DCDS
A semi-Lagrangian scheme for a degenerate second order mean field game system
Elisabetta Carlini Francisco J. Silva
In this paper we study a fully discrete Semi-Lagrangian approximation of a second order Mean Field Game system, which can be degenerate. We prove that the resulting scheme is well posed and, if the state dimension is equals to one, we prove a convergence result. Some numerical simulations are provided, evidencing the convergence of the approximation and also the difference between the numerical results for the degenerate and non-degenerate cases.
keywords: degenerate second order system Mean field games numerical methods. semi-Lagrangian schemes convergence analysis
DCDS
A model problem for Mean Field Games on networks
Fabio Camilli Elisabetta Carlini Claudio Marchi
In [14], Guéant, Lasry and Lions considered the model problem ``What time does meeting start?'' as a prototype for a general class of optimization problems with a continuum of players, called Mean Field Games problems. In this paper we consider a similar model, but with the dynamics of the agents defined on a network. We discuss appropriate transition conditions at the vertices which give a well posed problem and we present some numerical results.
keywords: Mean Field Games numerical methods. stochastic optimal control Networks

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