What is the process used to solve a Cournot homogeneous duopoly?

The process by which the Cournot homogeneous duopoly is solved is called the Cournot model of duopoly, named after Augustin Cournot. The driving force of this model, according to the founder, was the observation of competition in the duopoly of water springs. The competition of firms is dependent on the selection of simultaneous quantities. Firms have to be strategic and rational economically, all aimed at maximizing profits based on their competitors' decisions. This phenomenon propagated the existence of this model to solve homogeneous duopoly.