Political Situation once Mars gets colonized

We're decades away from having a Mars colony, and decades more from it being self sufficient. In that time period, the prospects of such a colony exercising political independence is doubtful. While it's dependent on Earth (and e.g. SpaceX is dependent on US government support for its launch site and many of its more hazardous materials), then it can't meaningfully ignore the host country of facilities on Earth.

So in Musk's lifetime, the most he can hope for is a corporate funded US controlled research base of some sort.

I think legally the treaties on outer space are that it's common hold and therefore not subject to countries exercising exclusive sovreignty, though obviously such a claim, as with Antartica, is easier for everyone to agree on when there's severe technical difficulties with no equivalent benefit to be had in investing in this.

Should that change, and some technical advance renders a Mars colony much easier than expected these days or much more valuable than expected, then that official neutrality that will be renegotiated, and it would probably look like the scramble for africa with more of a veneer of trying to be respectful. But we're well into sci-fi territory at that point.

In my opinion before we even get to that point Elon and others will first have to figure out how to include only people with psychological and physical profiles conducive to such a lifestyle. Even one unstable person could cause entire pods or groups of pods to be destroyed and mass evacuations, assuming evacuation is feasible. Limited versions of these experiments have occurred on earth with sub-optimal results. There are also some long term low-gravity induced health issues that will have to be addressed and that is work-in-progress.

Here [1] was some recent discussion on this as well.

I suspect that initially there will be teams of robots belonging to different governments and maybe a small handful of astronaut engineers managing them locally with bigger teams back here on earth. I envision robot-vs-robot sabotage leading to problems here on earth. The same may occur with asteroid mining despite there being vast numbers of asteroids to mine. At some point there will probably be more space-soldiers and defensive equipment than engineers. The folks that wrote the fictional series Star Trek had the optimistic view that humans would clash in a major world war in 2024 and then all get along swimmingly afterwards. I do not share their optimism but then my view would have entirely changed the Star Trek series into a different kind of show.

To really answer your question I think we would have to fully understand how the land in Antarctica is managed and how we ended up with people agreeing to share pieces of land. [2]

[1] - https://news.ycombinator.com/item?id=31612545

[2] - https://www.youtube.com/watch?v=DbKNlFcg02c [video]