Matrix block formulation for Closed-Loop Memoryless Discrete-Time Nash solution

This paper studies Nash strategy for N-players discrete-time linear-quadratic games, in the framework of closed-loop memoryless information structure. Such a strategy being strongly time consistent, an original approach, based on step by step backward in time computation, is provided to facilitate the design of associated controls and value functions. It is shown that this matrix block formulation allows to recover the Coupled Riccati type Equations. An example illustrates this method.