On competition between wireless service providers

Pricing in telecommunication networks has received much attention in recent years, as the huge commercial interest drives the transition from a monopolistic network to a commercial one with competitive service providers (SPs). The present paper considers a pricing game in a communication market covered by two wireless access points (APs) and analyzes two commercial models: monopoly (two APs controlled by one SP) and duopoly (two APs controlled by different SPs). We prove, under mild conditions, the existence and uniqueness of a Nash equilibrium for both cases and derive their analytical expressions. In order to compare the impact of monopoly and duopoly on social welfare and SPs profits, we define two metrics to quantify such impacts: PoCS (price of competition on social welfare) which is the ratio of social welfare of monopoly to that of duopoly, and PoCP (price of competition on profits) which is the ratio of profit of monopoly to the sum profit of duopoly. We prove that for symmetric cross interference, the tight lower bound of PoCS is 3/4, and that of PoCP is 1; on the other hand, both PoCS and PoCP are unbounded from above.