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

@article{Cirant2018TheVS, title={The variational structure and time-periodic solutions for mean-field games systems}, author={Marco Cirant and L. Nurbekyan}, journal={arXiv: Analysis of PDEs}, year={2018} }

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… Expand

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