I am making this game multiplayer: http://jsfiddle.net/PxpVr/16/embedded/result/

I've created the lobby and have basic controls worked out. Now I'm brainstorming on how to sync players' movements. Can anyone help? I know there also come problems with latency, but I'm wondering if a game so simple would have these problems. Thanks in advance

Stack is python/django, postgresql, jquery, using websocket (django-channels) for real-time updates