I am writing the player's behavior for an arena game, and I'm wondering if you could offer some strategies. I'm writing it in Python, but I'm just interested in the high level game play.

Here are the game aspects:

1. Arena is a circle of a given size. The arena's size shrinks every round to help break any ties.
2. Players are much smaller circles, and can be on teams of 1 or 2 players.
3. Players attack by colliding with other players, and based on the physics of the collision (speed of both players, angle), one could force another player out of the arena. Once a player is out of the arena, they are out of the game (for that round).
4. The goal is to be on the only team with players left in the arena. All other players have been pushed (through collisions or mistakes) out of the arena.
5. It is possible for there to be no winner if the last two players exit the arena at the same time.
6. Once the player has been programmed, the game just runs. There is no human intervention in the game.

I'm thinking it's easiest to implement a few simple programmatic rules for my player to follow. For example, stay close to center of the arena, attack opponents from the inner side of the arena, etc.

Are there any good simple game strategies? Would adding a random aspect to the game help? For example, to avoid predictability by the other team or something.

Thanks in advance.