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This paper is concerned with an overlapping information linear-quadratic (LQ)Stackelberg stochastic differential game with two leaders and two followers,where the diffusion terms of the state equation contain both the control andstate variables. A distinct feature lies in that, the noisy informationavailable to the leaders and the followers may be asymmetric and haveoverlapping part. Using a coupled system of Riccati equations, the followersfirst solve an LQ nonzero-sum stochastic differential Nash game with partialinformation, and then the leaders solve a partial information LQ nonzero-sumstochastic differential Nash game driven by a conditional mean-field typeforward-backward stochastic differential equation (CMF-FBSDE). By maximumprinciple, completion of squares and decoupling methods, the state-estimatefeedback representation of the Stackelberg-Nash equilibrium is obtained.

An overlapping information linear-quadratic Stackelberg stochastic differential game with two leaders and two followers