Game Theory lost all credibility when it advocated nuking Russia pre-emptively. Besides, most game theory studies don't even consider the possibility of self-destructive action, let alone evaluate whether they're actually advocating such a thing.
But most people interpreted (value of the world after nuking Russia) to be quite low because Russia would automatically launch a retaliation, and the same vice versa from Russia's perspective. So with this utility game theory predicted the Mutually Assured Destruction standoff that so far has turned out correct.
Now did it? As far as I know, the whole MAD thing was based on precommitting to strike if struck, therefore negating the benefit of first strike for both parties.
Whether a persons advocacy is consistent with the theory or not, however, is an important point. And so far as I know, Nash's claim that game theory supported a pre-emptive nuclear strike against the USSR was never claimed to be in any way flawed from a game-theoretic perspective.
