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This paper studies the optimal extraction and taxation of nonrenewablenatural resources. It is well known that the market values of the mainstrategic resources such as oil, natural gas, uranium, copper,..., etc,fluctuate randomly following global and seasonal macroeconomic parameters,these values are modeled using Markov switching L\'evy processes. We formulatethis problem as a differential game. The two players of this differential gameare the mining company whose aim is to maximize the revenues generated from itsextracting activities and the government agency in charge of regulating andtaxing natural resources. We prove the existence of a Nash equilibrium. Thecorresponding Hamilton Jacobi Isaacs equations are completely solved and thevalue functions as well as the optimal extraction and taxation rates arederived in closed-form. A Numerical example is presented to illustrate ourfindings.

Optimal Extraction and Taxation of Strategic Natural Resources: A Differential Game Approach