| Issue |
ESAIM: M2AN
Volume 51, Number 1, January-February 2017
|
|
|---|---|---|
| Page(s) | 63 - 88 | |
| DOI | https://doi.org/10.1051/m2an/2016015 | |
| Published online | 28 November 2016 | |
A numerical method for Mean Field Games on networks
1 Dip. di Matematica, “Sapienza” Università di Roma, p.le A.
Moro 5, 00185 Roma, Italy.
cacace@mat.uniroma1.it
2 Dip. di Scienze di Base e Applicate per l’Ingegneria,
“Sapienza” Università di Roma, via Scarpa 16, 00161 Roma, Italy.
camilli@sbai.uniroma1.it
3 Dip. di Ingegneria dell’Informazione, Università di Padova,
via Gradenigo 6/B, 35131 Padova, Italy.
claudio.marchi@unipd.it
Received:
14
July
2015
Revised:
25
November
2015
Accepted:
23
February
2016
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.
Mathematics Subject Classification: 91A15 / 35R02 / 35B30 / 49N70 / 65M06
Key words: Networks / mean field games / finite difference schemes / convergence
© EDP Sciences, SMAI 2016
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