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

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  • 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
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    References listed on IDEAS

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    2. 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.
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    4. 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.
    5. 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.
    6. 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.
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    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.

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