N. Groot, B. De Schutter, and H. Hellendoorn, "Existence conditions for an optimal affine leader function in the reverse Stackelberg game," Proceedings of the 15th IFAC Workshop on Control Applications of Optimization (CAO'12), Rimini, Italy, pp. 56-61, Sept. 2012.
We investigate the solvability of the reverse Stackelberg game. Here, a leader player acts first by presenting a leader function that maps the follower decision space into the leader decision space. Subsequently, the follower acts by determining his optimal decision variable. Such a game setting can be adopted within a multi-level optimization approach for large-scale control problems like road tolling. However, due to the complexity of the general game, results often rely on specific examples. As a starting point towards developing a systematic approach for the use of reverse Stackelberg games in control, a characterization of cases is given in which the desired leader equilibrium can be achieved by an affine leader function. Here, we focus on the single-leader single-follower deterministic, static (one-shot) case. This characterization follows a geometric approach and extends the special cases considered in the existing literature to also incorporate the more general case in which nonconvex and nonsmooth sublevel sets apply.