Probabilistic Theory of Mean Field Games with Applications I-II, 1st ed. 2018
Probability Theory and Stochastic Modelling Series, Vol. 83-84

This two-volume set offers an expansive overview of the probabilistic approach to game models and their applications.  Considered the first comprehensive treatment of the theory of mean field games, much of the content is original and has been designed especially for the purpose of this book.

Volume I of the set is entirely devoted to the theory of mean field games without a common noise, whereas Volume II analyzes mean field games in which the players are subject to games with a common noise.

Together, both Volume I and Volume II will benefit researchers in the field as well as PhD and graduate students working on the subject due to the self-contained nature and applications with explicit examples throughout.  

Preface to Volume I.- Part I: The Probabilistic Approach to Mean Field Games.- Learning by Examples: What is a Mean Field Game?.- Probabilistic Approach to Stochastic Differential Games.- Stochastic Differential Mean Field Games.- FBSDEs and the Solution of MFGs without Common Noise.- Part II: Analysis on Wasserstein Space and Mean Field Control.- Spaces of Measures and Related Differential Calculus.- Optimal Control of SDEs of McKean-Vlasov Type.- Epologue to Volume I.- Extensions for Volume I. References.- Indices.- Foreword.- Preface to Volume II.- Part I: MFGs with a Common Noise.- Optimization in a Random Environment.- MFGs with a Common Noise: Strong and Weak Solutions.- Solving MFGs with a Common Noise.- Part II: The Master Equation, Convergence, and Approximation Problems.- The Master Field and the Master Equation.- Classical Solutions to the Master Equation.- Convergence and Approximations.- Epilogue to Volume II.- Extensions for Volume II.- References.- Indices.

First comprehensive presentation of state of the art theory of mean field games with special emphasis on the probabilistic approach Numerous applications with explicit examples including numerical solutions Self-contained treatment of related topics such as analysis on Wasserstein space and mean field control problems