Reference:
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.
Abstract:
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.