This two-volume book offers a comprehensive treatment of the
probabilistic approach to mean field game models and their applications.
The book is self-contained in nature and includes original material and
applications with explicit examples throughout, including numerical
solutions.
Volume II tackles the analysis of mean field games in which the players
are affected by a common source of noise. The first part of the volume
introduces and studies the concepts of weak and strong equilibria, and
establishes general solvability results. The second part is devoted to
the study of the master equation, a partial differential equation
satisfied by the value function of the game over the space of
probability measures. Existence of viscosity and classical solutions are
proven and used to study asymptotics of games with finitely many
players.
Together, both Volume I and Volume II will greatly benefit mathematical
graduate students and researchers interested in mean field games. The
authors provide a detailed road map through the book allowing different
access points for different readers and building up the level of
technical detail. The accessible approach and overview will allow
interested researchers in the applied sciences to obtain a clear
overview of the state of the art in mean field games.