Language: English
Published by John Wiley & Sons Inc, 1980
ISBN 10: 0471021490 ISBN 13: 9780471021490
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Language: English
Published by Princeton University Press, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
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Published by Presses Universitaires de France - PUF, 1998
ISBN 10: 2130473393 ISBN 13: 9782130473398
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Published by Princeton University Press, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
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Published by Princeton University Press, 2019
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ISBN 10: 0691190704 ISBN 13: 9780691190709
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Published by Princeton University Press, US, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
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Paperback. Condition: New. 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 it originated 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.
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Published by Princeton University Press, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
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Published by Princeton University Press, US, 2019
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Paperback. Condition: New. 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 it originated 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.
Language: English
Published by Princeton University Press, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
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Language: English
Published by John Wiley & Sons Inc, 1979
ISBN 10: 0471021490 ISBN 13: 9780471021490
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Published by Princeton University Press, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
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Published by Princeton University Press, 2019
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Published by Princeton University Press, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
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Published by Springer-Verlag GmbH, 2011
ISBN 10: 3642146597 ISBN 13: 9783642146596
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Condition: Sehr gut. Zustand: Sehr gut | Seiten: 359 | Sprache: Englisch | Produktart: Bücher | Keine Beschreibung verfügbar.
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Published by Princeton University Press, US, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
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Paperback. Condition: New. 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 it originated 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.
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Language: English
Published by Princeton University Press, 2019
ISBN 10: 0691190704 ISBN 13: 9780691190709
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Language: English
Published by Princeton University Press, US, 2019
ISBN 10: 0691190712 ISBN 13: 9780691190716
Seller: Rarewaves.com UK, London, United Kingdom
Paperback. Condition: New. 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 it originated 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.
Language: English
Published by Princeton University Press, 2019
ISBN 10: 0691190704 ISBN 13: 9780691190709
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Published by Princeton University Press, US, 2019
ISBN 10: 0691190704 ISBN 13: 9780691190709
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Hardback. Condition: New. 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 it originated 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.
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Language: English
Published by Princeton University Press, US, 2019
ISBN 10: 0691190704 ISBN 13: 9780691190709
Seller: Rarewaves USA United, OSWEGO, IL, U.S.A.
Hardback. Condition: New. 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 it originated 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.