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The master equation and the convergence problem in mean field games /
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While originating in economics, this theory now has applications in areas as di...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, New Jersey :
Princeton University Press,
2019.
|
| Colección: | Annals of mathematics studies ;
no. 201. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Cardaliaguet, Pierre, |e author. | |
| 245 | 1 | 4 | |a The master equation and the convergence problem in mean field games / |c Pierre Cardaliaguet, François Delarue, Jean-Michel Lasry, Pierre-Louis Lions. |
| 264 | 1 | |a Princeton, New Jersey : |b Princeton University Press, |c 2019. | |
| 264 | 4 | |c ©2019 | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies ; |v Number 201 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (EBSCO, viewed June 21, 2019). | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t 1. Introduction -- |t 2. Presentation of the Main Results -- |t 3. A Starter: The First-Order Master Equation -- |t 4. Mean Field Game System with a Common Noise -- |t 5. The Second-Order Master Equation -- |t 6. Convergence of the Nash System -- |t A. Appendix -- |t References -- |t Index |
| 520 | |a This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While originating in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players, as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics. | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Game theory. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Mean field theory. | |
| 650 | 6 | |a Théorie des jeux. | |
| 650 | 6 | |a Équations différentielles. | |
| 650 | 6 | |a Théorie de champ moyen. | |
| 650 | 7 | |a MATHEMATICS |x Applied. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Game Theory. |2 bisacsh | |
| 650 | 7 | |a Differential equations |2 fast | |
| 650 | 7 | |a Game theory |2 fast | |
| 650 | 7 | |a Mean field theory |2 fast | |
| 700 | 1 | |a Delarue, François, |d 1976- |e author. | |
| 700 | 1 | |a Lasry, J. M., |e author. | |
| 700 | 1 | |a Lions, P. L. |q (Pierre-Louis), |e author. | |
| 776 | 0 | 8 | |i Print version: |a Cardaliaguet, Pierre. |t Master Equation and the Convergence Problem in Mean Field Games : (ams-201). |d Princeton : Princeton University Press, ©2019 |z 9780691190709 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 201. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctvckq7qf |z Texto completo |
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