Mean Field Games
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Probabilistic Theory Of Mean Field Games With Applications I
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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-01
Probabilistic Theory Of Mean Field Games With Applications I written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-01 with Mathematics categories.
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 results to 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.
Mean Field Games
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Author : Yves Achdou
language : en
Publisher: Springer Nature
Release Date : 2021-01-19
Mean Field Games written by Yves Achdou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-19 with Mathematics categories.
This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.
Mean Field Games And Mean Field Type Control Theory
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Author : Alain Bensoussan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-16
Mean Field Games And Mean Field Type Control Theory written by Alain Bensoussan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-16 with Science categories.
Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem.
Probabilistic Theory Of Mean Field Games With Applications Ii
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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-08
Probabilistic Theory Of Mean Field Games With Applications Ii written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Mathematics categories.
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 II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. 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.
Paris Princeton Lectures On Mathematical Finance 2010
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Author : Areski Cousin
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-29
Paris Princeton Lectures On Mathematical Finance 2010 written by Areski Cousin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-29 with Mathematics categories.
The Paris-Princeton Lectures in Financial Mathematics, of which this is the fourth volume, publish cutting-edge research in self-contained, expository articles from outstanding specialists - established or on the rise! The aim is to produce a series of articles that can serve as an introductory reference source for research in the field. The articles are the result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with five articles by: 1. Areski Cousin, Monique Jeanblanc and Jean-Paul Laurent, 2. Stéphane Crépey, 3. Olivier Guéant, Jean-Michel Lasry and Pierre-Louis Lions, 4. David Hobson and 5. Peter Tankov.
Mean Field Theory
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Author : Vladimir M Kolomietz
language : en
Publisher: World Scientific
Release Date : 2020-05-08
Mean Field Theory written by Vladimir M Kolomietz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-08 with Science categories.
This book describes recent theoretical and experimental developments in the study of static and dynamic properties of atomic nuclei, many-body systems of strongly interacting neutrons and protons. The theoretical approach is based on the concept of the mean field, describing the motion of a nucleon in terms of a self-consistent single-particle potential well which approximates the interactions of a nucleon with all the other nucleons. The theoretical approaches also go beyond the mean-field approximation by including the effects of two-body collisions.The self-consistent mean-field approximation is derived using the effective nucleon-nucleon Skyrme-type interaction. The many-body problem is described next in terms of the Wigner phase space of the one-body density, which provides a basis for semi-classical approximations and leads to kinetic equations. Results of static properties of nuclei and properties associated with small amplitude dynamics are also presented. Relaxation processes, due to nucleon-nucleon collisions, are discussed next, followed by instability and large amplitude motion of excited nuclei. Lastly, the book ends with the dynamics of hot nuclei. The concepts and methods developed in this book can be used for describing properties of other many-body systems.
Mean Field Games
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Author : François Delarue
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-14
Mean Field Games written by François Delarue and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-14 with Mathematics categories.
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.
Existence And Stability Of Nash Equilibrium
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Author : Guilherme Carmona
language : en
Publisher: World Scientific
Release Date : 2013
Existence And Stability Of Nash Equilibrium written by Guilherme Carmona and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Business & Economics categories.
The book aims at describing the recent developments in the existence and stability of Nash equilibrium. The two topics are central to game theory and economics and have been extensively researched. Recent results on existence and stability of Nash equilibrium are scattered and the relationship between them has not been explained clearly. The book will make these results easily accessible and understandable to researchers in the field. Book jacket.