1. The Dr. Strangelove Game. In the Cold War days, the United States and the Soviet Union had both conventional ground and nuclear forces. The Soviets had superior conventional forces. If the Soviets launched a ground attack on NATO countries in Europe, the United States could decide to use either nuclear or conventional ground forces to retaliate. A conventional retaliation would leave the Soviet Union better off and the United States worse off by an equal amount. If the United States retaliated with nuclear force, a nuclear war would ensue and the United States would be 100 times worse off than in the conventional case. The Soviet Union would suffer just as much as the United States in the nuclear case.

Draw the game tree for this problem and find the backward induction solution (rollback equilibrium). Next, suppose that the United States pre-commits to nuclear deterrent, if the Soviets will attack. Draw a new game tree for this case and find the backward induction solution. Compare and comment about both solutions.