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In this article, we are concerned with the zero-sum stochastic differential game problems with the cost functional depending not only onbut also onThe main approach is the anticipated backward stochastic differential equations under weaker conditions. For these equations, we prove the existence and uniqueness theorem and the comparison theorems. Then, by using these techniques, we get the saddle-point strategy for the zero-sum stochastic differential games when the Isaacs’ condition holds.

Anticipated backward stochastic differential equations and their applications to zero-sum stochastic differential games