IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v523y2019icp310-325.html
   My bibliography  Save this article

Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation

Author

Listed:
  • Bonnemain, Thibault
  • Ullmo, Denis

Abstract

Motivated by the study of a Mean Field Game toy model called the “seminar problem”, we consider the Fokker–Planck equation in the small noise regime for a specific drift field. This gives us the opportunity to discuss the application to diffusion problem of the WKB approach “à la Maslov (Maslov and Fedoriuk, 1981)”, making it possible to solve directly the time dependent problem in an especially transparent way.

Suggested Citation

  • Bonnemain, Thibault & Ullmo, Denis, 2019. "Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 310-325.
    • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:310-325
    DOI: 10.1016/j.physa.2019.01.143
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119301499
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.01.143?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    2. Swiecicki, Igor & Gobron, Thierry & Ullmo, Denis, 2016. "“Phase diagram” of a mean field game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 467-485.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    2. Amir Mosavi & Pedram Ghamisi & Yaser Faghan & Puhong Duan, 2020. "Comprehensive Review of Deep Reinforcement Learning Methods and Applications in Economics," Papers 2004.01509, arXiv.org.
    3. A. Bensoussan & K. Sung & S. Yam, 2013. "Linear–Quadratic Time-Inconsistent Mean Field Games," Dynamic Games and Applications, Springer, vol. 3(4), pages 537-552, December.
    4. Amirhosein Mosavi & Yaser Faghan & Pedram Ghamisi & Puhong Duan & Sina Faizollahzadeh Ardabili & Ely Salwana & Shahab S. Band, 2020. "Comprehensive Review of Deep Reinforcement Learning Methods and Applications in Economics," Mathematics, MDPI, vol. 8(10), pages 1-42, September.
    5. Kashif Mehmood & Muhammad Tabish Niaz & Hyung Seok Kim, 2019. "A Power Control Mean Field Game Framework for Battery Lifetime Enhancement of Coexisting Machine-Type Communications," Energies, MDPI, vol. 12(20), pages 1-23, October.
    6. Ivan Cherednik, 2019. "Artificial intelligence approach to momentum risk-taking," Papers 1911.08448, arXiv.org, revised Mar 2020.
    7. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Papers 2105.07213, arXiv.org.
    8. Jin Ma & Eunjung Noh, 2020. "Equilibrium Model of Limit Order Books: A Mean-field Game View," Papers 2002.12857, arXiv.org, revised Mar 2020.
    9. Philippe Casgrain & Sebastian Jaimungal, 2018. "Mean-Field Games with Differing Beliefs for Algorithmic Trading," Papers 1810.06101, arXiv.org, revised Dec 2019.
    10. Michael Ludkovski & Xuwei Yang, 2017. "Mean Field Game Approach to Production and Exploration of Exhaustible Commodities," Papers 1710.05131, arXiv.org.
    11. Philippe Casgrain & Sebastian Jaimungal, 2020. "Mean‐field games with differing beliefs for algorithmic trading," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 995-1034, July.
    12. Martin Frank & Michael Herty & Torsten Trimborn, 2019. "Microscopic Derivation of Mean Field Game Models," Papers 1910.13534, arXiv.org.
    13. Pierre Gosselin & Aïleen Lotz & Marc Wambst, 2021. "A statistical field approach to capital accumulation," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(4), pages 817-908, October.
    14. Qing Tang & Fabio Camilli, 2020. "Variational Time-Fractional Mean Field Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 573-588, June.
    15. Minyi Huang, 2013. "A Mean Field Capital Accumulation Game with HARA Utility," Dynamic Games and Applications, Springer, vol. 3(4), pages 446-472, December.
    16. Benazzoli, Chiara & Campi, Luciano & Di Persio, Luca, 2019. "ε-Nash equilibrium in stochastic differential games with mean-field interaction and controlled jumps," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    17. Marcel Nutz & Yuchong Zhang, 2019. "A Mean Field Competition," Management Science, INFORMS, vol. 44(4), pages 1245-1263, November.
    18. Kalai, Ehud & Shmaya, Eran, 2018. "Large strategic dynamic interactions," Journal of Economic Theory, Elsevier, vol. 178(C), pages 59-81.
    19. Erhan Bayraktar & Yuchong Zhang, 2016. "A rank based mean field game in the strong formulation," Papers 1603.06312, arXiv.org, revised Oct 2016.
    20. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach [On the Existence and Uniqueness of Stationary Equilibrium in Bewley Economies with Production]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:310-325. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.