  This paper focuses on linear-quadratic (LQ for short) mean-field games
described by forward-backward stochastic differential equations (FBSDEs for
short), in which the individual control region is postulated to be convex. The
decentralized strategies and consistency condition are represented by a kind of
coupled mean-field FBSDEs with projection operators. The well-posedness of
consistency condition system is obtained using the monotonicity condition
method. The $\epsilon$-Nash equilibrium property is discussed as well.
