@inbook{e491359db1df482fae3a3f74bab0c9ce,

title = "FBSDEs and the Solution of MFGs Without Common Noise",

abstract = "The goal of this chapter is to develop a general methodology for the purpose of solving mean field games using the forward-backward SDE formulations introduced in Chapter 3 We first proceed with a careful analysis of forward-backward mean field SDEs, that is of McKean-Vlasov type, which shows how Schauder{\textquoteright}s fixed point theorem can be used to prove existence of a solution. As a by-product, we derive two general solvability results for mean field games: first from the FBSDE representation of the value function, and then from the stochastic Pontryagin maximum principle. In the last section, we revisit some of the examples introduced in the first chapter, and illustrate how our general existence results can be applied.",

author = "Ren{\'e} Carmona and Fran{\c c}ois Delarue",

note = "Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG.",

year = "2018",

doi = "10.1007/978-3-319-58920-6_4",

language = "English (US)",

series = "Probability Theory and Stochastic Modelling",

publisher = "Springer Nature",

pages = "215--345",

booktitle = "Probability Theory and Stochastic Modelling",

address = "United States",

}