Models and applications of Optimal Transport in Economics, Traffic and Urban Planning

TL;DR

This paper explores the use of optimal transport models in economics, traffic, and urban planning, highlighting their theoretical foundations and practical applications in congestion, urban development, and economic problems.

Contribution

It introduces new models integrating optimal transport with traffic congestion and urban planning, connecting them with Monge-Kantorovich theory and PDEs.

Findings

Congestion-aware transport models link to PDEs.

Urban planning models based on optimal transport.

Economic problems translated into optimal transport framework.

Abstract

Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into account traffic congestion effects is the first topic, and it shows various links with Monge-Kantorovich theory and PDEs. Then, two models for urban planning are introduced. The last section is devoted to two problems from economics and their translation in the language of optimal transport.