Title: Topics in Equilibrium Transportation
Motivated by problems from Economics, I will present a general
framework for "Equilibrium Transportation", which embeds the
Monge-Kantorovich "Optimal Transportation" theory, but is more
general, and more natural in some applications. In the discrete
case, this framework allows for a unified description of Gale and
Shapley's stable marriage problem, as well as Koopmans and
Beckmann's optimal assignment problem.
I will sketch the link with "Galois connections" and recent results
by Trudinger on the local theory of prescribed Jacobian equations.
I will then turn to computational issues, and will present an
extension of Sinkhorn's algorithm that allows for efficient
approximate computation of these problems.
Finally, I will discuss statistical estimation of these models and
give properties of the Maximum Likelihood Estimator.