Lectures on mean field game systems
报告专家：魏雅薇 教授（南开大学）
报告时间：6月26日-28日上午9：00-12:00
课程地点：国家天元数学西南中心516
课程摘要：Mean field game theory is devoted to the analysis of (stochastic) differential games with infinitely many players. The term mean field comes for an analogy with the mean field models in mathematical physics. Mean field game system is a kind of PDE model to study the mean field games. The idea of this approach is guessing the equations that Nash equilibria of the large population differential games should satisfy. The mean field game system consists of a Hamilton-Jacobi equation for a value function and a Fokker-Planck equation for a mean-field density. In the first part of this lecture, we will talk about the basic calculus of mean field game system, including derivation of mean field system, Hamilton-Jacobi equations, Fokker-Planck equation and the mean field game system with a non-local coupling. In the second part of this lecture, we will study the degenerate nonlinear PDE systems arising from the mean field games with degenerate diffusion, where the generic player may have a forbidden direction at some point, where we will prove the existence and uniqueness for the PDE systems, which describe the Nash equilibria in the games.
Contents
1. Mean field game system
1.1 Derivation of mean field system
1.2 Hamilton-Jacobi equations
1.3 Fokker-Planck equation
1.4 The mean field game system with a non-local coupling
2. Mean field game systems with degenerate diffusion.
2.1 Grushin diffusion
2.2 Infinitely degenerate diffusion
专家简介：魏雅薇，教授，博士生导师，教育部重点实验室副主任，美国数学学会《数学评论》评论员，本科毕业于上海交通大学数学科学学院，博士毕业于德国波茨坦大学；主持国家自然科学基金面上项目2项、青年项目1项，主持天津自然科学基金项目1项；主要研究退化型非线性偏微分方程、非线性偏微分方程及应用、控制理论、博弈理论及应用等，多篇代表成果发表在Journal of Functional Analysis, Calculus of variations and PDEs, Journal of Differential Equations等国际知名期刊。
邀请人：吕琦
