A Nash–Stackelberg equilibrium model for internet and network service providers in the demand market—a scenario-based approach

This paper evaluates the optimal pricing for two Internet service providers and two network providers; all are competing on price, which is based on quality. To find the optimal prices of service and network providers and to determine optimal scenarios, a two-stage competition is modeled. In the first stage, network providers compete on market prices by setting the quality in four scenarios. At this stage, we found the equilibrium prices in the market. In the second stage, by obtaining market prices, service providers compete on network prices. Finally, the equilibrium solutions are compared with each other by considering the intensity of market competition in price and quality. It is shown that equilibrium never occurs in the case when the smaller service provider has a higher Internet quality than the other (scenario 2) and the more significant service provider offers a higher Internet quality (scenario 4). Besides, when both Internet service providers offer low-quality Internet (scenario 1) and high-quality Internet (scenario 3), the companies make the most profit. By increasing and decreasing the competition in quality, equilibrium would still exist for the first scenario, and the third scenario, respectively. The intensity of market competition in price behaves oppositely as quality.