  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 and
state variables. A distinct feature lies in that, the noisy information
available to the leaders and the followers may be asymmetric and have
overlapping part. Using a coupled system of Riccati equations, the followers
first solve an LQ nonzero-sum stochastic differential Nash game with partial
information, and then the leaders solve a partial information LQ nonzero-sum
stochastic differential Nash game driven by a conditional mean-field type
forward-backward stochastic differential equation (CMF-FBSDE). By maximum
principle, completion of squares and decoupling methods, the state-estimate
feedback representation of the Stackelberg-Nash equilibrium is obtained.
