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.

中文翻译：

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时变网络中的动态均衡

通过考虑纳什均衡来预测公共环境中的自私行为是博弈论的核心概念。对于由随时间流游戏建模的动态交通分配问题，其中每个粒子都试图尽快到达目的地，动态均衡称为随时间推移的纳什流。到目前为止，该模型只考虑用于每个弧都配备有恒定容量、限制流出速率和传输时间的网络，以确定粒子穿过弧所需的时间。然而，现实世界的交通网络可能会受到时间变化的影响，例如，在某个时间段内由建筑工程或特殊速度区引起。为了适当地模拟这些交通场景，我们通过与时间相关的容量和与时间相关的运输时间来扩展随时间推移的流量模型。我们的第一个主要结果是随着时间的推移对纳什流结构的表征。与静态网络模型类似，动态平衡中粒子的策略可以用特定的静态流来表征，称为带重置的细流。第二个主要结果是纳什流随时间的存在，我们通过这些细流逐步扩展随时间的流，以建设性的方式展示了这一点。