# MATJ5109 MA3: Differential Calculus on the Wasserstein Space and Mean Field Games (JSS30) (1 cr)

**Study level:**

Postgraduate studies

**Grading scale:**

Pass - fail

**Language:**

English

**Responsible organisation:**

Faculty of Mathematics and Science

**Curriculum periods:**

2020-2021, 2021-2022

## Description

The goal of this course is to introduce some aspects of the calculus in the space of probability measures and to explain how these notions apply to the theory of mean field games (optimal control problems with infinitely many controllers). We will first briefly survey the various notions related to differentiability in the space of probability measures. Then we will discuss a typical example of problem of calculus of variation in this space and its relation with mean field games.

## Learning outcomes

After the course the student is familiar with the basic notion of

a) differentiability with respect to probability measures and

b) mean field games.

The student knows examples of mean field games and is able to apply the concept of differentiability with respect to probability measures.

## Description of prerequisites

The course requires the knowledge of mathematical analysis in master student level and basics in measure theory.

## Completion methods

### Method 1

**Evaluation criteria:**

Examination at the end of the course

Select all marked parts

**Parts of the completion methods**

x

### Participation in teaching (1 cr)

**Type:**

Participation in teaching

**Grading scale:**

Pass - fail

**Evaluation criteria:**

Examination at the end of the course

**Language:**

English