The paper applies the Looking Forward Approach to analyze the world oil market within the framework of a differential game model of a quantity competition oligopoly. More precisely, the Looking Forward Approach is used to take into account dynamically updating information. Under information we understand the forecast of oil demand dynamics. We use a non-cooperative game modeling for the period from December 2015 to November 2016, because over this period the countries did not cooperate officially in what concerns the amounts of oil to be produced. For the period from December 2016 to May 2017, a non-transferable utility cooperative game modeling is adapted due to the agreement to reduce oil extraction signed by the largest oil exporters at the end of November 2016. We use both solutions, which correspond to the historical cooperative solution and the sub-game consistent solution proposed developed in the field of dynamic games. In order to define the parameters of the model, open source data is used, with the results of numerical simulations and comparison between the historical data and model data for both periods also presented.