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On the long time convergence of potential MFG

Masoero, Marco (2019), On the long time convergence of potential MFG, NoDEA. Nonlinear Differential Equations and Applications, 26, p. 32. 10.1007/s00030-019-0560-z

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
NoDEA. Nonlinear Differential Equations and Applications
Volume
26
Publisher
Springer
Pages
32
Publication identifier
Metadata
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Author(s)
Masoero, Marco
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We look at the long time behavior of potential Mean Field Games (briefly MFG) using some standard tools from weak KAM theory. We first show that the time-dependent minimization problem converges to an ergodic constant −λ, then we provide a class of examples where the value of the stationary MFG minimization problem is strictly greater than −λ. This will imply that the trajectories of the time-dependent MFG system do not converge to static equilibria.
Subjects / Keywords
mean field games; convergence