Mean Field Games and Nonlinear Markov Processes

Vassili N. Kolokoltsov; Jiajie Li; Wei Yang

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arXiv · 1112.3744

Mean Field Games and Nonlinear Markov Processes

Vassili N. Kolokoltsov·Jiajie Li·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 Lévy-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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Vassili N. Kolokoltsov, Jiajie Li, Wei Yang. 2012-04-06. Mean Field Games and Nonlinear Markov Processes. https://arxiv.org/abs/1112.3744

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