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This article proposes a two-stage oligopoly model for the crude oil market. In a game of several Stackelberg leaders, market power increases endogenously as the spare capacity of the competitive fringe goes down. This effect is due to the specific cost function characteristics of extractive industries. The model captures the increase of OPEC market power before the financial crisis and its drastic reduction in the subsequent turmoil at the onset of the global recession. The two-stage model better replicates the price path over the years 2003-2011 than a standard simultaneous-move, one-stage Nash-Cournot model with a fringe. I also discuss how most large-scale numerical equilibrium models, widely applied in the energy sector, over-simplify and misinterpret market power exertion. Furthermore, I show that this two-stage Stackelberg model can be solved numerically as a Mixed Complementarity Problem with heterogeneous firms and discuss uniqueness.