论文标题
时变网络中的动态平衡
Dynamic Equilibria in Time-Varying Networks
论文作者
论文摘要
通过考虑纳什均衡来预测公共环境中的自私行为是游戏理论的核心概念。对于由流动的流量游戏模型的动态流量分配问题，每个粒子都试图尽快到达其目的地，动态平衡称为Nash Flow随时间。到目前为止，仅考虑了每个ARC配备恒定容量，限制流出速率的网络，并在运输时间内确定粒子穿越弧线所需的时间。但是，现实世界中的交通网络可能会受到时间变化的影响，例如，在某个时候是由施工工程或特殊速度区域引起的。为了适当地建模这些流量方案，我们通过时间相关的容量和时间相关的过境时间将流程越过时间模型扩展。我们的第一个主要结果是随着时间的推移表征NASH流的结构。与静态网络模型相似，动态平衡中粒子的策略可以以特定的静态流量为特征，称为带有重置的薄流。第二个主要结果是随着时间的推移存在纳什流，我们通过通过这些薄流逐步逐步扩展流动来显示，我们以建设性的方式展示了流动。
Predicting selfish behavior in public environments by considering Nash equilibria is a central concept of game theory. For the dynamic traffic assignment problem modeled by a flow over time game, in which every particle tries to reach its destination as fast as possible, the dynamic equilibria are called Nash flows over time. So far, this model has only been considered for networks in which each arc is equipped with a constant capacity, limiting the outflow rate, and with a transit time, determining the time it takes for a particle to traverse the arc. However, real-world traffic networks can be affected by temporal changes, for example, caused by construction works or special speed zones during some time period. To model these traffic scenarios appropriately, we extend the flow over time model by time-dependent capacities and time-dependent transit times. Our first main result is the characterization of the structure of Nash flows over time. Similar to the static-network model, the strategies of the particles in dynamic equilibria can be characterized by specific static flows, called thin flows with resetting. The second main result is the existence of Nash flows over time, which we show in a constructive manner by extending a flow over time step by step by these thin flows.
