This paper develops simple models to study the performance of BitTorrent, a second-generation peer-to-peer (P2P) application. The authors first present a fluid model to study the scalability, performance, and efficiency of file-sharing mechanisms. They then consider the built-in incentive mechanism in BitTorrent and analyze its effect on network performance. Numerical results based on simulations and real traces from the Internet are provided. The paper addresses several key issues in P2P networks, including peer evolution, scalability, file sharing efficiency, and incentives to prevent free-riding. The authors develop a deterministic fluid model to study the system's behavior and incorporate realistic scenarios such as peer abandonment and downloading bandwidth constraints. They also derive expressions for the average downloading time and the effectiveness of file sharing, showing that BitTorrent is highly efficient in sharing files. The paper further analyzes the stability of the fluid model and characterizes the variability of the number of peers using a Gaussian approximation. It discusses the incentive mechanism in BitTorrent, which aims to discourage free-riding by allowing peers to upload to a limited number of peers with high downloading rates. The authors study the optimal selfish behavior of users under this mechanism and show that there can be no Nash equilibrium in a general network setting but that a Nash equilibrium exists when peers are grouped by their uploading and downloading bandwidths. Finally, the paper presents experimental results validating the fluid model through simulations and real traces, demonstrating that the model accurately predicts the behavior of BitTorrent-like networks.This paper develops simple models to study the performance of BitTorrent, a second-generation peer-to-peer (P2P) application. The authors first present a fluid model to study the scalability, performance, and efficiency of file-sharing mechanisms. They then consider the built-in incentive mechanism in BitTorrent and analyze its effect on network performance. Numerical results based on simulations and real traces from the Internet are provided. The paper addresses several key issues in P2P networks, including peer evolution, scalability, file sharing efficiency, and incentives to prevent free-riding. The authors develop a deterministic fluid model to study the system's behavior and incorporate realistic scenarios such as peer abandonment and downloading bandwidth constraints. They also derive expressions for the average downloading time and the effectiveness of file sharing, showing that BitTorrent is highly efficient in sharing files. The paper further analyzes the stability of the fluid model and characterizes the variability of the number of peers using a Gaussian approximation. It discusses the incentive mechanism in BitTorrent, which aims to discourage free-riding by allowing peers to upload to a limited number of peers with high downloading rates. The authors study the optimal selfish behavior of users under this mechanism and show that there can be no Nash equilibrium in a general network setting but that a Nash equilibrium exists when peers are grouped by their uploading and downloading bandwidths. Finally, the paper presents experimental results validating the fluid model through simulations and real traces, demonstrating that the model accurately predicts the behavior of BitTorrent-like networks.