Long time average of mean field games

Pierre Cardaliaguet; Jean-Michel Lasry; Pierre-Louis Lions; Alessio Porretta

doi:10.3934/nhm.2012.7.279

Article Contents

2012, Volume 7, Issue 2: 279-301. Doi: 10.3934/nhm.2012.7.279

This issue Previous Article A semi-discrete approximation for a first order mean field game problem Next Article A-priori estimates for stationary mean-field games

Long time average of mean field games

1.
Ceremade, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16
2.
56 Rue d'Assas, 75006 Paris
3.
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientica 1, 00133 Roma

Received: October 31, 2011

Revised: February 29, 2012

Published: May 2012

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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.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35K55.

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