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The Variational Structure and Time-Periodic Solutions for Mean-Field Games Systems
Minimax theory and its applications, Tome 3 (2018) no. 2
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We observe that mean-field game (MFG) systems admit a two-player infinite-dimensional general-sum differential game formulation. We show that particular regimes of this game reduce to previously known variational principles. Furthermore, based on the game-perspective we derive new variational formulations for first-order MFG systems with congestion. Finally, we use these findings to prove the existence of time-periodic solutions for viscous MFG systems with a coupling that is not a non-decreasing function of density.
Mots-clés : Infinite-dimensional differential games, congestion problems, saddle-point formula tion 
@article{MTA_2018_3_2_a2,
     author = {Marco Cirant,Levon Nurbekyan},
     title = {The {Variational} {Structure} and {Time-Periodic} {Solutions} for {Mean-Field} {Games} {Systems}},
     journal = {Minimax theory and its applications},
     year = {2018},
     volume = {3},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2018_3_2_a2/}
}
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Marco Cirant,Levon Nurbekyan. The Variational Structure and Time-Periodic Solutions for Mean-Field Games Systems. Minimax theory and its applications, Tome 3 (2018) no. 2. http://geodesic.mathdoc.fr/item/MTA_2018_3_2_a2/