Mean Field Games and Nonlinear Markov Processes

Vassili N. Kolokoltsov, Jiajie Li, Wei Yang

Research output: Working paper

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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 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.
Original languageEnglish
Place of PublicationIthaca
Pages1-63
Number of pages63
Publication statusUnpublished - 2012

Keywords

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

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