Statistical Stackelberg game control: Open-loop minimal cost variance case

Abstract This paper considers a statistical Stackelberg stochastic differential game, in which the m th cost cumulants of the leader and the follower are sequentially optimized. This shapes the probability distribution of the cost functions of the leader and the follower. More specifically, we investigate the Stackelberg game, in which the leader optimizes the variance or the second cumulant of the cost function. The full solution is derived for the minimal cost variance Stackelberg game control problem, which is a special case of a more general statistical Stackelberg game. A numerical example illustrates our method.