Cooperative peer-to-peer applications are designed to share the resources of each participating computer for the common good of everyone. However, users do not necessarily have an incentive to donate resources to the system if they can use the system's resources for free. This thesis presents mechanisms to enforce fair sharing of limiting resources in peer-to-peer systems. Storage fairness is enforced by requiring nodes to publish their storage records and allowing auditing to those records. Bandwidth fairness is enforced by having nodes locally track the amount of data transferred and limiting each node's interactions to a small number of nodes that are proven trustworthy. Thus, a node must provide good service to receive good service. For storage systems to be efficient, nodes should provide overcapacity. Based on an economic analysis of utility functions, we show how the overcapacity parameter should be set and why clustering of the system would benefit users.