Wheelers Books

This title is firm sale. Please select carefully as returns are not accepted.

The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201)
  

The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) (Hardback)

By Cardaliaguet, Pierre
By Delarue, Francois
By Lasry, Jean-Michel
By Lions, Pierre-Louis

This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While originating in economics, this theory now has applica...tions in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players, as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
Read more

ISBN 9780691190709
Format Hardback
Alternate Format(s) View All (1 other possible title(s) available)
Language English (translated from: English)
Series Annals of Mathematics Studies (part: 2)
Availability
Internationally sourced on backorder; allow 4-8 weeks

Full details for this title

ISBN-13 9780691190709
Stock Available
Status Internationally sourced on backorder; allow 4-8 weeks
Publisher unlisted
Imprint Princeton University Press
Publication Country United States United States
Format Hardback
 › 1 other possible formats available
Language English
Translated from English
Author(s) By Cardaliaguet, Pierre
By Delarue, Francois
By Lasry, Jean-Michel
By Lions, Pierre-Louis
Series Annals of Mathematics Studies (part: 2)
Category Differential Equations
Game Theory
Number of Pages 224
Dimensions Width: 156mm
Height: 235mm
Dewey Code Not specified
Weight Not specified - defaults to 1,000g
Interest Age 19+ years
Reading Age 19+ years
NBS Text Mathematics
ONIX Text College/higher education;Professional and scholarly

TOP