Does game theory support predictions of humanity's eventual self-destruction?

I'm not a mathematician, economist, conspiracy theorist, religious, social, or political scientist. This question isn't put forth to invoke any extreme or irrational responses, nor opinionated speculations. But what I want to know is this: what kind of evidence is there for humanity's eventual self-destruction by the means of its own ingenuity? What kind of informed expectations can we permit ourselves to have in discerning the future of sapiens as a species, whilst simultaneously considering their evolution in thought, in the sense of intellectual capacities? Does the advancement of technology (especially nanotechnology), game theory, and a society's propensity to sensationalism indicate the demise of humanity?