Question

Problem 5 – The October 1962 Cuban Missile Crisis (20 points) During October 1962 the United States and the Soviet Union engaged in a stand off over the Soviet Union’s attempted deployment of nuclear missiles to Cuba. We will model part of the crisis dynamics as they looked on October 22, 1962 when President Kennedy announced the naval blockade of Cuba stating that Soviet ships carrying nuclear missile equipment would be turned back if attempting to enter Cuba. Consider this a sequential move game where the first mover Premier Krushchev can choose to retract (R) the ships or order them to challenge (C) the blockade. If Krushchev retracts, the game ends and it will be perceived as a political failure for Krushchev and a win for Kennedy with payoff 2 of (−1, 1), meaning a payoff of −1 to Krushchev and 1 to Kennedy. If Krushchev challenges the blockade, Kennedy will observe the challenge and now has an option to enforce (E) the blockade or to fold (F), the latter meaning letting the ships proceed to Cuba. If Kennedy folds the game ends, and Krushchev will deploy nuclear missiles to Cuba and achieve an improved strategic position, resulting in payoffs of (5, −5). If Kennedy enforces the blockade, the crisis will escalate with the distinct possibility of nuclear war ensuing. We will assign payoffs (−100, −100) to the act of enforcing the blockade.

1. Draw the extensive form game between Krushchev and Kennedy.

2. What are the pure strategy Nash equilibria of the game? Explain.

3. What is the subgame perfect Nash equilibrium of the game? Explain.

4. In reality, Kruschev retracted the ships. The following is an open ended question: In order to understand this action, how is it in your mind best understood given the previous analysis? Is the equilibrium concept not appropriate? Would you consider changes in the game? Etc...

Answer 1

The given information is shown as an extensive form game as follows: Krushchev Retract (R) Challenge (C) (-1,1) Kennedy Enforce (E) Fold (F) (-100, -100) (5,-5) Use the backward induction method to solve it. If Krushchev retracts, then the payoff will be (-1,1). Kennedy has two options: to enforce or to fold. Out of the two, Kennedy is better off if he folds since the payoff is more. Therefore, the pure strategy Nash equilibria are (C.F) = (5,-5) and (R,R) = (-1,1). Out of the two pure strategy Nash equilibria, Krushchev is better off if he challenges and Kennedy folds. Therefore, the subgame perfect Nash equilibria is (C.F) = (5,-5). Krushchev retracted the ships. It means that Krushchev got a payoff of -1, while Kennedy received a payoff of 1. It means that Krushchev was skeptic that if he challenges Kennedy, and Kennedy enforces, then it will do much higher harm than good. So, even though it is not an equilibrium point, still it is a rational approach to face a harm from which it is still easy to recover, than to harm yourself from something, from which recovery is not possible.