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

摘要

Bilevel programming problems are often found in practice. In this paper, wehandle one such bilevel application problem from the domain of environmentaleconomics. The problem is a Stakelberg game with multiple objectives at theupper level, and a single objective at the lower level. The leader in this caseis the regulating authority, and it tries to maximize its total tax revenueover multiple periods while trying to minimize the environmental damages causedby a mining company. The follower is the mining company whose sole objective isto maximize its total profit over multiple periods under the limitations set bythe leader. The solution to the model contains the optimal taxation andextraction decisions to be made by the players in each of the time periods. Weconstruct a simplistic model for the Stackelberg game and provide an analyticalsolution to the problem. Thereafter, the model is extended to incorporaterealism and is solved using a bilevel evolutionary algorithm capable ofhandling multiple objectives.