  We introduce a mean field game for a family of filtering problems related to
the classic sequential testing of the drift of a Brownian motion. To the best
of our knowledge this work presents the first treatment of mean field filtering
games with stopping and an unobserved common noise in the literature. We show
that the game is well-posed, characterize the solution, and establish the
existence of an equilibrium under certain assumptions. We also perform
numerical studies for several examples of interest.
