{"title":"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","authors":"Fabio Bagagiolo, Rosario Maggistro, R. Pesenti","doi":"10.3934/JDG.2021007","DOIUrl":null,"url":null,"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.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Origin-to-destination network flow with path preferences and velocity controls: A mean field game-like approach\",\"authors\":\"Fabio Bagagiolo, Rosario Maggistro, R. Pesenti\",\"doi\":\"10.3934/JDG.2021007\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":42722,\"journal\":{\"name\":\"Journal of Dynamics and Games\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2020-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamics and Games\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/JDG.2021007\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/JDG.2021007","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Origin-to-destination network flow with path preferences and velocity controls: A mean field game-like approach
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.
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.