Phenomena in inverse Stackelberg games, part 2: Dynamic problems

Dynamic two-person games are considered, in which the roles of the players are hierarchical. One player behaves as a leader, the other one as a follower. Such games are named after Stackelberg. In the current paper, a special type of such games is considered, known in the literature as inverse Stackelberg games. In such games, the leader announces his strategy as a mapping from the follower's decision space into his own decision space. Arguments for studying such problems are given. This paper specifically studies dynamic games, i.e. the underlying model is described by an ordinary differential equation. The decisions of both players have a time component. As in the static case, the routine way of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying specific examples.