Answer :
During the Cold War, the United States and the Soviet union hoped the theory of deterrence, or deterrence policy, or mutually assured destruction would prevent either from using nuclear weapons against the other out of fear of the devastating impacts of retaliation.
The correct answer is B) Brinkmanship.
During the Cold War, the United States and the Soviet Union hoped the Brinkmanship policy would prevent either country from using nuclear weapons against the other.
When facing a conflict, the Brinkmanship policy is a dangerous strategy in that one part of the conflict tries to get an advantage by pushing events or risky situations during the course of the conflict. That was the case of the Cuban Missile Crisis in October 1962, when the world was at the brink of another world war.
The other options of the question were a) the Eisenhower doctrine, c) mutual disarmament, and d) mutual assured destruction.