On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players

Vassili N. Kolokoltsov, Marianna Troeva, Wei Yang

Research output: Contribution to journalArticle

20 Citations (Scopus)

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 coeffcients. We show that individual optimal strategies based on any solution of the main consistency equation for the backward-forward mean led game model represent a 1=N-Nash equilibrium for approximating systems of N agents.
Original languageEnglish
Pages (from-to)208-230
Number of pages23
JournalDynamic Games and Applications
Volume4
Issue number2
Early online date1 Oct 2013
DOIs
Publication statusPublished - 1 Dec 2014

Keywords

  • nonlinear diffusion
  • kinetic equation
  • forward-backward system
  • dynamic law of large numbers
  • rates of convergence
  • tagged particle

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