Well, are you thinking nation states? Then you kinda also need a population that is cool with a sort of blitzkrieg being waged "on their behalf" against the rest of the world (and they should think twice if that machinery wouldn't also logically end up being turned onto them). Otherwise, what's the race for, unless to use it offensively? So you either subjugate or eradicate the world, and then what? Who wants that?

Political power is when people act in concert, when leaders have people behind them because those people agree with how they're being lead etc., it's not something that happens unilaterally. You can physically force people, but for what when you can have robots that you don't have to force?

So that kind of leaves wiping out nearly all humans, for a few hundred thousand remaining people to get served by robots and play golf. Which I would say is what we're kinda on track for. But that wouldn't be a race between nations, that race would just be pretend to get the tech online; it would rather be a race between all humans and a bunch of sick people.