Optimal pricing for peer-to-peer sharing with network externalities

Abstract: 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.