(I'm skeptical of the very premise of colonizing Mars, but putting that aside..)
I expect what forms on Mars, at least initially, will resemble the high seas a lot more than it does any country. You'll have facilities owned and commanded by corporations operating under flags of convenience, more or less free to engage in any nastiness they like (at least until a navy or coastguard with guns shows up to enforce their will on the facility.)
Perhaps, though that seems like an unstable equilibrium. By the time we have communities up there, they're have their powerful and their not powerful, just like we terrestrials.
