In our previous study—area-partition-involved collaborative patrolling (APCP) game, we proposed a cooperative patrolling game by utilizing multiple patrol vehicles to protect the chemical cluster. Except for fixed countermeasures like intrusion detection, the APCP game was proved to reduce the security risks of chemical clusters being attacked by terrorists effectively. However, some general assumptions (i.e., complete information game and perfect rational players) in the game model make it difficult to be applied in reality since the game model is not robust enough to deal with some common uncertainties on attackers. In this paper, we extend the APCP game model by considering the uncertainties of the game model from two aspects: (1) One is the bounded rationality of attackers. Attackers may adopt the ε-optimal response strategy without maximizing their payoffs strictly. In this circumstance, we propose the bounded rational APCP game solver. (2) The other is the uncertainties of the defender’s estimation on the attacker’s parameters. Some parameters regarding attackers are changed from exact values to distribution-free intervals. Correspondingly, we propose the interval APCP game solver. Through extensive simulations on a chemical cluster (i.e., the Antwerp Chemical Cluster), results of the case study indicate that when considering two types of uncertainties mentioned above, the defender’s payoff will be slightly reduced, whereas the more robust patrolling routes are more easily convinced and adopted by the management department of chemical clusters and improve the process safety of chemical clusters.

在我们先前的研究中，涉及区域分区的协同巡逻（APCP）游戏中，我们提出了一种利用多个巡逻车保护化学物质簇的协同巡逻游戏。除了采取诸如入侵检测之类的固定对策外，事实证明，APCP游戏可有效降低恐怖分子袭击化学团簇的安全风险。但是，游戏模型中的一些一般性假设（例如，完整的信息游戏和完美的理性玩家）使得难以在现实中应用，因为游戏模型的鲁棒性不足以应对攻击者的一些常见不确定性。本文从两个方面考虑了博弈模型的不确定性，对APCP博弈模型进行了扩展：（1）一是攻击者的有限理性。攻击者可以采用ε-最佳的应对策略，而没有严格地最大化其收益。在这种情况下，我们提出了有界有理APCP游戏求解器。（2）另一个是防御者对攻击者参数的估计的不确定性。有关攻击者的某些参数已从精确值更改为无分发间隔。相应地，我们提出了区间APCP游戏求解器。通过对化学集群（即安特卫普化学集群）的广泛模拟，案例研究的结果表明，当考虑上述两种不确定性时，防御者的收益将略有减少，而更健壮的巡逻路线更容易被说服并被化工集群管理部门采用，提高了化工集群的工艺安全性。