“…First, the game problem has the Stackelberg or leader-follower feature, which means the two players act as different roles during the game. Thus the usual approach to deal with game problems, such as Yong [25], Hamadène [7], Wu [23], An and Øksendal [1], Wang and Yu [21], Yu [29], Hui and Xiao [10,11], Shi [17] where the two players act as equivalent roles, does not apply. Second, the game problem has the asymmetric information between the two players, which was not considered in Yong [26], Øksendal et al [15] and Bensoussan et al [5].…”