Reference
N. Groot, B. De Schutter, and H. Hellendoorn, "Optimal affine leader functions
in reverse Stackelberg games: Existence conditions and characterization,"
Journal of Optimization Theory and Applications, vol. 168,
no. 1, pp. 348-374, 2016.
Abstract
A generalizing analysis is made in order to ease the solvability of the
generally complex single-leader-single-follower reverse Stackelberg game. This
game is of a hierarchical nature and can therefore be implemented as a
structure for multi-level decision-making problems, like in road pricing. In
particular, a leader function of the affine type is analyzed in order to
procure a systematic approach to solving the game to optimality. To this end,
necessary and sufficient existence conditions for this optimal affine leader
function are developed. Compared to earlier results reported in the literature,
differentiability of the follower objective functional is relaxed, and locally
strict convexity of the sublevel set at the desired reverse Stackelberg
equilibrium is replaced with the more general property of an exposed point.
Moreover, a full characterization of the set of optimal affine leader functions
that is derived, which use in the case of secondary optimization objectives as
well as for a constrained decision space, is illustrated.
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BibTeX
@article{GroDeS:15-012,
author = {Groot, Noortje and De Schutter, Bart and Hellendoorn, Hans},
title = {Optimal Affine Leader Functions in Reverse {Stackelberg} Games:
{Existence} Conditions and Characterization},
journal = {Journal of Optimization Theory and Applications},
volume = {168},
number = {1},
pages = {348--374},
year = {2016}
}