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

Author

Listed:
  • Piermarco Cannarsa

    (Università di Roma “Tor Vergata”)

  • Wei Cheng

    (Nanjing University)

  • Cristian Mendico

    (Università di Roma “Tor Vergata”)

  • Kaizhi Wang

    (Shanghai Jiao Tong University)

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.

Suggested Citation

  • Piermarco Cannarsa & Wei Cheng & Cristian Mendico & Kaizhi Wang, 2020. "Long-Time Behavior of First-Order Mean Field Games on Euclidean Space," Dynamic Games and Applications, Springer, vol. 10(2), pages 361-390, June.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:2:d:10.1007_s13235-019-00321-3
    DOI: 10.1007/s13235-019-00321-3
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    References listed on IDEAS

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    1. P. Cardaliaguet, 2013. "Long Time Average of First Order Mean Field Games and Weak KAM Theory," Dynamic Games and Applications, Springer, vol. 3(4), pages 473-488, December.
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