A semi-discrete approximation for a first order mean field game problem

Fabio Camilli, Francisco Silva
2012 Networks and Heterogeneous Media  
In this article we consider a model first order mean field game problem, introduced by J.M. Lasry and P.L. Lions in [17] . Its solution (v, m) can be obtained as the limit of the solutions of the second order mean field game problems, when the noise parameter tends to zero (see [17] ). We propose a semi-discrete in time approximation of the system and, under natural assumptions, we prove that it is well posed and that it converges to (v, m) when the discretization parameter tends to zero.
more » ... ends to zero. Keywords. First order mean field game, semi-discrete in time approximation.
doi:10.3934/nhm.2012.7.263 fatcat:4t3vc5gnjvhmbotc5ewofw4pxe