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.
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BibTeX
@inproceedings{GroDeS:12-038,
author = {Groot, Noortje and De Schutter, Bart and Hellendoorn, Hans},
title = {A Full Characterization of the Set of Optimal Affine Solutions
to the Reverse {Stackelberg} Game},
booktitle = {Proceedings of the 51st IEEE Conference on Decision and
Control},
address = {Maui, Hawaii},
pages = {6483--6488},
month = dec,
year = {2012}
}