Long-Time Behavior of First-Order Mean Field Games on Euclidean Space

Piermarco Cannarsa (), Wei Cheng (), Cristian Mendico () and Kaizhi Wang ()
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Piermarco Cannarsa: Università di Roma “Tor Vergata”
Wei Cheng: Nanjing University
Cristian Mendico: Università di Roma “Tor Vergata”
Kaizhi Wang: Shanghai Jiao Tong University

Dynamic Games and Applications, 2020, vol. 10, issue 2, No 3, 390 pages

Abstract: Abstract The aim of this paper is to study the long-time behavior of solutions to deterministic mean field games systems on Euclidean space. This problem was addressed on the torus $${\mathbb {T}}^n$$Tn in Cardaliaguet (Dyn Games Appl 3:473–488, 2013), where solutions are shown to converge to the solution of a certain ergodic mean field games system on $${\mathbb {T}}^n$$Tn. By adapting the approach in Fathi and Maderna (Nonlinear Differ Equ Appl NoDEA 14:1–27, 2007), we identify structural conditions on the Lagrangian, under which the corresponding ergodic system can be solved in $${\mathbb {R}}^{n}$$Rn. Then, we show that time-dependent solutions converge to the solution of such a stationary system on all compact subsets of the whole space.

Keywords: Mean field games; Weak KAM theory; Long-time behavior; Viscosity solutions; 35A01; 35B40; 35F21 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13235-019-00321-3

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