Year: 2012
Type: article
Abstract: Mean field games have been introduced by J.-M. Lasry and P.-L. Lions in [13, 14, 15] as the limit case of stochastic differential games when the number of players goes to $+\infty$. In the case of quadratic costs, we present two changes of variables that allow to transform the mean field games (MFG) equations into two simpler systems of equations. The first change of variables, introduced in [11], leads to two heat equations with nonlinear source terms. The second change of variables, which is introduced for the first time in this paper, leads to two Hamilton-Jacobi-Bellman equations. Numerical methods based on these equations are presented and numerical experiments are carried out.
Source: Networks and Heterogeneous Media
Author: Olivier Guéant
Institutions: Laboratoire Jacques-Louis Lions, Université Paris Diderot
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: bronze
OpenAlex ID: W2019816035