Mean field games based on the stable-like processes

Vassili Kolokoltsov, Marianna Troeva, Wei Yang

Research output: Contribution to journalArticle

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 L´evy-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
Article number33
Pages33
Number of pages65
JournalMatematicheskaya Teoriya Igr i Ee Prilozheniya
Volume5
Issue number4
Publication statusPublished - 2013

Fingerprint

Mean Field
Game
Empirical Measures
Nonlinear Process
Kinetic Equation
Nash Equilibrium
Markov Process
Generator

Keywords

  • stable-lilke processes
  • kinetic equation
  • forward-backward system
  • dynamic law of large numbers
  • rates of convergence
  • tagged particle
  • ε-Nash equilibrium

Cite this

Kolokoltsov, V., Troeva, M., & Yang, W. (2013). Mean field games based on the stable-like processes. Matematicheskaya Teoriya Igr i Ee Prilozheniya, 5(4), 33. [33].
Kolokoltsov, Vassili ; Troeva, Marianna ; Yang, Wei. / Mean field games based on the stable-like processes. In: Matematicheskaya Teoriya Igr i Ee Prilozheniya. 2013 ; Vol. 5, No. 4. pp. 33.
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Kolokoltsov, V, Troeva, M & Yang, W 2013, 'Mean field games based on the stable-like processes' Matematicheskaya Teoriya Igr i Ee Prilozheniya, vol. 5, no. 4, 33, pp. 33.

Mean field games based on the stable-like processes. / Kolokoltsov, Vassili; Troeva, Marianna; Yang, Wei.

In: Matematicheskaya Teoriya Igr i Ee Prilozheniya, Vol. 5, No. 4, 33, 2013, p. 33.

Research output: Contribution to journalArticle

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KW - rates of convergence

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