Geodesic
A numerical method for Mean Field Games on networks
Cacace, Simone1 ; Camilli, Fabio2  ; Marchi, Claudio3
1 Dip. di Matematica, “Sapienza” Università di Roma, p.le A. Moro 5, 00185 Roma, Italy.
2 Dip. di Scienze di Base e Applicate per l’Ingegneria, “Sapienza” Università di Roma, via Scarpa 16, 00161 Roma, Italy.
3 Dip. di Ingegneria dell’Informazione, Università di Padova, via Gradenigo 6/B, 35131 Padova, Italy.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 63-88

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2016015
Classification : 91A15, 35R02, 35B30, 49N70, 65M06
Keywords: Networks, mean field games, finite difference schemes, convergence

Cacace, Simone 1 ; Camilli, Fabio 2 ; Marchi, Claudio 3

1 Dip. di Matematica, “Sapienza” Università di Roma, p.le A. Moro 5, 00185 Roma, Italy.
2 Dip. di Scienze di Base e Applicate per l’Ingegneria, “Sapienza” Università di Roma, via Scarpa 16, 00161 Roma, Italy.
3 Dip. di Ingegneria dell’Informazione, Università di Padova, via Gradenigo 6/B, 35131 Padova, Italy. 
@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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :