Geodesic
A numerical method for Mean Field Games on networks
Cacace, Simone 1   ; Camilli, Fabio 2 idref     ; 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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 1, pp. 63-88 Cet article a éte moissonné depuis la source Numdam

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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.

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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. 
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     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},
     year = {2017},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {1},
     doi = {10.1051/m2an/2016015},
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     zbl = {1356.91028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2016015/}
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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

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