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Regularity Theory for Mean-Field Game Systems

2016-09-14 Mathematics
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Release : 2016-09-14
Genre : Mathematics
Kind : eBook
Book Rating : 343/5 ( reviews)

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Book Synopsis Regularity Theory for Mean-Field Game Systems by : Diogo A. Gomes

Download or read book Regularity Theory for Mean-Field Game Systems written by Diogo A. Gomes. This book was released on 2016-09-14. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.

Probabilistic Theory of Mean Field Games with Applications II

2018-03-08 Mathematics
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Release : 2018-03-08
Genre : Mathematics
Kind : eBook
Book Rating : 366/5 ( reviews)

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Book Synopsis Probabilistic Theory of Mean Field Games with Applications II by : René Carmona

Download or read book Probabilistic Theory of Mean Field Games with Applications II written by René Carmona. This book was released on 2018-03-08. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probabilistic Theory of Mean Field Games with Applications I

2018-03-01 Mathematics
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Release : 2018-03-01
Genre : Mathematics
Kind : eBook
Book Rating : 202/5 ( reviews)

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Book Synopsis Probabilistic Theory of Mean Field Games with Applications I by : René Carmona

Download or read book Probabilistic Theory of Mean Field Games with Applications I written by René Carmona. This book was released on 2018-03-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Advances in Dynamic and Mean Field Games

2018-01-03 Mathematics
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Release : 2018-01-03
Genre : Mathematics
Kind : eBook
Book Rating : 195/5 ( reviews)

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Book Synopsis Advances in Dynamic and Mean Field Games by : Joseph Apaloo

Download or read book Advances in Dynamic and Mean Field Games written by Joseph Apaloo. This book was released on 2018-01-03. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and graduate students.

Mean Field Games

2021-01-19 Mathematics
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Release : 2021-01-19
Genre : Mathematics
Kind : eBook
Book Rating : 373/5 ( reviews)

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Book Synopsis Mean Field Games by : Yves Achdou

Download or read book Mean Field Games written by Yves Achdou. This book was released on 2021-01-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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