  Bilevel programming problems are often found in practice. In this paper, we
handle one such bilevel application problem from the domain of environmental
economics. The problem is a Stakelberg game with multiple objectives at the
upper level, and a single objective at the lower level. The leader in this case
is the regulating authority, and it tries to maximize its total tax revenue
over multiple periods while trying to minimize the environmental damages caused
by a mining company. The follower is the mining company whose sole objective is
to maximize its total profit over multiple periods under the limitations set by
the leader. The solution to the model contains the optimal taxation and
extraction decisions to be made by the players in each of the time periods. We
construct a simplistic model for the Stackelberg game and provide an analytical
solution to the problem. Thereafter, the model is extended to incorporate
realism and is solved using a bilevel evolutionary algorithm capable of
handling multiple objectives.
