User subscription dynamics in communication markets

In order to understand the competition and interactions between different technologies, it is of fundamental importance to study how users select these technologies operated by different network service providers (NSPs) . In this paper, we study the dynamics of user subscription in a wireless communication market that includes a continuum of users. First, we focus on a monopoly market with only one NSP that provides to each user with an unreliable quality-of-service (QoS) subject to the number of subscribers. Users dynamically make their decisions regarding whether or not they subscribe to the NSP. It is shown that there exists a unique equilibrium point in the dynamics and that the dynamics is guaranteed to converge under some sufficient conditions that can be interpreted as that the provided QoS does not vary too rapidly with respect to the change of user subscriptions. Then, we extend the analysis to a duopoly market by adding into the market another NSP that has sufficient resources and thereby provides to each user a constant QoS.