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 
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/
@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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