The Interaction of Positive Externalities and Congestion Effects

We study a system where a service is shared by many identical customers; the service is provided by a single resource. As expected each customer experiences congestion, a negative externality, from the others’ usage of the shared resource in our model. In addition, we assume each customer experiences a positive externality from others’ usage; this is in contrast to prior literature that assumes a positive externality that depends only on the mere presence of other users. We consider two points of view in studying this model: the behavior of self-interested users who autonomously form a “club”, and the behavior of a service manager. We first characterize the usage patterns of self-interested users, as well as the size of the club that self-interested users would form autonomously. We find that this club size is always smaller than that chosen by a service manager; however, somewhat surprisingly, usage in the autonomous club is always efficient. Next, we carry out an asymptotic analysis in the regime where the positive externality is increased without bound. We find that in this regime, the asymptotic behavior of the autonomous club can be quite different from that formed by a service manager: for example, the autonomous club may remain of finite size, even if the club formed by a service manager has infinitely many members.