  The goal of this paper is to demonstrate that common noise may serve as an
exploration noise for learning the solution of a mean field game. This concept
is here exemplified through a toy linear-quadratic model, for which a suitable
form of common noise has already been proven to restore existence and
uniqueness. We here go one step further and prove that the same form of common
noise may force the convergence of the learning algorithm called `fictitious
play', and this without any further potential or monotone structure. Several
numerical examples are provided in order to support our theoretical analysis.
