Optimal open loop cheating in dynamic reversed Linear–Quadratic Stackelberg games

The distinctive characteristic of a ‘Reversed Stackelberg Game’ is that the leader plays twice, first by announcing his future action, second by implementing a possibly different action given the follower's reaction to his announcement. In such a game, if the leader uses the normal Stackelberg solution to find (and announce) his optimal strategy, there is a strong temptation for him to cheat, that is, to implement another action than the one announced. In this paper, within the framework of a standard discrete time Linear–Quadratic Dynamic Reversed Stackelberg game, we discuss and derive the best possible open-loop cheating strategy for an unscrupulous leader.