Mean Field Games and Nonlinear Markov Processes

Vassili N. Kolokoltsov, Jiajie Li, Wei Yang

Research output: Working paper

Abstract

In this paper, we investigate the mean field games with K classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process associated with rather general integro-differential generators of Levy-Khintchine type (with variable coefficients), with the major stress on applications to stable and stable-like processes, as well as their various modifications like tempered stable-like processes or their mixtures with diffusions. We show that nonlinear measure-valued kinetic equations describing the dynamic law of large numbers limit for system with large number N of agents are solvable and that their solutions represent 1/N-Nash equilibria for approximating systems of N agents.
LanguageEnglish
Place of PublicationIthaca
Pages1-63
Number of pages63
Publication statusUnpublished - 2012

Fingerprint

Nonlinear Process
Markov Process
Mean Field
Game
Empirical Measures
Law of large numbers
Kinetic Equation
Variable Coefficients
Nash Equilibrium
Generator

Keywords

  • stable-like processes
  • kinetic equation
  • Hamilton-Jacobi-Bellman equation
  • dynamic law of large numbers
  • propagation of chaos
  • rates of convergence
  • tagged particle

Cite this

Kolokoltsov, V. N., Li, J., & Yang, W. (2012). Mean Field Games and Nonlinear Markov Processes. (pp. 1-63). Ithaca.
Kolokoltsov, Vassili N. ; Li, Jiajie ; Yang, Wei. / Mean Field Games and Nonlinear Markov Processes. Ithaca, 2012. pp. 1-63
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Kolokoltsov, VN, Li, J & Yang, W 2012 'Mean Field Games and Nonlinear Markov Processes' Ithaca, pp. 1-63.

Mean Field Games and Nonlinear Markov Processes. / Kolokoltsov, Vassili N.; Li, Jiajie; Yang, Wei.

Ithaca, 2012. p. 1-63.

Research output: Working paper

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T1 - Mean Field Games and Nonlinear Markov Processes

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AU - Yang, Wei

PY - 2012

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N2 - In this paper, we investigate the mean field games with K classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process associated with rather general integro-differential generators of Levy-Khintchine type (with variable coefficients), with the major stress on applications to stable and stable-like processes, as well as their various modifications like tempered stable-like processes or their mixtures with diffusions. We show that nonlinear measure-valued kinetic equations describing the dynamic law of large numbers limit for system with large number N of agents are solvable and that their solutions represent 1/N-Nash equilibria for approximating systems of N agents.

AB - In this paper, we investigate the mean field games with K classes of agents who are weakly coupled via the empirical measure. The underlying dynamics of the representative agents is assumed to be a controlled nonlinear Markov process associated with rather general integro-differential generators of Levy-Khintchine type (with variable coefficients), with the major stress on applications to stable and stable-like processes, as well as their various modifications like tempered stable-like processes or their mixtures with diffusions. We show that nonlinear measure-valued kinetic equations describing the dynamic law of large numbers limit for system with large number N of agents are solvable and that their solutions represent 1/N-Nash equilibria for approximating systems of N agents.

KW - stable-like processes

KW - kinetic equation

KW - Hamilton-Jacobi-Bellman equation

KW - dynamic law of large numbers

KW - propagation of chaos

KW - rates of convergence

KW - tagged particle

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Kolokoltsov VN, Li J, Yang W. Mean Field Games and Nonlinear Markov Processes. Ithaca. 2012, p. 1-63.