Evacuation planning is an essential part of disaster management where the goal is to relocate people under imminent danger to safety. Although government authorities may prescribe routes and a schedule, evacuees generally behave as self-interested agents and may choose their action according to their own selfish interests. It is crucial to understand the degree of inefficiency this can cause to the evacuation process. However, existing research has mainly focused on selfish routing, i.e., they consider route selection as the only strategic action. In this paper, we present a strategic routing and scheduling game, named the Evacuation Planning Game (EPG), where evacuees choose both their route and the time of departure. We focus on confluent evacuation plans, where, if two routes meet at a node then their remaining portion is identical. We also use dynamic flows to model the time-varying traffic on roads during evacuation. We show that every instance of EPG has at least one pure strategy Nash equilibrium. We then present a polynomial time algorithm, the Sequential Action Algorithm (SAA), for finding equilibria in a given instance. Additionally, we provide bounds on how bad an equilibrium state can be compared to a socially optimal state. Finally, We use Harris County of Houston, Texas as our study area and construct a game instance for it. Our results show that, by utilizing SAA, we can efficiently find equilibria in this instance that have social objective close to the optimal value.

翻译：疏散规划是灾害管理的核心环节，其目标是将处于危险中的人员转移至安全区域。尽管政府当局可能指定疏散路线和时间表，但撤离者通常会作为自利主体，根据自身利益选择行动。理解这种行为对疏散过程造成的效率损失至关重要。然而，现有研究主要关注自私路径选择（即仅将路线选择视为战略性行为）。本文提出了一种战略性的路径与时间调度博弈模型——疏散规划博弈（Evacuation Planning Game, EPG），其中撤离者同时选择其路线和出发时间。我们聚焦于汇流型疏散计划（即若两条路径在某节点汇合，则后续路段完全一致），并采用动态流模型刻画疏散过程中道路的时变交通状态。研究表明：每个EPG实例至少存在一个纯策略纳什均衡。我们进一步提出多项式时间算法——序列行动算法（Sequential Action Algorithm, SAA）以求解给定实例的均衡状态。此外，我们给出了均衡状态相对于社会最优状态的最大效率损失上界。最后，以得克萨斯州哈里斯县（休斯顿）为研究区域构建博弈实例，实验结果表明：利用SAA可高效求解该实例中社会目标接近最优值的均衡状态。