Mean field games based on the stable-like processes

Kolokoltsov, Vassili and Troeva, Marianna and Yang, Wei (2013) Mean field games based on the stable-like processes. Matematicheskaya Teoriya Igr i Ee Prilozheniya, 5 (4). p. 33. 33.

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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.