The recent and unprecedented surge of public interest in peer-to-peer file sharing has led to a variety of interesting research questions. In this paper, we will address the incentive issues that arise in such file sharing systems. In particular, there is a free-rider problem in traditional peerto-peer networks such as Napster: individual users are provided with no incentive for sharing their own files and thereby adding value to the network. Instead, such services currently rely upon altruistic behavior from their users. We take a different approach, examining the design implications of the assumption that users will selfishly act to maximize their own rewards. We construct a formal game theoretic model of the system and analyze equilibria of user strategies under several novel payment mechanisms. Finally, we support and extend upon the predictions of our game theoretic model by presenting experimental results from a multi-agent reinforcement learning model.