Impact of network effect and congestion effect on price competition among wireless service providers

The rapidly growing popularity of online social services has greatly spurred mobile users' online social interactions, which in turn has boosted their demand for data usage. However, wireless service providers' revenue growth is constrained by the capacity of the physical network infrastructure, and is further challenged by the price competition among different wireless providers. To fully understand the potential benefit brought by social services, we study mobile users' data usage behavior subject to social network effect in the social domain and congestion effect in the physical wireless domain, based on which we explore wireless providers' pricing strategies under competition. In particular, we cast the interactions between mobile users and wireless providers as a two-stage Stackelberg game: In Stage I, each provider decides its pricing strategy to maximize its revenue in competition with other providers' pricing strategies; In Stage II, given the providers' pricing strategies, users choose data usage subject to both social network effect and congestion effects. We analyze the two-stage game using backward induction. For Stage II, we establish the existence and uniqueness of a link demand equilibrium (LDE) under certain conditions. For Stage II, we establish the existence of a mixed strategy pricing equilibrium (PE), and further develop a recursive back-tracking algorithm to find the PE. Our results provide insight on the impact of wireless providers' competition on their revenues.