A spatial Pareto exchange economy problem

Xavier Bacon (1, 2) , Guillaume Guillaume Carlier (2, 3) , Bruno Nazaret (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales

We use convex duality techniques to study a spatial Pareto problem with transport costs and derive a spatial second welfare theorem. The existence of an integrable equilibrium distribution of quantities is nontrivial and established under general monotonicity assumptions. Our variational approach also enables us to give a numerical algorithmà la Sinkhorn and present simulations for equilibrium prices and quantities in one-dimensional domains and a network of French cities.

Mots clés: Sinkhorn algorithm; Entropic optimal transport; Second welfare theorem; Convex duality; Optimal transport; Exchange economy Pareto optimality

Domaines: Optimisation et contrôle [math.OC]

Xavier Bacon, Guillaume Guillaume Carlier, Bruno Nazaret. A spatial Pareto exchange economy problem. 2021. ⟨hal-03480323v2⟩