On the Equilibrium Sets of Subscribers to a Telecommunications Service

This paper examines the formation and properties of subscriber sets of a bidirectional telecommunications service. Most bi-directional telecommunications systems have demand or consumption externalities in that the benefit to a subscriber depends upon the number of subscribers to the system or upon who they are. When a new telecommunications system is to be set up, even an establishment that feels it convenient and is willing to subscribe will not do so alone. It will either subscribe with others or agree to subscribe in anticipation of others joining. The success or failure that a new service experiences depends upon whether they attract enough users to become feasible and profitable. This means that there exist two significant sets. The one is the minimum subscriber set for the system to be feasible and the other is the ultimate expansion level of it. The former is called the critical mass and the latter the equilibrium user set. Although some authors have proposed this idea, their argument would be rather intuitive. In this paper, I give a rigorous definition of these sets in the context of the stability and unstability of them. Heterogeneous and nonanonymous users are assumed to formulate the model. Equilibria of the system are defined as a set of users in which the benefit to the smallest usage subscriber is equal to zero. A dynamic approach is applied to examine the stability of the system. The condition for a two-part tariff system to be feasible is derived.