A  model problem for Mean Field Games on networks

Fabio Camilli; Elisabetta Carlini; Claudio Marchi

doi:10.3934/dcds.2015.35.4173

Article Contents

2015, Volume 35, Issue 9: 4173-4192. Doi: 10.3934/dcds.2015.35.4173

This issue Previous Article Continuous Riemann solvers for traffic flow at a junction Next Article High order variational integrators in the optimal control of mechanical systems

A model problem for Mean Field Games on networks

1.
"Sapienza" Università di Roma, Dip. di Scienze di Base e Applicate per l'Ingegneria, via Scarpa 16, 0161 Roma
2.
"Sapienza" Università di Roma, Dipartimento di Matematica, P.le A. Moro 5, 00185 Roma
3.
Dipartimento di Matematica Pura ed Applicata, Università di Padova, via Trieste 63, 35121 Padova

Received: February 28, 2014

Revised: August 31, 2014

Published: May 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 91A15, 35R02; Secondary: 35B30, 49N70, 65M06.

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References

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