连续巡逻游戏
Continuous Patrolling Games
摘要：
我们研究了一个在网络$Q$上的巡逻博弈，网络被认为是一个度量空间。攻击者选择$Q$的一个点（不一定是一个节点），在选定的固定持续时间的时间间隔内进行攻击。巡逻者在$Q$上选择一条单位速度路径，如果她在攻击时间间隔内访问了被攻击点，则拦截攻击（并获胜）。这个零和游戏模拟了保护道路或管道免受对抗攻击的问题。最大化巡逻者的收益是攻击被拦截的概率。我们的研究结果包括以下几个方面：（一）游戏的任何网络$Q$的解决方案，只要进行攻击所需的时间是足够短的，（二）游戏的解决方案，所有树网络，满足一定的条件，他们的极端，和（三）解决方案的游戏的任何攻击持续时间的明星与一个长弧和其余的弧长度相等。我们提出了一个猜想的解决方案的游戏任意树，并建立在一定的情况下。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
