Presentation on YouTube.

This talk examines a particular set of first-order mean-field games (MFGs) related to price formation. By utilizing Poincaré's Lemma, we can remove one of the equations, reducing the problem to a single function known as the potential, which presents a different approach to solving the MFGs system. By solving a convex variational problem, we can determine the potential. Additionally, we establish the relation between solutions of the MFGs system and the variational problem. To demonstrate our findings, we apply them to the linear-quadratic model.

[1] Y. Ashrafyan, T. Bakaryan, D. Gomes and J. Gutierrez A Variational Approach For Price Formation Models In One Dimension. arXiv, 2022.
[2] T. Bakaryan, R. Ferreira and D. Gomes A potential approach for planning mean-field games in one dimension Communications on Pure and Applied Analysis, 21, 6, 2147-2187, 2022.

Biography: Julian received both B.S. in Mathematics and B.S. in Engineering in 2014 from Escuela Colombiana de Ingenieria, Colombia. After receiving his M.Sc. in Mathematical Sciences in 2017 from Universidad Nacional Autónoma de México, México, he joined Professor Diogo Gomes in 2018, where he is currently a Ph.D. candidate in applied mathematics at King Abdullah University of Science and Technology, Saudi Arabia. His research interests are primarily about the aspects of optimal control, optimal transport, calculus of variations, and partial differential equations involved in mean-field games.