The paper applies Looking Forward Approach to analyze the world oil market with the framework of a differential game model of quantity competition oligopoly. Namely Looking Forward Approach is used to take into account dynamically updating information. Under the information we understand the forecast of the oil demand dynamics. We focus on the period from December 2015 to November 2016 and suppose that during this time interval countries did not cooperate officially on the amounts of oil to be produced. Therefore, their behavior can be modeled using the non-cooperative game model. As a solution concept for this conflict-controlled process we use feedback Nash equilibrium. In order to define the parameters of model open source data is used, results of numerical simulations and comparison with the historical data are presented.