We introduce endogenous investments for increasing conventional and non-conventional oil extraction capacity in the integrated assessment model WITCH. The international price of oil emerges as the Nash equilibrium of a non-cooperative game. When carbon emissions are not constrained, oil is used throughout the century, with unconventional oil taking over conventional oil from mid-century onward. When carbon emissions are constrained, oil consumption drops dramatically and the oil price is lower than in the BaU. Unconventional oil is not extracted. Regional imbalances in the distribution of stabilisation costs are magnified and the oil-exporting countries bear, on average, costs three times larger than in previous estimates.