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.
Series
Edition
Language
Place of publication
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 45 mm
Weight
ISBN-13
978-3-319-56435-7 (9783319564357)
DOI
10.1007/978-3-319-56436-4
Schweitzer Classification
René Carmona is the Paul M. Wythes '55 Professor of Engineering and Finance at Princeton University in the department of Operations Research and Financial Engineering, and Director of Graduate Studies of the Bendheim Center for Finance. His publications include over one hundred articles and eight books in probability and statistics. He was elected Fellow of the Institute of Mathematical Statistics in 1984, and of the Society for Industrial and Applied Mathematics in 2010. He is on the editorial board of several peer-reviewed journals and book series. Professor Carmona has developed computer programs for teaching statistics and research in signal analysis and financial engineering. He has worked for many years on energy, the commodity markets and more recently in environmental economics, and he is recognized as a leading researcher and expert in these areas.
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.
