In this talk, we discuss a mean-field game price formation model. This model describes a large number of rational agents that can trade a commodity with an exogenous supply. The price is determined by a balance condition between supply and demand. We discuss the well-posedness of the model, the uniqueness and regularity of the price function. Then, we examine two explicit models - the linear-quadratic problem and a model with finitely many agents. Time permitting, we will examine the connections between this problem and optimal transport with constraints.
Diogo Gomes is a Professor of Applied Mathematics and Computational Science (AMCS), and from 2018 also Chair of the AMCS Program. Gomes' research interests are in partial differential equations (PDE), namely on viscosity solutions of elliptic, parabolic and Hamilton-Jacobi equations as well as in related mean-field models. Applications of his work include: from computer vision to population dynamics and numerical methods.
Professor Diogo Gomes received his Ph.D. in Mathematics from the University of California at Berkley in 2000 and was awarded a Habilitation in Mathematics from Universidade Tecnica de Lisboa in 2006. He did his Post-Doc at the Institute for Advanced Study in Princeton in 2000 and completed an additional one at the University of Texas at Austin in 2001. Before joining KAUST, Professor Gomes has been a Professor in the Mathematics Department at the Instituto Superior Tecnico since 2001.