We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence of the scheme and we also propose a least squares method for the solution of the discrete system. Numerical experiments are carried out.
Accepté le :
DOI : 10.1051/m2an/2016015
Mots clés : Networks, mean field games, finite difference schemes, convergence
@article{M2AN_2017__51_1_63_0,
author = {Cacace, Simone and Camilli, Fabio and Marchi, Claudio},
title = {A numerical method for {Mean} {Field} {Games} on networks},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {63--88},
publisher = {EDP-Sciences},
volume = {51},
number = {1},
year = {2017},
doi = {10.1051/m2an/2016015},
mrnumber = {3601001},
zbl = {1356.91028},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2016015/}
}
TY - JOUR AU - Cacace, Simone AU - Camilli, Fabio AU - Marchi, Claudio TI - A numerical method for Mean Field Games on networks JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 63 EP - 88 VL - 51 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2016015/ DO - 10.1051/m2an/2016015 LA - en ID - M2AN_2017__51_1_63_0 ER -
%0 Journal Article %A Cacace, Simone %A Camilli, Fabio %A Marchi, Claudio %T A numerical method for Mean Field Games on networks %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 63-88 %V 51 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2016015/ %R 10.1051/m2an/2016015 %G en %F M2AN_2017__51_1_63_0
Cacace, Simone; Camilli, Fabio; Marchi, Claudio. A numerical method for Mean Field Games on networks. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 63-88. doi : 10.1051/m2an/2016015. http://www.numdam.org/articles/10.1051/m2an/2016015/
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