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(+2)

I think the concept is almost there. While you say that you're avoiding your own bullets, that's not really the case. I mean, they come out of you, but you never intend to shoot them. So, effectively, they're just like enemies from any other game.

It would have been really interesting if there was some reason to shoot (maybe you have to shoot certain objects to keep yourself alive, for example) and the player could control when to shoot. If that were the case, then a lot more strategy and risk-taking could be involved, forcing the player to make interesting choices. So, I think your game is a good start.

(+2)

What if the arena becomes smaller over time and you need to shoot at the walls to make it bigger?