  A linear quadratic (LQ) stochastic optimization problem with delay involving
weakly-coupled large population is investigated in this paper. Different to
classic mean field (MF) game, here agents cooperate with each other to minimize
the so-called \emph{social} objective. With the aid of \emph{delayed
person-by-person optimality} principle, one arrives at an auxiliary LQ delayed
control problem by decentralized information. A decentralized strategy is
obtained by feat of an MF type anticipated forward-backward stochastic
differential delay equation (AFBSDDE) consistency condition. The discounting
method with delay feature is employed to solve the consistency condition
system. Finally, by some estimates of AFBSDDEs we derive the asymptotic social
optimality.
