Continuous Patrolling Games

• 成果类型: Article
• 署名作者: Alpern, Steve; Bui, Thuy; Lidbetter, Thomas; Papadaki, Katerina
• 署名单位: University of Warwick; Rutgers University System; Rutgers University Newark; Rutgers University New Brunswick; University of Virginia; University of London; London School Economics & Political Science
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.2346
• 发表日期: 2022
• 页码: 3076-3089
• 关键词: time

摘要

We study a patrolling game played on a network Q, considered as a metric space. The Attacker chooses a point of Q (not necessarily a node) to attack during a chosen time interval of fixed duration. The Patroller chooses a unit speed path on Q and intercepts the attack (and wins) if she visits the attacked point during the attack-time interval. This zero-sum game models the problem of protecting roads or pipelines from an adversarial attack. The payoff to the maximizing Patroller is the probability that the attack is intercepted. Our results include the following: (i) a solution to the game for any network Q, as long as the time required to carry out the attack is sufficiently short; (ii) a solution to the game for all tree networks that satisfy a certain condition on their extremities; and (iii) a solution to the game for any attack duration for stars with one long arc and the remaining arcs equal in length. We present a conjecture on the solution of the game for arbitrary trees and establish it in certain cases.