In this article, the authors have developed a simple oligopolistic model to formalize the interactions between service providers and end-users by considering that the rationality of customers varies over time. This article assessed the impact of the dynamics of consumer confusion on the competition and profitability of service providers who are considered rational and competitive with one another to maximize their respective gains in the face of a confused fraction of consumers while others are not confused. This article shows the existence and uniqueness of the Nash equilibrium. The authors used the best response dynamic algorithm for learning Nash equilibrium. We have shown that when the number of confused customers is large, the ISP interest this and they offer moderately high prices with low quality of service. On the other hand, over time, rationality increases, forcing the ISPs to change their strategies by offering better services so that their demand increases. We also add that when customer behavior changes quickly, the ISPs follow clearer strategies with customer satisfactory services.