In our previous research publications, we established a significant connection between consistent conjectures and those of Cournot–Nash. We developed a new mathematical model based on a two-stage game specifically for the oligopolistic market. In this two-stage game, the role of the players correspond to the agents operating within the oligopoly, and the role of their game strategies is played by the conjectures accepted by these agents. We successfully demonstrated that if a Nash equilibrium exists within this two-stage game, it aligns with one of the consistent equilibria observed in the oligopolistic market. In our proposed study, we aim to identify the specific conditions through which we can substantiate the consistency of the equilibrium within the oligopoly by means of the Nash equilibrium in this two-stage game. This finding is of particular significance as it provides a pathway to expand the notion of consistency for the conjectural variations to mathematical models that differ from the oligopolistic market. Examples of such models include financial markets, the natural gas industry, the oil industry, and various others.