Data demand dynamics and profit maximization in communications markets

In this paper, we focus on the users´ aggregate data demand dynamics in a wireless communications market served by a monopolistic wireless service provider (WSP). Based on the equilibrium data demand, we optimize the WSP´s data plans and long-term network capacity decisions to maximize its profit. For a market where two different data plans are offered, it is shown that the existence of a unique equilibrium data demand depends on the data plans, and the convergence of data demand dynamics is subject to the network congestion cost, which is closely related to the WSP´s network capacity. A sufficient condition on the network congestion cost indicates that the WSP needs to provide a sufficiently large network capacity to guarantee the convergence of data demand dynamics. Then, we formalize the problem of optimizing the WSP´s data plans and network capacities to maximize its profit, and solve it numerically.