We present an approach to support massively multiplayer games on peer-to-peer overlays. Our approach exploits the fact that players in MMGs display locality of interest, and therefore can form self-organizing groups based on their locations in the virtual world. To this end, we have designed scalable mechanisms to distribute the game state to the participating players and to maintain consistency in the face of node failures. The resulting system dynamically scales with the number of online players. It is more flexible and has a lower deployment cost than centralized games servers. We have implemented a simple game we call SimMud, and experimented with up to 4000 players to demonstrate the applicability of this approach.