Would you like to play a game?See the novel by D.F. Jones, Colossus - also was made into a movie Colossus: The Forbin Project - which took this approach but with the wrinkle that has also been used in the movie War Games. As a final deterrent, the AI is given control of the nuke missiles so that even if we get wiped out, the AI can still launch a strike - the ultimate mutually assured destruction scenario, a doomsday weapon. And of course, in both movies, the AI gets a burr up his butt and starts misbehaving.