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.
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Acknowledgements
The research of Vassili N. Kolokoltsov has been partially supported by IPI of the Russian Academy of Science, Russian Foundation for Basic Research (Grants No. 11-01-12026, No. 12-07-00115), and the Ministry of Education and Science of the Russian Federation (Grant No. 4402). The research of Marianna Troeva has been partially supported by the Ministry of Education and Science of the Russian Federation (Grant No. 4402).
The authors also would like to thank the referees for their valuable suggestions.
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Kolokoltsov, V.N., Troeva, M. & Yang, W. On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players. Dyn Games Appl 4, 208–230 (2014). https://doi.org/10.1007/s13235-013-0095-6
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DOI: https://doi.org/10.1007/s13235-013-0095-6