A network model for urban planning

TL;DR

This paper introduces a mathematical network model for urban development, capturing interactions between workers and firms, and analyzing city evolution through a coupled Mean-Field Game and Optimal Transport framework.

Contribution

It presents a novel coupled Mean-Field Game and Optimal Transport model for urban dynamics, with proven existence and uniqueness of solutions.

Findings

Existence and uniqueness of the model solution established.

Numerical simulations demonstrate model behavior.

Insights into urban population interactions and city evolution.

Abstract

We study a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is described by a network with the edges representing at the same time residential areas and communication routes. The two populations compete for space while interacting through the labour market. The resulting model is described by a two population Mean-Field Game system coupled with an Optimal Transport problem.We prove existence and uniqueness of the solution and we provide several numerical simulations.