Origin-to-destination network flow with path preferences and velocity controls: A mean field game-like approach

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Fabio Bagagiolo, Rosario Maggistro, R. Pesenti
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引用次数: 3

Abstract

In this paper we consider a mean field approach to modeling the agents flow over a transportation network. In particular, beside a standard framework of mean field games, with controlled dynamics by the agents and costs mass-distribution dependent, we also consider a path preferences dynamics obtained as a generalization of the so-called noisy best response dynamics. Such a preferences dynamics says the agents choose their path having access to global information about the network congestion state and based on the observation of the decision of the agents that have preceded. We prove the existence of a mean field equilibrium obtained as a fixed point of a map over a suitable set of time-varying mass-distributions, defined edge by edge in the network. We also address the case where the admissible set of controls is suitably bounded depending on the mass-distribution on the edge itself.
具有路径偏好和速度控制的起点到目的地网络流:一种类似于平均场游戏的方法
在本文中,我们考虑了一种平均场方法来建模运输网络上的代理人流动。特别地,除了平均场对策的标准框架之外,在由代理控制的动力学和成本-质量分布相关的情况下,我们还考虑作为所谓的有噪声最佳响应动力学的推广而获得的路径偏好动力学。这样的偏好动态表明,代理可以访问有关网络拥塞状态的全局信息,并基于对先前代理的决策的观察来选择他们的路径。我们证明了在网络中逐边定义的一组适当的时变质量分布上,作为映射的不动点获得的平均场平衡的存在性。我们还讨论了可容许控制集根据边缘本身的质量分布适当有界的情况。
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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