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.

The variational structure and time-periodic solutions for mean-field games systems / Cirant, Marco; Nurbekyan, Levon. - In: MINIMAX THEORY AND ITS APPLICATIONS. - ISSN 2199-1413. - 3:2(2018), pp. 227-260.

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

Cirant, Marco;
2018-01-01

Abstract

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.
2018
The variational structure and time-periodic solutions for mean-field games systems / Cirant, Marco; Nurbekyan, Levon. - In: MINIMAX THEORY AND ITS APPLICATIONS. - ISSN 2199-1413. - 3:2(2018), pp. 227-260.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2857648
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