Matching with optimal transport on one side

par Prof. Guillaume CARLIER (Université Paris-Dauphine)

mercredi 7 déc. 2016, 16:00 → 16:50 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

We consider a matching problem between a population of consumers and a population of producers, we look for equilibrium prices that is prices for which the distribution of demand and supply coincide. Producers minimize production cost minus price which can be described by means of optimal transport. But on the consumers’ side, the picture is slightly different, indeed a realistic assumption is that consumer maximize their utility under a price constraint. I will prove existence of an equilibrium and, formally, discuss connections with some (nonconvex) optimal transport problems which somehow mix L^1 and L^\infty criteria. This is a joint work in progress with Alfred Galichon and Ivar Ekeland.