Matrix block formulation of closed-loop memoryless Stackelberg strategy for discrete-time games

Stackelberg strategies with closed-loop information structure are well known to be delicate to design in general. Nevertheless when they are restricted to the case of memoryless ones, that is when the controls are function of the time and the current state, then they are strongly time consistent. Due to this property, it is possible to compute step by step backward in time the value functions associated with the Stackelberg equilibrium. A new method, using a matrix block formulation is provided here to facilitate this numerical computation. An example illustrates this method.