Does a country strictly gain if it acts as a leader in a resource market under bilateral monopoly? Using differential games, we show that the answer is "yes"" when leadership can be exercised globally (global Stackelberg leadership), but possibly ""no"" when it is exercised only at each stage (stagewise Stackelberg leadership). On the other hand, world welfare under Nash equilibrium is strictly higher than under global Stackelberg equilibrium. Regardless of which country is the leader, world welfare under stagewise Stackelberg leadership is higher than under global Stackelberg leadership."