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Probabilistic theory of mean field games with applications II: mean field games with common noise and master equations

By: Contributor(s): Material type: TextTextSeries: Probability theory and stochastic modelling; No. 84Publication details: Springer 2018 ChamDescription: xxiv, 697 p. Includes bibliographical references and indexISBN:
  • 9783319564357
Subject(s): DDC classification:
  • 530.144 C2P7
Summary: 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. https://www.springer.com/gp/book/9783319564357
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Holdings
Item type Current library Item location Collection Shelving location Call number Status Date due Barcode
Books Vikram Sarabhai Library Rack 33-A / Slot 1699 (2nd Floor, East Wing) Non-fiction General Stacks 530.144 C2P7-II (Browse shelf(Opens below)) Available 201412

Table of contents

Foreword
Preface to Volume II
Part I: MFGs with a Common Noise
Optimization in a Random Environment
MFGs with a Common Noise: Strong and Weak Solutions
Solving MFGs with a Common Noise
Part II: The Master Equation, Convergence, and Approximation Problems
The Master Field and the Master Equation
Classical Solutions to the Master Equation
Convergence and Approximations
Epilogue to Volume II
Extensions for Volume II
References
Indices.

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.

https://www.springer.com/gp/book/9783319564357

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