We introduce endogenous investments for building-up extraction capacity of conventional and non-conventional oil 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 and the oil price drop dramatically. Unconventional oil is not extracted. Global mitigation costs confirm are similar to previous estimates. However, regional imbalances are magnified: oil-exporting countries bear costs twice as large while oil-importing regions have much lower costs, if compared to previous estimates.