A Mean Field Game of Sequential Testing

Abstract

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.