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Probabilistic Theory of Mean Field Games with Applications I

Mean Field FBSDEs, Control, and Games

  • René Carmona
  • François Delarue

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 83)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. The Probabilistic Approach to Mean Field Games

    1. Front Matter
      Pages 1-1
    2. René Carmona, François Delarue
      Pages 3-65
    3. René Carmona, François Delarue
      Pages 67-127
    4. René Carmona, François Delarue
      Pages 129-213
    5. René Carmona, François Delarue
      Pages 215-345
  3. Analysis on Wasserstein Space and Mean Field Control

    1. Front Matter
      Pages 347-347
    2. René Carmona, François Delarue
      Pages 349-512
    3. René Carmona, François Delarue
      Pages 513-617
    4. René Carmona, François Delarue
      Pages 619-680
  4. Back Matter
    Pages 681-713

About this book

Introduction

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.

Keywords

Mean Field Games Mean Field Control Master Equations Forward Backward Stochastic Differential Equations Analysis on Wasserstein Space Game Theory Optimal Stochastic Control Applications in Economics and Social Science

Authors and affiliations

  • René Carmona
    • 1
  • François Delarue
    • 2
  1. 1.ORFE Department, Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Institut Universitaire de France & Laboratoire J.A. DieudonnéUniversité Nice Sophia AntipolisNiceFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-58920-6
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-56437-1
  • Online ISBN 978-3-319-58920-6
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • Buy this book on publisher's site