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Mean Field Games with a Quadratic Hamiltonian: A Constructive Scheme

  • Olivier Guéant
Chapter
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 12)

Abstract

Mean field games models describing the limit case of a large class of stochastic differential games, as the number of players goes to +, were introduced by Lasry and Lions [C R Acad Sci Paris 343(9/10) (2006); Jpn. J. Math. 2(1) (2007)]. We use a change of variables to transform the mean field games equations into a system of simpler coupled partial differential equations in the case of a quadratic Hamiltonian. This system is then used to exhibit a monotonic scheme to build solutions of the mean field games equations.

Keywords

Mean field games Forward–backward equations Monotonic schemes 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.UFR de Mathématiques, Laboratoire Jacques-Louis LionsUniversité Paris-DiderotParisFrance

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