On the time consistency of equilibria in a class of additively separable differential games

A class of state-redundant differential games is detected, where players can be partitioned into two groups, so that the state dynamics and the payoff functions of all players are additively separable w.r.t. controls and states of any two players belonging to different groups. We prove that, in this class of games, open-loop Nash and feedback Stackelberg equilibria coincide, both being strongly time consistent. This allows us to bypass the issue of the time inconsistency that typically affects the open-loop Stackelberg solution.