Geodesic
Hypoelliptic Mean Field Games – a Case Study
Minimax theory and its applications, Tome 5 (2020) no. 2
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We study hypoelliptic mean-field games (MFG) that arise in stochastic control problems of degenerate diffusions. Here, we consider MFGs with quadratic Hamiltonians and prove the existence and uniqueness of solutions. Our main tool is the Hopf-Cole transform that converts the MFG into an eigenvalue problem. We prove the existence of a principal eigenvalue and a positive eigenfunction, which are then used to construct the unique solution to the original MFG.
Mots-clés : Mean-Field Games, stationary problems, hypoelliptic operator, eigenvalue problems 
@article{MTA_2020_5_2_a7,
     author = {Ermal Feleqi,Diogo Gomes and Teruo Tada},
     title = {Hypoelliptic {Mean} {Field} {Games} {\textendash} a {Case} {Study}},
     journal = {Minimax theory and its applications},
     year = {2020},
     volume = {5},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a7/}
}
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Ermal Feleqi,Diogo Gomes; Teruo Tada. Hypoelliptic Mean Field Games – a Case Study. Minimax theory and its applications, Tome 5 (2020) no. 2. http://geodesic.mathdoc.fr/item/MTA_2020_5_2_a7/