Free final time Stackelberg differential games

In this paper, we analyse a new formulation of Stackelberg differential games.We assume that the Leader can control not only the dynamics of the game, but also the length of the programming interval.This formulation of a free final time Stackelberg differential game is not explicitly considered in the literature and presents some interesting issues.After a formal definition of this kind of differential game, we show, using a practical example, the main difficulties associated with this new definition.We close the article by presenting two open questions related to this issue.