When social network effect meets congestion effect in wireless networks: Data usage equilibrium and optimal pricing

The rapid growth of online social networks has strengthened wireless users' social relationships, which in turn has resulted in more data traffic due to network effect in the social domain. Nevertheless, the boosted demand for wireless services may challenge the limited wireless capacity. To build a thorough understanding, we study mobile users' data usage behavior by jointly considering the network effect due to their social relationships in the social domain and the congestion effect in the physical wireless domain. Specifically, we develop a Stackelberg game for socially aware data usage: in Stage I, a wireless provider first decides the data pricing to all users in order to maximize its revenue, and then in Stage II, users decide their data usage, for the given price, subject to mutual interactions under both social network effect and congestion effect. We analyze the two-stage game via backward induction. In particular, for Stage II, we first provide conditions for the existence and the uniqueness of a user demand equilibrium (UDE). Then, we propose algorithms to find the UDE and for users to reach the UDE in a distributed manner. We further investigate the impact of different system parameters on the UDE. Next, for Stage I, we develop an optimal pricing algorithm to maximize the wireless provider's revenue. We numerically evaluate the performance of our proposed algorithms using real data, and thereby draw useful engineering insights for the operation of wireless providers: 1) when social network effect dominates congestion effect, the marginal gain of the total usage increases with the social ties and the number of users, or decreases with the congestion coefficient; in contrast, when congestion effect dominates social network effect, the marginal gain decreases (or increases, respectively) with these parameters and 2) when social network effect is strong, a lower price should be set to increase the total revenue; in contrast, when congestion effect is strong, a higher price is preferred.