We characterize the open-loop and the Markov perfect Stackelberg equilibria for a differential game in which a cartel and a fringe extract a nonrenewable resource. Both agents have stock dependent costs. The comparison of initial market shares, across different equilibria, depends on which firm has the cost advantage. The cartel's steady state market share is largest in the open loop equilibrium and smallest in the competitive equilibrium. The initial price may be larger in the Markov equilibria, so a decrease in market power may make the equilibrium appear less competitive. The benefit to cartelization increases with market share.