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Long Time Average of First Order Mean Field Games and Weak KAM Theory

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  • P. Cardaliaguet

Abstract

We show that the long time average of solutions of first order mean field game systems in finite horizon is governed by an ergodic system of mean field game type. The well-posedness of the latter system and the uniqueness of the ergodic constant rely on weak KAM theory. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:3:y:2013:i:4:p:473-488
    DOI: 10.1007/s13235-013-0091-x
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    Citations

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    Cited by:

    1. Piotr Więcek, 2020. "Discrete-Time Ergodic Mean-Field Games with Average Reward on Compact Spaces," Dynamic Games and Applications, Springer, vol. 10(1), pages 222-256, March.
    2. Martin Frank & Michael Herty & Torsten Trimborn, 2019. "Microscopic Derivation of Mean Field Game Models," Papers 1910.13534, arXiv.org.
    3. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    4. 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.
    5. Diogo A. Gomes & Levon Nurbekyan & Mariana Prazeres, 2018. "One-Dimensional Stationary Mean-Field Games with Local Coupling," Dynamic Games and Applications, Springer, vol. 8(2), pages 315-351, June.
    6. Olivier Gallay & Fariba Hashemi & Max-Olivier Hongler, 2019. "Imitation, Proximity, And Growth — A Collective Swarm Dynamics Approach," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-43, August.

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