IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v4y2014i2p208-230.html
   My bibliography  Save this article

On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players

Author

Listed:
  • Vassili Kolokoltsov
  • Marianna Troeva
  • Wei Yang

Abstract

In this paper, we investigate the mean field games of N agents who are weakly coupled via the empirical measures. The underlying dynamics of the representative agent is assumed to be a controlled nonlinear diffusion process with variable coefficients. We show that individual optimal strategies based on any solution of the main consistency equation for the backward-forward mean filed game model represent a 1/N-Nash equilibrium for approximating systems of N agents. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Vassili Kolokoltsov & Marianna Troeva & Wei Yang, 2014. "On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players," Dynamic Games and Applications, Springer, vol. 4(2), pages 208-230, June.
    • Handle: RePEc:spr:dyngam:v:4:y:2014:i:2:p:208-230
    DOI: 10.1007/s13235-013-0095-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s13235-013-0095-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s13235-013-0095-6?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. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    2. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    3. Cepeda, Eduardo & Fournier, Nicolas, 2011. "Smoluchowski's equation: Rate of convergence of the Marcus-Lushnikov process," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1411-1444, June.
    4. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    5. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    6. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    7. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
    8. Jourdain, Benjamin & Roux, Raphaël, 2011. "Convergence of a stochastic particle approximation for fractional scalar conservation laws," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 957-988, May.
    9. repec:dau:papers:123456789/3001 is not listed on IDEAS
    10. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
    11. Piasecki, Jarosław & Sadlej, Krzysztof, 2003. "Deterministic limit of tagged particle motion: Effect of reflecting boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 171-180.
    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. Jean-Pierre Fouque & Zhaoyu Zhang, 2018. "Mean Field Game with Delay: A Toy Model," Risks, MDPI, vol. 6(3), pages 1-17, September.
    2. Fabio Priuli, 2015. "Linear-Quadratic $$N$$ N -Person and Mean-Field Games: Infinite Horizon Games with Discounted Cost and Singular Limits," Dynamic Games and Applications, Springer, vol. 5(3), pages 397-419, September.
    3. Alain Bensoussan & Boualem Djehiche & Hamidou Tembine & Sheung Chi Phillip Yam, 2020. "Mean-Field-Type Games with Jump and Regime Switching," Dynamic Games and Applications, Springer, vol. 10(1), pages 19-57, March.
    4. Mathieu Laurière & Olivier Pironneau, 2016. "Dynamic Programming for Mean-Field Type Control," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 902-924, June.
    5. V. N. Kolokoltsov & O. A. Malafeyev, 2017. "Mean-Field-Game Model of Corruption," Dynamic Games and Applications, Springer, vol. 7(1), pages 34-47, March.

    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. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    2. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    3. 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.
    4. Yakut, Oguz, 2021. "Implementation of hydraulically driven barrel shooting control by utilizing artificial neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1206-1223.
    5. X. Qin & G. Huang, 2009. "An Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(4), pages 661-695, March.
    6. Md. Yousuf Gazi & Khandakar Tahmida Tafhim, 2019. "Investigation of Heavy-mineral Deposits Using Multispectral Satellite Imagery in the Eastern Coastal Margin of Bangladesh," Earth Sciences Malaysia (ESMY), Zibeline International Publishing, vol. 3(2), pages 16-22, October.
    7. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    8. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    9. Tansel, Aysit & Karao?lan, Deniz, 2016. "The Causal Effect of Education on Health Behaviors: Evidence from Turkey," IZA Discussion Papers 10020, Institute of Labor Economics (IZA).
    10. Timothy K.M. Beatty & Erling Røed Larsen & Dag Einar Sommervoll, 2005. "Measuring the Price of Housing Consumption for Owners in the CPI," Discussion Papers 427, Statistics Norway, Research Department.
    11. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    12. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    13. repec:dau:papers:123456789/5389 is not listed on IDEAS
    14. Wong, Patricia J.Y., 2015. "Eigenvalues of a general class of boundary value problem with derivative-dependent nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 908-930.
    15. 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.
    16. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    17. Chein-Shan Liu & Zhuojia Fu & Chung-Lun Kuo, 2017. "Directional Method of Fundamental Solutions for Three-dimensional Laplace Equation," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 112-123, December.
    18. Alberto Cabada & Om Kalthoum Wanassi, 2020. "Existence Results for Nonlinear Fractional Problems with Non-Homogeneous Integral Boundary Conditions," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    19. Odysseas Kosmas & Pieter Boom & Andrey P. Jivkov, 2021. "On the Geometric Description of Nonlinear Elasticity via an Energy Approach Using Barycentric Coordinates," Mathematics, MDPI, vol. 9(14), pages 1-16, July.
    20. Hossein Karshenas & Concha Bielza & Pedro Larrañaga, 2015. "Interval-based ranking in noisy evolutionary multi-objective optimization," Computational Optimization and Applications, Springer, vol. 61(2), pages 517-555, June.
    21. B. S. C. Campello & C. T. L. S. Ghidini & A. O. C. Ayres & W. A. Oliveira, 2022. "A residual recombination heuristic for one-dimensional cutting stock problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 194-220, April.

    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:spr:dyngam:v:4:y:2014:i:2:p:208-230. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.