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

doi:10.1007/s13235-013-0095-6

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

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

22 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 language	English
Pages (from-to)	208-230
Number of pages	23
Journal	Dynamic Games and Applications
Volume	4
Issue number	2
Early online date	1 Oct 2013
DOIs	https://doi.org/10.1007/s13235-013-0095-6
Publication status	Published - 1 Dec 2014

Keywords

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

Access to Document

10.1007/s13235-013-0095-6

Cite this

@article{c1da781c62ce494aacd0a9e118e7683c,

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

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.",

keywords = "nonlinear diffusion, kinetic equation, forward-backward system, dynamic law of large numbers, rates of convergence, tagged particle",

author = "Kolokoltsov, {Vassili N.} and Marianna Troeva and Wei Yang",

year = "2014",

month = dec,

day = "1",

doi = "10.1007/s13235-013-0095-6",

language = "English",

volume = "4",

pages = "208--230",

journal = "Dynamic Games and Applications ",

issn = "2153-0785",

number = "2",

}

TY - JOUR

T1 - On the rate of convergence for the mean-field approximation of controlled diffusions with large number of players

AU - Kolokoltsov, Vassili N.

AU - Troeva, Marianna

AU - Yang, Wei

PY - 2014/12/1

Y1 - 2014/12/1

N2 - 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.

AB - 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.

KW - nonlinear diffusion

KW - kinetic equation

KW - forward-backward system

KW - dynamic law of large numbers

KW - rates of convergence

KW - tagged particle

UR - http://link.springer.com/journal/13235

U2 - 10.1007/s13235-013-0095-6

DO - 10.1007/s13235-013-0095-6

M3 - Article

VL - 4

SP - 208

EP - 230

JO - Dynamic Games and Applications

JF - Dynamic Games and Applications

SN - 2153-0785

IS - 2

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Cite this