Whether the recursive self-improvement is possible or not, is the property of the universe. Also other details, like how much additional time and energy is necessary for another increase in intelligence.
The answer to this question can make some outcomes more likely. For example, if recursive self-improvement is possible, and at some level you can get a huge increase in intelligence very quickly and relatively cheaply, one of the centers of power could easily overpower the other ones. Perhaps even in situations where every super-agent would read and analyze the source code of all other super-agents all the time; the increased intelligence could allow one of them to make changes that will seem harmless to the other ones.
On the other hand the multiple centers of power scenario is more likely if humankind spreads to many planets, and there is some natural limit how high an intelligence can become before it somehow collapses or starts needing insane amounts of energy; so no super-agent could be smart enough to conquer the rest of the world.
The project of Friendly AI would benefit from being approached in a much more down-to-earth way. Discourse about the subject seems to be dominated by a set of possibilities which are given far too much credence:
Add up all of that, and you have a great recipe for enjoyable irrelevance. Negate every single one of those ideas, and you have an alternative set of working assumptions that are still consistent with the idea that Friendly AI matters, and which are much more suited to practical success:
The simplest reason to care about Friendly AI is that we are going to be coexisting with AI, and so we should want it to be something we can live with. I don't see that anything important would be lost by strongly foregrounding the second set of assumptions, and treating the first set of possibilities just as possibilities, rather than as the working hypothesis about reality.
[Earlier posts on related themes: practical FAI, FAI without "outsourcing".]