Mean Field Games and Nonlinear Markov Processes

Details Mean Field Games and Nonlinear Markov Processes Mean Field Games and Nonlinear Markov Processes

2011-12-16

arxiv.org/abs/1112.3744v2

Mathematics

Probability

60 pages, results reported at SIAM (Contol) July 2011, Vienna ECCS'11 Sep. 2011, Warwick (Topics in Control) Dec. 2011, 2nd ve

Scientific paper

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). 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.

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