Mean Field Games and Nonlinear Markov Processes

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Kolokoltsov, Vassili N. and Li, Jiajie and Yang, Wei (2012) Mean Field Games and Nonlinear Markov Processes. Preprint / Working Paper. arXiv.org, Ithaca. (Unpublished) (http://arxiv.org/abs/1112.3744)

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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.

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