Oil production strategies define to a large extent the future of the world crude oil market. This paper aims at modelling the long-term world crude oil supply and demand, as well as the global oil price. The main assumption is that non-OPEC and OPEC oil producers act as price-taker and strategic players respectively. The world crude oil demand is modelled as a linear price dependent function. We compare four scenarios to diagnose the OPEC’s supply behaviour: “cartel”, “oligopoly”, “mixed-cartel” and “mixed-oligopoly”. A Mixed Complementarity Problem, MCP, is used to find the Nash equilibrium point of each game scenario. The OPEC countries maximize their individual total discounted profits in “oligopoly” scenario and their joint profit in “cartel” scenario. In “mixed-cartel” and “mixed-oligopoly” scenarios, OPEC members implement their market power on the quantities allocated to export rather than their total supply. It seems to happen often that OPEC members change their level of collaboration. As the historical statistics of 2012–2015 lie between the model results of “mixed-cartel” and “oligopoly” scenarios, it seems that OPEC’s strategy has been a mixture of the both scenarios and the reason of price collapse in 2015 was that OPEC cartel structure weakened. Model outputs show that oil price will soar again in all scenarios. OPEC’s production strategy can push this price soar back most in the “mixed-oligopoly” scenario to 2026.