Constructing a dynamic game model of trade of an exhaustible resource, this paper compares feedback Nash and Stackelberg equilibria when the exporting country sets quantity rather than price. We consider two different leadership scenarios: leadership by the importing country, and leadership by the exporting country. We numerically show that as compared to the Nash equilibrium, both countries are better off if the importing country is a leader, but that the follower is worse off if the exporting country is a leader. Consequently, the world welfare is highest under the importing country's leadership and lowest under the exporting country's leadership.