The analysis of differential games with a large number of players finds applications in various research fields, from physics to economics and finance. The aim of Mean Field Games theory is to provide a suitable approximation of such problems with a higher tractability.
Lernziel
This course aims to give a broad understanding of the basic ideas of Mean Field Games, the main mathematical tools and the possible applications.
Inhalt
We first present and analyze toy models of Mean Field Games in order to familiarize with the subject and to understand what kind of problems can be solved with this theory.
We recall some basic principles of optimal control theory and stochastic differential equations.
We explore two different approaches to Mean Field Games. From an analytic point of view it consists of a coupled system of PDEs. From a probabilistic point of view it amounts to a particular type of stochastic differential equations.
Literatur
1) Notes on Mean Field Games. P. Cardaliaguet 2) Mean Field Games. J.M. Lasry, P.L. Lions 3) Probabilistic theory of Mean Field Games and applications. R. Carmona, F. Delarue
Voraussetzungen / Besonderes
Basic courses in analysis including basic knowledge of ordinary/partial differential equations. Basic knowledge of stochastic analysis including Brownian Motion and stochastic differential equations.
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs