  In this paper, we analyse how a peer-to-peer sharing platform should price
its service (when imagined as an excludable public good) to maximize profit,
when each user's participation adds value to the platform service by creating a
positive externality to other participants. To characterize network
externalities as a function of the number of participants, we consider
different bounded and unbounded user utility models. The bounded utility model
fits many infrastructure sharing applications with bounded network value, in
which complete coverage has a finite user valuation (e.g., WiFi or hotspot).
The unbounded utility model fits the large scale data sharing and explosion in
social media, where it is expected that the network value follows Metcalfe's or
Zipf's law. For both models, we analyze the optimal pricing schemes to select
heterogeneous users in the platform under complete and incomplete information
of users' service valuations. We propose the concept of price of information
(PoI) to characterize the profit loss due to lack of information, and present
provable PoI bounds for different utility models. We show that the PoI=2 for
the bounded utility model, meaning that just half of profit is lost, whereas
the PoI>=2 for the unbounded utility model and increases as for a less concave
utility function. We also show that the complicated differentiated pricing
scheme which is optimal under incomplete user information, can be replaced by a
single uniform price scheme that is asymptotic optimal. Finally, we extend our
pricing schemes to a two-sided market by including a new group of `pure'
service users contributing no externalities, and show that the platform may
charge zero price to the original group of users in order to attract the pure
user group.

Computer Science and Game Theory