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

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.

arXiv comment31 pages

References in corpus (3)

• Weak solutions for mean field games with congestion
• One-dimensional, forward-forward mean-field games with congestion
• Monotone numerical methods for finite-state mean-field games

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