A leader-follower stochastic linear quadratic differential game with time delay

In this paper, we are concerned with the leader-follower stochastic differential game of Itô type with time delay appearing in the leader’s control. The open-loop solution is explicitly given in the form of the conditional expectation with respect to several symmetric Riccati equations. The key technique is to establish the nonhomogeneous relationship between the forward variables and the backward ones obtained in the optimization problems of both the follower and the leader.

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