The mean-field framework was developed to study systems with an infinite number of
rational agents in competition, which arise naturally in many applications. The systematic …

We construct a small time strong solution to a nonlocal Hamilton–Jacobi equation (1.1)
introduced in [48], the so-called master equation, originating from the theory of Mean Field …

These notes are an introduction to Mean Field Game (MFG) theory, which models differential
games involving infinitely many interacting players. We focus here on the Partial Differential …

This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M.
Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic …

Emerging industrial platforms such as the Internet of Things (IoT), Industrial Internet (II) in the
US and Industrie 4.0 in Europe have tremendously accelerated the development of new …

The price of anarchy, originally introduced to quantify the inefficiency of selfish behavior in
routing games, is extended to mean field games. The price of anarchy is defined as the ratio …

This paper presents an inverse problem for mean field games where we find the mean field
problem statement for which the given dynamics is the solution. We use distributed traffic as …

Mean field games (MFGs) are dynamic games with infinitely many infinitesimal agents. In
this context, we study the efficiency of Nash MFG equilibria; namely, we compare the social …

This paper considers a linear-quadratic (LQ) mean field control problem involving a major
player and a large number of minor players, where the dynamics and costs depend on …

This paper studies the connection between a class of mean-field games and a social welfare
optimization problem. We consider a mean-field game in function spaces with a large …