Overview
- 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
Part of the book series: Probability Theory and Stochastic Modelling (PTSM, volume 83)
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Table of contents (7 chapters)
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Front Matter
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The Probabilistic Approach to Mean Field Games
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Front Matter
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Analysis on Wasserstein Space and Mean Field Control
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Front Matter
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Back Matter
Keywords
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 I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its resultsto the analysis of stochastic mean field control problems.
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Probabilistic Theory of Mean Field Games with Applications I
Book Subtitle: Mean Field FBSDEs, Control, and Games
Authors: René Carmona, François Delarue
Series Title: Probability Theory and Stochastic Modelling
DOI: https://doi.org/10.1007/978-3-319-58920-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2018
Hardcover ISBN: 978-3-319-56437-1Published: 12 March 2018
Softcover ISBN: 978-3-030-13260-6Published: 01 November 2019
eBook ISBN: 978-3-319-58920-6Published: 01 March 2018
Series ISSN: 2199-3130
Series E-ISSN: 2199-3149
Edition Number: 1
Number of Pages: XXVI, 714
Topics: Probability Theory and Stochastic Processes, Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations, Economic Theory/Quantitative Economics/Mathematical Methods