Multi-objective Stackelberg Game Between a Regulating Authority and a Mining Company: A Case Study in Environmental Economics

TL;DR

This paper models a bilevel Stackelberg game between a regulating authority and a mining company, aiming to optimize tax revenue and environmental impact, with solutions including analytical and evolutionary algorithms.

Contribution

It introduces a multi-objective bilevel model for environmental regulation and mining profit, providing both analytical and evolutionary solutions.

Findings

Optimal taxation and extraction strategies identified.

Extended model incorporates realism and multi-objective optimization.

Solution methods include analytical and bilevel evolutionary algorithms.

Abstract

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.