Long time average of mean field games | Zendy

Pierre Cardaliaguet | Zendy; JeanMichel Lasry | Zendy; PierreLouis Lions | Zendy; Alessio Porretta | Zendy

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Long time average of mean field games

Author(s) -

Pierre Cardaliaguet,

JeanMichel Lasry,

PierreLouis Lions,

Alessio Porretta

Publication year - 2012

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2012.7.279

Subject(s) - ergodic theory , mean field theory , infinity , mathematics , convergence (economics) , exponential function , exponential growth , hamiltonian system , rate of convergence , mathematical analysis , physics , computer science , economics , quantum mechanics , computer network , channel (broadcasting) , economic growth

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. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdA

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