Probabilistic Theory of Mean Field Games with Applications I

Released on by René Carmona
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  • Probabilistic Theory of Mean Field Games with Applications I Book Detail

  • Author : René Carmona
  • Release Date : 2018-03-01
  • Publisher : Springer
  • Genre : Mathematics
  • Pages : 728
  • ISBN 13 : 3319589202
  • File Size : 2,2 MB
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Probabilistic Theory of Mean Field Games with Applications I by René Carmona PDF Summary

Book Description: 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.

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Mean Field Games

Mean Field Games

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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 equilibr

Mean Field Games

Mean Field Games

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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, 202