The idea has its roots in a game called Spheres of Chaos (
http://www.spheresofchaos.com/ -- It's free, although last time I tried it I had problems with it on Win7), which is a very pretty psychedelic asteroids clone with tons of additional options and enemies as well as up to 8 local players. Has a few game modes, including a 'battle' and the upgrades.
Taking what I remember from playing that when I was younger is how I came up with the shields. Lives + instant death doesn't work wonderfully in this arena and the game always played better in a co-operative mode as a result.
Changing this to rounds + shields and a requirement to destroy all the asteroids before your shots damage other players should balance this I think, although I won't know until I get those systems working. Maybe I'll add the lives/instant death as well as a second mode.
Should have a playable local version by this time next week anyway. Hoping to test it at TIGjam UK 4 if I can persuade people.