题目：A minimal-time mean field game model inspired by crowd motion

报告人：Guilherme MAZANTI，INRIA（法国国家信息与自动化研究所）

时间：2024年3月13日（周三）16：00-17：00

地点：第五教学楼5107教室

摘要：

Mean field games (MFGs for short) were introduced in the mid-2000s to model situations with infinitely many rational and indistinguishable agents in interaction, allowing for a simplification in the study of games with a large number of players through a mean field limit. Since their introduction, MFGs have been extensively studied in the literature from several points of view, including analysis of existence and uniqueness of their equilibria, approximation of games with many players by mean field games, numerical approximations of equilibria of mean field games, learning in mean field games, among many other topics.

In this talk, we will provide an introduction to mean field games by presenting the mathematical analysis of a mean field game model inspired by crowd motion, in which a crowd of pedestrians move in a given domain and wish to reach some target set inside the domain in minimal time. In order to model congestion, our MFG model assumes that the maximal velocity at which an agent of the crowd can move depends on the distribution of other agents around their position. After providing the mathematical formulation of this game, we will show existence of equilibria and prove that equilibria satisfy a system of partial differential equations, known as the MFG system.

This talk is based on joint works with Romain Ducasse, Samer Dweik, Saeed Sadeghi Arjmand, and Filippo Santambrogio.