I _think_ the idea is that the first one to hit self improving AGI will, in a short period of time, pull _so_ far ahead that competition will quickly die out, no longer having any chance to compete economically.

At the same time, it'd give the country controlling it so much economic, political and military power that it becomes impossible to challenge.

I find that all to be a bit of a stretch, but I think that's roughly what people talking about "the AI race" have in mind.