Motivated by problems from Economics,
I will present a framework for "Equilibrium Transportation", which embeds the Monge-Kantorovich "Optimal Transportation" problem, 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. This talk is partly based on a series of joint works with Scott Kominers (Harvard) and Simon Weber (Sciences Po).