and each patroller's direction and speed, as long as the long-run
rate patrollers are dispatched is capped at some constant. An attack at any
point on the perimeter requires the same amount of time, during which it will
be detected by each passing patroller independently with the same probability.
The defender wants to maximize the probability of detecting an attack before it
completes, while the attacker wants to minimize it. We study two scenarios,
depending on whether the patrollers are undercover or wear a uniform.
Conventional wisdom would suggest that the attacker gains advantage if he can
see the patrollers going by so as to time his attack, but we show that the
defender can achieve the same optimal detection probability by carefully
spreading out the patrollers probabilistically against a learning attacker.Comment: 17 pages, 1 figur
