Jameson Graber (Baylor University)
Date
Tuesday February 6, 20249:30 am - 10:30 am
Location
Jeffery Hall, Room 319 (Via Zoom)PDEs & Applications Seminar
Tuesday, February 6th, 2024
Time: 9:30 a.m. Place: Jeffery Hall, Room 319 (Via Zoom)
Speaker: Jameson Graber (Baylor University)
Title: The Master Equation in Mean Field Game Theory
Abstract: Mean field game theory was developed to analyze Nash games with large numbers of players in the continuum limit. The master equation, which can be seen as the limit of an N-player Nash system of PDEs, is a nonlinear PDE equation over time, space, and measure variables that formally gives the Nash equilibrium for a given population distribution. In this talk, I will emphasize the fact that the master equation can be seen as a nonlinear transport equation. In particular, the Nash equilibrium is unique if and only if the characteristics do not cross, and when they do cross, we are faced with the question of making a rational selection among multiple equilibria. I will provide some examples to show how subtle this problem is, and in particular, I will show that the usual theory of entropy solutions is in general not sufficient for the purposes of equilibrium selection.