The variational structure and time-periodic solutions for mean-field games systems

2018/04/24 by Marco Cirant, Cirant, Marco, Levon Nurbekyan +1
Mathematics · #35A01 #35Q91 #35Q93 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35A01 #msc:35Q91 #msc:35Q93

paper · pdf · doi:10.48550/arxiv.1804.08943

31 pages

arxiv created 2018/04/24 · arxiv updated 2018/04/25

Abstract

Here, 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.

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