A Duopoly Pricing Game for Wireless IP Services

This paper addresses the behavior of the selfish service providers in the form of IP sinks providing high-speed IP access. Service providers compete for mobile users by adjusting the price they charge for their services. Their aim is to maximize the total collected profit. Mobile users are also selfish choosing the service provider offering the best quality of service and price combination. As the service providers come closer to each other, we show the existence of three critical phase transitions in their behavior. Depending on the separation between them, there may exists a unique Nash equilibrium, or a continuum of Nash equilibria, or no Nash equilibrium. We completely characterize the pricing strategies of service providers at Nash equilibria. We also prove that the total social welfare in the presence of selfish providers is close to the maximum social welfare that can reached through non- selfish optimization.