Workshop on Transport, optimization, equilibrium in economics

Since Gaspard Monge formulated the problem of finding an optimal transportation plan for piles of soil in his 1781 "Memoire sur les deblais et remblais," the problem of transporting a given distribution of mass from one location to another distribution of mass in a different location, while minimizing a certain cost of research. Following the seminal results of Brenier, optimal transportation has received a lot of attention in the last 15 years, leading to a very active field of research in applied mathematics. That it also provides a powerful and versatile tol for a wide range of economic applications is now becoming apparent. Mass transportation duality is useful in formulating the problem of existence, uniqueness and purity fo equilibrium in hedonic models. It has natural connections with multidimensional screening and urban economics that deserve to be better explored. In econometrics, it lies at the heart of improvements of estimates of monotone functions (such as cumulative distribution and quantile functions), and of the problem of testing economic model specification, to name only a few applications.

In order to gather researchers at the forefront of developments of these economic applications, to increase their awareness of each other's work, to identify the most important unexplored problems and pave the way for collaborations, a first one day meeting ("Transportation Day") has been organized at Columbia University on june 25th 2007 (participants: Guillaume Carlier (Paris Dauphine), Victor Chernozhukov (MIT), Pierre-André Chiappori (Columbia), Ivar Ekeland (UBC and PIMS), Alfred Galichon (Ecole polytechnique), Marc Henry (Columbia), Robert McCann (UToronto), Lars Nesheim (UCL), Heleno Pioner (Chicago) and Jay Sethuraman (Columbia)). Due to the numerous potential applications of mass transportation methods to economics, the Columbia meeting was also intended to become the first of a long series of annual meetings in rotating venues.

The aim of the workshop "Transport, optimization, equilibrium in economics" is to bring together economists and mathematicians with common interests in subjects related to the mathematics of transportation in a broad sense. On the mathematical side, the goal will be to present a wide spectrum of techniques and models of transportation (optimal transportation, networks, congestion modeling, optimal location) both from the theoretical and numerical point. On the economic side, recent works of Ekeland, Chiappori, McCann and Nesheim have shown that optimal transportation techniques are powerful tools for the analysis of matching problems and hedonic equilibria. Transportation theory has a wide range of potential applications in econometrics, urban economics, adverse selection problems and nonlinear pricing, topics which naturally fall in the scope of the meeting.

The workshop will last 5 working days. To benefit from the pluridisciplinary character of this workshop, we plan an alternance of lectures (4 per day) and of open sessions (1 per day).