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...
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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton ; NJ
Princeton University Press
[2019]
|
| Series: | Annals of mathematics studies
Number 201 |
| Subjects: | |
| Online Access: | DE-1043 DE-1046 DE-858 DE-898 DE-859 DE-860 DE-91 DE-20 DE-706 DE-739 Volltext |
| Summary: | 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 |
| Physical Description: | 1 Online-Ressource (X, 212 Seiten) |
| ISBN: | 9780691193717 |
| DOI: | 10.1515/9780691193717 |
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| isbn | 9780691193717 |
| language | English |
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| spelling | Cardaliaguet, Pierre (DE-588)1026854687 aut The master equation and the convergence problem in mean field games Pierre Cardaliaguet ; Pierre-Louis Lions ; Jean-Michel Lasry ; François Delarue Princeton ; NJ Princeton University Press [2019] © 2019 1 Online-Ressource (X, 212 Seiten) txt rdacontent c rdamedia cr rdacarrier Annals of mathematics studies Number 201 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 In English MATHEMATICS / Game Theory bisacsh Differential equations Game theory Mean field theory Delarue, François 1976- (DE-588)1156345413 aut Lasry, Jean-Michel (DE-588)171091930 aut Erscheint auch als Druck-Ausgabe 978-0-691-19071-6 Annals of mathematics studies Number 201 (DE-604)BV040389493 201 https://doi.org/10.1515/9780691193717 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Cardaliaguet, Pierre Delarue, François 1976- Lasry, Jean-Michel The master equation and the convergence problem in mean field games Annals of mathematics studies MATHEMATICS / Game Theory bisacsh Differential equations Game theory Mean field theory |
| title | The master equation and the convergence problem in mean field games |
| title_auth | The master equation and the convergence problem in mean field games |
| title_exact_search | The master equation and the convergence problem in mean field games |
| title_full | The master equation and the convergence problem in mean field games Pierre Cardaliaguet ; Pierre-Louis Lions ; Jean-Michel Lasry ; François Delarue |
| title_fullStr | The master equation and the convergence problem in mean field games Pierre Cardaliaguet ; Pierre-Louis Lions ; Jean-Michel Lasry ; François Delarue |
| title_full_unstemmed | The master equation and the convergence problem in mean field games Pierre Cardaliaguet ; Pierre-Louis Lions ; Jean-Michel Lasry ; François Delarue |
| title_short | The master equation and the convergence problem in mean field games |
| title_sort | the master equation and the convergence problem in mean field games |
| topic | MATHEMATICS / Game Theory bisacsh Differential equations Game theory Mean field theory |
| topic_facet | MATHEMATICS / Game Theory Differential equations Game theory Mean field theory |
| url | https://doi.org/10.1515/9780691193717 |
| volume_link | (DE-604)BV040389493 |
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