On the long time convergence of potential MFG

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01850874
Contributor : Marco Masoero <>
Submitted on : Friday, July 27, 2018 - 6:29:37 PM
Last modification on : Friday, April 19, 2019 - 4:54:47 PM
Long-term archiving on : Sunday, October 28, 2018 - 2:14:40 PM

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Marco Masoero. On the long time convergence of potential MFG. 2018. ⟨hal-01850874⟩

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