Probabilistic Theory of Mean Field Games with Applications II

Mean Field Games with Common Noise and Master Equations

  • René Carmona
  • François Delarue

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 84)

Table of contents

  1. Front Matter
    Pages i-xxiv
  2. MFGs with a Common Noise

    1. Front Matter
      Pages 1-1
    2. René Carmona, François Delarue
      Pages 3-106
    3. René Carmona, François Delarue
      Pages 107-153
    4. René Carmona, François Delarue
      Pages 155-235
  3. The Master Equation, Convergence, and Approximation Problems

    1. Front Matter
      Pages 237-237
    2. René Carmona, François Delarue
      Pages 239-321
    3. René Carmona, François Delarue
      Pages 323-446
    4. René Carmona, François Delarue
      Pages 447-539
    5. René Carmona, François Delarue
      Pages 541-663
  4. Back Matter
    Pages 665-697

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 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.

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/10.1007/978-3-319-56436-4
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-56435-7
  • Online ISBN 978-3-319-56436-4
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • About this book