In this paper, we analyse how a peer-to-peer sharing platform should price its service to maximize profit, when user participation increases the value of the service to others by causing positive externalities. Modelling the service as an excludable public good, we propose a bounded utility model to capture many infrastructure sharing applications with bounded network value, in which complete coverage generates finite user valuation (e.g., WiFi or hotspot). Unbounded utility models are used to capture the large-scale user interactions in social media, where the network value follows Metcalfe's or Zipf's law. For these utility models, we analyze the optimal pricing schemes in the case of heterogeneous users 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 asymptotic PoI bounds for different utility models. We also show that the difficult-to-implement differentiated pricing scheme, which is optimal under incomplete user information, can be replaced by a simple 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 who do not contribute to the public good, and show that the platform may charge zero price to the original group of users in order to attract this pure user group.

Mobile social network applications constitute an important platform for traffic information sharing, helping users collect and share sensor information about the driving conditions they experience on the traveled path in real time. In this paper we analyse the simple but fundamental model of a platform choosing between two paths: one with known deterministic travel cost and the other that alternates over time between a low and a high random cost states, where the low and the high cost states are only partially observable and perform respectively better and worse on average than the fixed cost path. The more users are routed over the stochastic path, the better the platform can infer its actual state and use it efficiently.At the Nash equilibrium, if asked to take the riskier path, in many cases selfish users (that are allowed to have access to the information collected by the platform) will myopically disregard the optimal path suggestions of the platform, leading to a suboptimal system without enough exploration on the stochastic path. We prove the interesting result that if the past collected information is hidden from users, the system becomes incentive compatible and even `sophisticated' users (in the sense that they have full capability to reverse-engineer the platform's recommendation and derive the path state distribution conditional on the recommendation) prefer to follow the platform's recommendations. In a more practical setting where the platform implements a model-free Q-learning algorithm to minimise the social travel cost, our analysis suggests that increasing the accuracy of the learning algorithm increases the range of system parameters for which sophisticated users follow the recommendations of the platform, becoming in the limit fully incentive compatible. Finally, we extend the two-path model to include more stochastic paths, and show that incentive compatibility holds under our information restriction mechanism.

Today, mobile users are intensively interconnected thanks to the emerging mobile social networks, where they share location-based information with each other when traveling on different routes and visit different areas of the city. In our model, the information collected is aggregated over all users' trips and made publicly available as a public good. Due to information overlap, the total useful content amount increases with the diversity in path choices made by the users, and it is crucial to motivate selfish users to choose different paths, despite the potentially higher costs associated with their trips. In this paper, we combine the benefits from social information sharing with the fundamental routing problem where a unit mass of non-atomic selfish users decides their trips in a non-cooperative game by choosing between a high-cost and a low-cost path. To remedy the inefficient low-content equilibrium where all users choose to explore a single path (the low-cost path), we propose and analyze two new incentive mechanisms that can be used by the social network application, one based on side payments and the other on restricting access to content for users that choose the low cost path. Under asymmetric information about user types (their valuations for content quality), both mechanisms efficiently penalize the participants that use the low-cost path and reward the participants that take the high-cost path. They lead to greater path diversity and hence to more total available content at the social cost of reduced user participation or restricted content to part of the users. We show that user heterogeneity can have opposite effects on social efficiency depending on the mechanism used. We also obtain interesting price of anarchy results that show some fundamental tradeoffs between achieving path diversity and maintaining greater user participation, motivating a combined mechanism to further increase the social welfare. Our model extends classical dynamic routing in the case of externalities caused from traffic on different paths of the network.