This book brings together several recent developments on the regularity theory for mean-
field game systems. We detail several classes of methods and present a concise overview of …

Here, we consider numerical methods for stationary mean-field games (MFG) and
investigate two classes of algorithms. The first one is a gradient-flow method based on the …

Here, we consider stationary monotone mean-field games (MFGs) and study the existence
of weak solutions induced by monotonicity. First, we introduce a regularized problem that …

Here, we consider one-dimensional first-order stationary mean-field games with congestion.
These games arise when crowds face difficulty moving in high-density regions. We look at …

Mean-field games (MFG) are models of large populations of rational agents who seek to
optimize an objective function that takes into account their state variables and the …

In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or
without congestion. Our aim is to understand the qualitative features of these games through …

In the absence of special transformations or explicit solutions, the analysis of MFGs often
relies on a priori bounds. Here, we investigate estimates that are commonly used. We begin …