The growth of video traffic makes it increasingly likely that multiple clients share a bottleneck link, giving video content providers an opportunity to optimize the experience of multiple users jointly. But today’s transport protocols are oblivious to video streaming applications and provide only connection-level fairness. We design and build Minerva, the first end-to-end transport protocol for multi-user video streaming. Minerva uses information about the player state and video characteristics to adjust its congestion control behavior to optimize for QoE fairness. Minerva clients receive no explicit information about other video clients, yet when multiple of them share a bottleneck link, their rates converge to a bandwidth allocation that maximizes QoE fairness. At the same time, Minerva videos occupy only their fair share of the bottleneck link bandwidth, competing fairly with existing TCP traffic. We implement Minerva on an industry standard video player and server and show that, compared to Cubic and BBR, 15-32% of the videos using Minerva experience an improvement in viewing experience equivalent to switching from 720p to 1080p.