Reference:
N. Groot,
B. De Schutter, and
H. Hellendoorn,
"Optimal leader functions for the reverse Stackelberg game: Splines
and basis functions," Proceedings of the 2013 European Control
Conference, Zürich, Switzerland, pp. 696-701, July 2013.
Abstract:
In order to deal with the control of large-scale infrastructures, a
multi-level approach may be required in which several groups of
decision makers have different objectives. A game formulation can help
to structure such a control task. The reverse Stackelberg game has a
hierarchical structure in which the follower player acts subsequent to
the leader's disclosure of her leader function, which maps the
follower decision space into the leader decision space. The problem of
finding a leader function such that the leader's objective function is
optimized, given an optimal response w.r.t. the follower objective
function, is in general a difficult problem. So far, the set of
optimal affine leader functions has been delineated. However, for the
more general class of nonlinear leader functions, no structured
solution approach exists yet. In this paper, we consider several
nonlinear structures for an optimal leader function based on basis
functions as well as based on interpolating splines and we show how
these approaches can be adopted to find an optimal leader function.