Reference:
N. Groot,
B. De Schutter, and
H. Hellendoorn,
"A full characterization of the set of optimal affine solutions to the
reverse Stackelberg game," Proceedings of the 51st IEEE Conference
on Decision and Control, Maui, Hawaii, pp. 6483-6488, Dec. 2012.
Abstract:
The class of reverse Stackelberg games can be used as a structure for
hierarchical decision making and can be adopted in multi-level
optimization approaches for large-scale control problems like road
tolling. In this game, 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 presenting his
optimal decision variables. In order to solve the - in general complex
- reverse Stackelberg game, a specific structure of the leader
function is considered in this paper, given a desired equilibrium that
the leader strives to achieve. We present conditions for the existence
of such an optimal affine leader function in the static reverse
Stackelberg game and delineate the set of all possible solutions of
the affine leader function structure. The parametrized
characterization of such a set facilitates further optimization, e.g.,
when considering the sensitivity to deviations from the optimal
follower response, as is illustrated by a simple example. Moreover, it
can be used to verify the existence of an optimal affine leader
function in a constrained decision space.