Open-Loop Leader-Follower Stochastic Differential Game with State Delay and Related FBSDEs

In this paper, we consider the leader-follower stochastic differential game with state delay. The open-loop strategies in a linear-quadratic (LQ) differential delayed game are constructed by generalized fully coupled forward-backward stochastic differential equation (FBSDE). We obtain the solvability of the LQ leader-follower game with state delay by showing the existence and uniqueness of the solution for the FBSDE.