IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v12y2021i1p7-d480221.html
   My bibliography  Save this article

Quantum Mean-Field Games with the Observations of Counting Type

Author

Listed:
  • Vassili N. Kolokoltsov

    (Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
    Higher School of Economics, 109028 Moscow, Russia)

Abstract

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ -Nash equilibrium for the corresponding N -player quantum game. The existence of solutions is suggested as an interesting open problem.

Suggested Citation

  • Vassili N. Kolokoltsov, 2021. "Quantum Mean-Field Games with the Observations of Counting Type," Games, MDPI, vol. 12(1), pages 1-14, January.
  • Handle: RePEc:gam:jgames:v:12:y:2021:i:1:p:7-:d:480221
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/12/1/7/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2073-4336/12/1/7/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Belavkin, Viacheslav P., 1992. "Quantum stochastic calculus and quantum nonlinear filtering," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 171-201, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Vassili N. Kolokoltsov, 2022. "Dynamic Quantum Games," Dynamic Games and Applications, Springer, vol. 12(2), pages 552-573, June.

    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. Romuald Élie & Emma Hubert & Thibaut Mastrolia & Dylan Possamaï, 2021. "Mean–field moral hazard for optimal energy demand response management," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 399-473, January.
    2. Fu, Guanxing & Horst, Ulrich, 2017. "Mean Field Games with Singular Controls," Rationality and Competition Discussion Paper Series 22, CRC TRR 190 Rationality and Competition.
    3. Qinglong Zhou & Gaofeng Zong, 2016. "Time-Inconsistent Stochastic Linear-quadratic Differential Game," Papers 1607.00638, arXiv.org.
    4. Alain Bensoussan & Guiyuan Ma & Chi Chung Siu & Sheung Chi Phillip Yam, 2022. "Dynamic mean–variance problem with frictions," Finance and Stochastics, Springer, vol. 26(2), pages 267-300, April.
    5. Arvind V. Shrivats & Dena Firoozi & Sebastian Jaimungal, 2022. "A mean‐field game approach to equilibrium pricing in solar renewable energy certificate markets," Mathematical Finance, Wiley Blackwell, vol. 32(3), pages 779-824, July.
    6. Dena Firoozi & Arvind V Shrivats & Sebastian Jaimungal, 2021. "Principal agent mean field games in REC markets," Papers 2112.11963, arXiv.org, revised Jun 2022.
    7. Luchnikov, I. & Métivier, D. & Ouerdane, H. & Chertkov, M., 2021. "Super-relaxation of space–time-quantized ensemble of energy loads to curtail their synchronization after demand response perturbation," Applied Energy, Elsevier, vol. 285(C).
    8. Zongxia Liang & Keyu Zhang, 2023. "Time-inconsistent mean field and n-agent games under relative performance criteria," Papers 2312.14437, arXiv.org, revised Apr 2024.
    9. René Carmona & Gökçe Dayanıklı & Mathieu Laurière, 2022. "Mean Field Models to Regulate Carbon Emissions in Electricity Production," Dynamic Games and Applications, Springer, vol. 12(3), pages 897-928, September.
    10. Shuzhen Yang, 2020. "Bellman type strategy for the continuous time mean-variance model," Papers 2005.01904, arXiv.org, revised Jul 2020.
    11. Boualem Djehiche & Minyi Huang, 2016. "A Characterization of Sub-game Perfect Equilibria for SDEs of Mean-Field Type," Dynamic Games and Applications, Springer, vol. 6(1), pages 55-81, March.
    12. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    13. Berkay Anahtarci & Can Deha Kariksiz & Naci Saldi, 2023. "Q-Learning in Regularized Mean-field Games," Dynamic Games and Applications, Springer, vol. 13(1), pages 89-117, March.
    14. 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.
    15. Pellegrini, Clément, 2010. "Existence, uniqueness and approximation of the jump-type stochastic Schrodinger equation for two-level systems," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1722-1747, August.
    16. Piotr Więcek, 2024. "Multiple-Population Discrete-Time Mean Field Games with Discounted and Total Payoffs: The Existence of Equilibria," Dynamic Games and Applications, Springer, vol. 14(4), pages 997-1026, September.
    17. Romuald Elie & Thibaut Mastrolia & Dylan Possamaï, 2019. "A Tale of a Principal and Many, Many Agents," Mathematics of Operations Research, INFORMS, vol. 44(2), pages 440-467, May.
    18. Vassili N. Kolokoltsov, 2022. "Dynamic Quantum Games," Dynamic Games and Applications, Springer, vol. 12(2), pages 552-573, June.
    19. Bo, Lijun & Wang, Shihua & Zhou, Chao, 2024. "A mean field game approach to optimal investment and risk control for competitive insurers," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 202-217.
    20. Li Miao & Lina Wang & Shuai Li & Haitao Xu & Xianwei Zhou, 2019. "Optimal defense strategy based on the mean field game model for cyber security," International Journal of Distributed Sensor Networks, , vol. 15(2), pages 15501477198, February.

    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:gam:jgames:v:12:y:2021:i:1:p:7-:d:480221. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.