Mean field games based on the stable-like processes

Vassili Kolokoltsov, Marianna Troeva, Wei Yang

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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.
Original languageEnglish
Article number33
Pages (from-to)33
Number of pages65
JournalMatematicheskaya Teoriya Igr i Ee Prilozheniya
Volume5
Issue number4
Publication statusPublished - 2013

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].