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Long time average of mean field games

Cardaliaguet, Pierre; Lasry, Jean-Michel; Lions, Pierre-Louis; Porretta, Alessio (2012), Long time average of mean field games, Networks and Heterogeneous Media, 7, 2, p. 279-301. http://dx.doi.org/10.3934/nhm.2012.7.279

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Type
Article accepté pour publication ou publié
Date
2012
Journal name
Networks and Heterogeneous Media
Volume
7
Number
2
Publisher
AIMS
Pages
279-301
Publication identifier
Metadata
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Author(s)
Cardaliaguet, Pierre
Lasry, Jean-Michel
Lions, Pierre-Louis
Porretta, Alessio
Abstract (EN)
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.
Subjects / Keywords
Mean Field Games; large time behavior; ergodic problem