Long Time Average of Mean Field Games with a Nonlocal Coupling
Porretta, Alessio; Lions, Pierre-Louis; Lasry, Jean-Michel; Cardaliaguet, Pierre (2013), Long Time Average of Mean Field Games with a Nonlocal Coupling, SIAM Journal on Control and Optimization, 51, 5, p. 3558–3591. http://dx.doi.org/10.1137/120904184
TypeArticle accepté pour publication ou publié
Journal nameSIAM Journal on Control and Optimization
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Abstract (EN)We study the long time average, as the time horizon tends to infinity, of the solution of a mean field game system with a nonlocal coupling. We show an exponential convergence to the solution of the associated stationary ergodic mean field game. Proofs rely on semiconcavity estimates and smoothing properties of the linearized system.
Subjects / Keywordsparabolic equations; long time behavior; mean field games
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