The Linear Quadratic Difference Nash Game Under $d$-Step-Delay Information Sharing Pattern

In this paper, we study the discrete time linear quadratic Nash game under $d$-step-delay information sharing pattern. The main contribution is to provide the explicit Nash strategy. Combining with the dynamic programming, the optimal controllers are the linear combination of the common estimation and the innovation of the local information, while the gain matrices are in the form of the Riccati equations.