P2P clusters like the Grid and PlanetLab enable in principle the same statistical multiplexing efficiency gains for computing as the Internet provides for networking. The key unsolved problem is resource allocation. Existing solutions are not economically efficient and require high latency to acquire resources. We designed and implemented Tycoon, a market based distributed resource allocation system based on an Auction Share scheduling algorithm. Preliminary results show that Tycoon achieves low latency and high fairness while providing incentives for truth-telling on the part of strategic users.