Linear-quadratic Stochastic Leaders-followers Differential Game with An Incomplete Information Structure

In order to adapt to the hierarchical network architecture of the industrial internet of things (IIoT), a kind of linear-quadratic (LQ) leaders-followers stochastic Stackelberg differential game with an incomplete information structure is studied in this paper, where the term “incomplete” means that at least one agent in games makes decisions based on partial information. The game is divided into two decision-making stages. The feedback Stackelberg-Nash equilibrium point and the corresponding dynamic evolution equations of the game are derived by using the stochastic maximum principle under partial information and the undetermined coefficient method. These results can be extended and applied to the description of the IIoT.