Authors:
- 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
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 84)
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Table of contents (7 chapters)
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Front Matter
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MFGs with a Common Noise
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Front Matter
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The Master Equation, Convergence, and Approximation Problems
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Front Matter
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Back Matter
About this book
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.Authors and Affiliations
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ORFE Department, Program in Applied and Computational Mathematics, Princeton University, Princeton, USA
René Carmona
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Institut Universitaire de France & Laboratoire J.A. Dieudonné, Université Nice Sophia Antipolis, Nice, France
François Delarue
Bibliographic Information
Book Title: Probabilistic Theory of Mean Field Games with Applications II
Book Subtitle: Mean Field Games with Common Noise and Master Equations
Authors: René Carmona, François Delarue
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-319-56436-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2018
Hardcover ISBN: 978-3-319-56435-7Published: 20 March 2018
Softcover ISBN: 978-3-030-13259-0Published: 29 October 2019
eBook ISBN: 978-3-319-56436-4Published: 08 March 2018
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XXIV, 700
Topics: Probability Theory and Stochastic Processes, Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations, Economic Theory/Quantitative Economics/Mathematical Methods