Geodesic
An Ergodic Problem for Mean Field Games: Qualitative Properties and Numerical Simulations
Minimax theory and its applications, Tome 3 (2018) no. 2
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This paper is devoted to some qualitative descriptions and some numerical results for ergodic Mean Field Games systems which arise, e.g., in the homogenization with a small noise limit. We shall consider either power type potentials or logarithmic type ones. In both cases, we shall establish some qualitative properties of the effective Hamiltonian ̄ H and of the effective drift ̄ b. In particular we shall provide two cases where the effective system keeps/looses the Mean Field Games structure, namely where ∇P ̄ H(P,α) coincides or not with ̄ b(P,α).
Mots-clés : Mean field games, periodic homogenization, small noise limit, ergodic problems, continuous dependence of solution on parameters, finite difference schemes 
@article{MTA_2018_3_2_a1,
     author = {Simone Cacace,Fabio Camilli,Annalisa Cesaroni,Claudio Marchi},
     title = {An {Ergodic} {Problem} for {Mean} {Field} {Games:} {Qualitative} {Properties} and {Numerical} {Simulations}},
     journal = {Minimax theory and its applications},
     year = {2018},
     volume = {3},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2018_3_2_a1/}
}
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Simone Cacace,Fabio Camilli,Annalisa Cesaroni,Claudio Marchi. An Ergodic Problem for Mean Field Games: Qualitative Properties and Numerical Simulations. Minimax theory and its applications, Tome 3 (2018) no. 2. http://geodesic.mathdoc.fr/item/MTA_2018_3_2_a1/