Peer-to-peer networking is gaining popularity as a architecture for sharing information goods and other computing resources. However, these networks suffer from a high level of free-riding, whereby some users consume network resources without providing any network resources. The high levels of free-riding observed by several recent studies have led some to suggest the imminent collapse of these communities as a viable information sharing mechanism. Our research develops analytic models to analyze the behavior of P2P networks in the presence of free-riding. In contrast to previous predictions, we find that P2P networks can operate effectively in the presence of significant free-riding. However, we also show that without external incentives, the level of free-riding in P2P networks is higher than socially optimal. Our research also explores the implications of these findings for entrepreneurs, network designers, and copyright holders.