| Softcover ISBN: | 978-1-4704-5586-6 |
| Product Code: | PSAPM/78 |
| List Price: | $120.00 |
| MAA Member Price: | $108.00 |
| AMS Member Price: | $96.00 |
| eBook ISBN: | 978-1-4704-6801-9 |
| Product Code: | PSAPM/78.E |
| List Price: | $120.00 |
| MAA Member Price: | $108.00 |
| AMS Member Price: | $96.00 |
| Softcover ISBN: | 978-1-4704-5586-6 |
| eBook: ISBN: | 978-1-4704-6801-9 |
| Product Code: | PSAPM/78.B |
| List Price: | $240.00 $180.00 |
| MAA Member Price: | $216.00 $162.00 |
| AMS Member Price: | $192.00 $144.00 |
| Softcover ISBN: | 978-1-4704-5586-6 |
| Product Code: | PSAPM/78 |
| List Price: | $120.00 |
| MAA Member Price: | $108.00 |
| AMS Member Price: | $96.00 |
| eBook ISBN: | 978-1-4704-6801-9 |
| Product Code: | PSAPM/78.E |
| List Price: | $120.00 |
| MAA Member Price: | $108.00 |
| AMS Member Price: | $96.00 |
| Softcover ISBN: | 978-1-4704-5586-6 |
| eBook ISBN: | 978-1-4704-6801-9 |
| Product Code: | PSAPM/78.B |
| List Price: | $240.00 $180.00 |
| MAA Member Price: | $216.00 $162.00 |
| AMS Member Price: | $192.00 $144.00 |
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Book DetailsProceedings of Symposia in Applied MathematicsVolume: 78; 2021; 284 ppMSC: Primary 35; 49; 91; 93
This volume is based on lectures delivered at the 2020 AMS Short Course “Mean Field Games: Agent Based Models to Nash Equilibria,” held January 13–14, 2020, in Denver, Colorado.
Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects.
The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.
ReadershipGraduate students and researchers interested in partial differential equations, probability theory, interacting particle systems, control theory, game theory, multi-agent models, and mathematical finance.
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Table of Contents
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An overview of the theory of mean field games
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Roland Malhamé and Christy Graves — Mean Field Games: A paradigm for individual-mass interctions
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François Delarue — Mean field games and master equation
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Connection with games with finitely many players
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Daniel Lacker — The mean field game convergence problem
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Kavita Ramanan — Refined convergence results for interacting diffusions and mean-field games
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Applications and numerical methods
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René Carmona — Applications of Mean Field Games in financial engineering and economic theory
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Mathieu Laurière — Numerical methods for mean field games and mean field type control
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Additional Material
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
This volume is based on lectures delivered at the 2020 AMS Short Course “Mean Field Games: Agent Based Models to Nash Equilibria,” held January 13–14, 2020, in Denver, Colorado.
Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects.
The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.
Graduate students and researchers interested in partial differential equations, probability theory, interacting particle systems, control theory, game theory, multi-agent models, and mathematical finance.
-
An overview of the theory of mean field games
-
Roland Malhamé and Christy Graves — Mean Field Games: A paradigm for individual-mass interctions
-
François Delarue — Mean field games and master equation
-
Connection with games with finitely many players
-
Daniel Lacker — The mean field game convergence problem
-
Kavita Ramanan — Refined convergence results for interacting diffusions and mean-field games
-
Applications and numerical methods
-
René Carmona — Applications of Mean Field Games in financial engineering and economic theory
-
Mathieu Laurière — Numerical methods for mean field games and mean field type control
