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While the fundamental premise of peer-to-peer (P2P) systems is that of voluntary resource sharing among individual peers, there is an inherent tension between individual rationality and collective welfare that threatens the viability of these systems. This paper surveys recent research at the intersection of economics and computer science that targets the design of distributed systems consisting of rational participants with diverse and selfish interests. In particular, we discuss major findings and open questions related to free-riding in P2P systems: factors affecting the degree of free-riding, incentive mechanisms to encourage user cooperation, and challenges in the design of incentive mechanisms for P2P systems.