We examine the strategic interaction between two governments in an international mixed duopoly market, in which a state-owned enterprise competes with private enterprises under different regimes of privatization policies with import tariffs and environmental taxes. We find that bilateral privatization leads to higher tariffs than no privatization, but unilateral privatization yields the highest tariff for a privatized country and the lowest tariff for a non-privatized country. However, a higher environmental tax is called for when a privatization policy is practiced. We also investigate a privatization choice game between two governments and show that unilateral privatization is the Nash equilibrium of the game. Finally, we compare the local optimum with the global optimum and show that the latter is independent of the regimes of privatization policies. We find a need for trade and environmental policy coordination between the two governments for global welfare maximization.