  We study the existence of strong solutions for mean-field forward-backward
stochastic differential equations (FBSDEs) with measurable coefficients and
their implication on the Nash equilibrium of a multi-population mean-field
game. More specifically, we allow the coefficients to be discontinuous in the
forward process and non-Lipschitz continuous concerning their time-sectional
distribution. Using the Pontryagin stochastic maximum principle and the
martingale approach, we apply our existence result to a multi-population
mean-field game (MPMFG) model where the interacting agents in the system are
grouped into multiple populations. Each population shares the same objective
function, and we take changes in population sizes into consideration.
