mean-field games

Stationary Mean-Field Games with Congestion

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B2 L5 R5220

Mean-field games MFG are models of large populations of rational agents who seek to optimize an objective function that takes into account their state variables and the distribution of the state variable of the remaining agents. MFG with congestion model problems where the agents’ motion is hampered in high-density regions. First, we study radial solutions for first- and second-order stationary MFG with congestion on R^d. Next, we consider second-order stationary MFG with congestion and prove the existence of stationary solutions. Additionally, we study first-order stationary MFG with congestion with quadratic or power-like Hamiltonians.

On mean-field game price models

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B9 L2 H1 R2322

Abstract 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. Brief Biography Diogo Gomes

Two-Scale Homogenization and Numerical Methods for Stationary Mean-Field Games

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KAUST

Mean-field games (MFGs) study the behavior of rational and indistinguishable agents in a large population. Agents seek to minimize their cost based upon statistical information on the population's distribution. In this dissertation, we study the homogenization of a stationary first-order MFG and seek to find a numerical method to solve the homogenized problem. More precisely, we characterize the asymptotic behavior of a first-order stationary MFG with a periodically oscillating potential. Our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems. Moreover, we prove the existence and uniqueness of the solution to these limit problems. Next, we notice that the homogenized problem resembles the problem involving effective Hamiltonians and Mather measures, which arise in several problems, including homogenization of Hamilton--Jacobi equations, nonlinear control systems, and Aubry--Mather theory. Thus, we develop algorithms to solve the homogenized problem, effective Hamiltonians, and Mather measures.

KAUST Ph.D. students win best paper awards at mean-field games conferences

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By Sonia Turosienski KAUST Ph.D. students David Evangelista and Xianjin Yang, who are supervised by Diogo Gomes, professor of applied mathematics and computational science, won best paper awards at conferences this summer for their work in mean-field game (MFG) theory. Mean-field games model and seek to explain the behavior of rational agents in a competitive environment and have been used in diverse areas of research, including studies on non-renewable resources and mining models; opinion dynamics; price impact and order book modeling; and networks and energy management. Evangelista was

Xianjin Yang

Xianjin Yang's research interests fall on mean-field games, which is an active research area in differential game theories. In his PhD period, Xianjin focuses on the homogenization and numerical methods for stationary mean-field games. Education and Early Career Xianjin Yang got his bachelor's degree in Software Engineering from Chongqing University of China in 2011. Then, he obtained his Master with majors in Computer Science from Zhejiang University of China in 2014. Later on, Xianjin Yang received his second Master's degree in Applied Mathematics from KAUST in 2016. He continues to study at

Diogo Gomes

Professor Diogo Gomes, a distinguished expert in Applied Mathematics and Computational Science at KAUST, leverages advanced mathematics – including partial differential equations, numerical methods and mean-field game models – to solve complex problems in social sciences, economics and finance

David Evangelista

David Evangelista is a Ph.D. Candidate at King Abdullah University of Science and Technology (KAUST), working in the areas of partial differential equations, mean-field games (MFG), and market microstructure. He is expect to receive a Ph.D. from KAUST in June 2019, under the direction of Professor Diogo A. Gomes. David's research interests are in optimal control theory, nonlinear partial differential equations, MFG, and market microstructure. MFG is a framework to study interactions of a large number of indistinguishable players that play differential games. MFG has become an active research