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arXiv · 1602.08520

Homogenization of a mean field game system in the small noise limit

Annalisa Cesaroni·Nicolas Dirr·Claudio Marchi
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Abstract

This paper concerns the simultaneous effect of homogenization and of the small noise limit for a $2^{\textrm {nd}}$ order mean field games (MFG) system with local coupling and quadratic Hamiltonian. We show under some additional assumptions that the solutions of our system converge to a solution of an effective $1^{\textrm {st}}$ order system whose effective operators are defined through a cell problem which is a $2^{\textrm {nd}}$ order system of ergodic MFG type. We provide several properties of the effective operators and we show that in general the effective system looses the MFG structure.

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Annalisa Cesaroni, Nicolas Dirr, Claudio Marchi. 2016-02-26. Homogenization of a mean field game system in the small noise limit. https://arxiv.org/abs/1602.08520

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