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

Filippo Santambrogio (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: 00-02; 90B06; 49J45; 90C25; 91B40; 91B50; 91D10; 35Q91 traffic congestion; wardrop equilibrium; optimal flows; equilibrium problems; Kantorovich potential; contract theory; Nash equilibrium

Domaines: Analyse classique [math.CA]; Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Filippo Santambrogio. Models and applications of Optimal Transport in Economics, Traffic and Urban Planning. 2009. ⟨hal-00519460⟩