This paper studies a dynamic game of environmental taxes between two countries in a Cournot duopoly. Based on the assumption of linear demand functions, we demonstrate that the environmental tax in the steady-state equilibrium is lower in a dynamic environmental tax game than in a static environmental one. Therefore, the dynamic behavior of the governments results in an increase in the environmental damage. Further, as a result of international cooperation on environmental taxes between two countries in the first period, there is an increase in the optimal environmental tax; this is due to the decrease in the effect of the rent-shifting
