We consider a model of mean field games system defined on a time interval [0, T] and investigate its asymptotic behavior as the horizon T tends to infinity. We show that the system, rescaled in a suitable way, converges to a stationary ergodic mean field game. The convergence holds with exponential rate and relies on energy estimates and the Hamiltonian structure of the system. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM

Cardaliaguet, P., Lasry, J., Lions, P., Porretta, A. (2012). Long time average of mean field games. NETWORKS AND HETEROGENEOUS MEDIA, 7(2), 279-301 [10.3934/nhm.2012.7.279].

Long time average of mean field games

PORRETTA, ALESSIO
2012-01-01

Abstract

We consider a model of mean field games system defined on a time interval [0, T] and investigate its asymptotic behavior as the horizon T tends to infinity. We show that the system, rescaled in a suitable way, converges to a stationary ergodic mean field game. The convergence holds with exponential rate and relies on energy estimates and the Hamiltonian structure of the system. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM
2012
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Mean Field Games; large time behavior; ergodic problem
L'articolo compare in un numero della rivista NHM interamente dedicato alla nascente teoria dei mean field games. La scelta della rivista fu dunque obbligata dal contesto dovuto alla gentile iniziativa degli editori di NHM, a cui decidemmo di offrire un importante contributo tra i primi ottenuti in questo ambito.
Cardaliaguet, P., Lasry, J., Lions, P., Porretta, A. (2012). Long time average of mean field games. NETWORKS AND HETEROGENEOUS MEDIA, 7(2), 279-301 [10.3934/nhm.2012.7.279].
Cardaliaguet, P; Lasry, J; Lions, P; Porretta, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/90393
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