论文标题
连续巡逻游戏
Continuous Patrolling Games
论文作者
论文摘要
我们研究在网络$ Q $上玩的巡逻游戏，被认为是度量空间。攻击者选择了$ Q $（不一定是节点）的点，以在固定持续时间的选择时间间隔内进行攻击。巡逻人员在$ Q $上选择了单位速度路径，并在攻击时间间隔内访问攻击点，拦截了攻击（并获胜）。该零和游戏模拟了保护道路或管道免受对抗性攻击的问题。最大化巡逻者的回报是攻击被拦截的概率。我们的结果包括以下内容：（i）对于任何网络$ Q $的解决方案，只要进行攻击所需的时间足够短，（ii）解决所有树网络的解决方案，可以满足其四肢的某些树网络的解决方案，（iii）解决游戏的解决方案，用于对一台较长的ARC和剩余的ARC的攻击持续时间。我们在游戏解决方案上为任意树的解决方案提出了一个猜想，并在某些情况下建立了它。
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.
