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Long time average of mean field games

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

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