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“Chicken game” in The 1962 Cuba Missile Crisis

Now, we regard this whole event as a game. The gain and loss of Cuba is too small to affect the payoffs of the game. Cuba has no power to make a choice in this game. So we ignore Cuba’s role here. The players of this game are the Soviet Union and the United States.

Opposite with the Soviet Union, America would get the contrary payoffs. The missiles installed by the Soviet Union in Cuba could pass through the missile warning and defense systems of the United States. Even the U.S. combat system could not make a timely response. If the Soviet Union succeeded in building up the missile bases, America would live in the shadow of security threats. Furthermore, the military superiority of America would be checked and balanced. The military strength of America would decrease relative to that of the Soviet Union. The bargaining chip of America in international affairs would be greatly reduced. America had to tolerate the survival and spread of Socialism in Latin America. Therefore, this game is a zero-sum game. The gain of one country is equal to the loss of the other one.

Khrushchev probably had considered the consequences that may possibly be caused by the missile installation. If America took a tough stance and conducted massive retaliation against the Soviet Union, the outcome would be the horrible nuclear war. But Khrushchev thought Kennedy was a weak president and dared not take the risk of starting a nuclear war. If everything was like what Khrushchev thought, America could do nothing except protesting against the missiles.

America and the Soviet Union had two choices, tough and weak. Being tough or weak is two pure strategies for America and the Soviet Union. In the view of the Soviet Union, If America insisted to be tough, the worst outcome might happen, and the Soviet Union had to consider being weak, withdrawing missiles from Cuba. But Khrushew believed Kennedy would compromise, and then the best response for the Soviet Union would be tough. The Soviet Union could have missile in Cuba and America would suffer loss.

Now we can establish a payoff diagram for the two players according to the gains and losses of the U.S. and the Soviet Union in different situations. Because a nuclear war can be as horrible as to destroy the human being, it is not unreasonable to set the payoffs to both parties under the worst situation as (-∞，-∞). In situations where one country is weak and the other country is tough, we assume the gain to the tough country is 10 and the loss to the weak country is -10. The first number of each cell refers to the payoff to the Soviet Union and the second number refers to the payoff to U.S.

On 16th October, 1962, the U.S. obtained conclusive evidence that the Soviet Union was installing short- and intermediate- range missile bases in Cuba. President Kennedy immediately convened the Council of State to discuss coping strategies.

In the conference, Military strongly suggested imposing surgical strike on Cuba. But this suggestion met with a lot of opposition. U.S. air strikes would definitely harm the technicians of the Soviet Union in Cuba, and the Soviet Union might strongly respond to that, resulting in a destroying-human nuclear war. The proposal conducting air strikes to destroy the missile bases in Cuba was denied. In the end, Kennedy decided to blockade the Soviet Union delivery of offensive weapons to Cuba and to force the Soviet Union to withdraw missile installed in Cuba during the confrontation.

On 22nd October, Kennedy delivered a speech on the television, stating that the Soviet Union constructing missile bases in Cuba “constitutes an explicit threat to the peace and security of all Americas”, “this secret, swift and extraordinary buildup” was “a deliberately provocative and unjustified change in the status quo which cannot be accepted by this country”. Kennedy stated “to halt this offensive buildup, a strict quarantine on all offensive military equipment under shipment to Cuba is being initiated”. (Kennedy, 1962) On 23rd October, Kennedy signed ‘No delivery of offensive weapons to Cuba Notice’. On 24th October, U.S. fleet on mission sailed into the blockade zone with the escort of 68 air force squadrons and 8 aircraft carriers. Moreover, U.S. massed the largest landing force ever since the end of the Second World War. The strategic air force came into the state of readiness. America assumed a posture of responding to sudden events and taking actions to Cuba.

Under the tough stance of the United States, the Soviet Union switched from being tough to a moderate position. On 22nd October, 1962, the Soviet Union returned the blockade note to the American Embassy at the Soviet Union as an unacceptable file. On 23rd October, the Soviet Union Government warned the United States not to play with fire, or it would bear serious responsibility. On 24th October, the Soviet Union Ordered 12 ships that carried offensive weapon to return. On 26th October, the Soviet Union Government sent a message that if the United States promised not to invade Cuba, the Soviet Union could withdraw the missiles. On 28th October, Khrushev replied to Kennedy by broadcasting, stating “I understand the worry of you and the American people about what you called offensive weapon. It is indeed a horrible weapon. You and I both understand, what kind of weapon it is”, “the Soviet Union Government had commanded to remove what you called offensive weapons, pack them and ship them back to the Soviet Union.”(White, 1999, p227-228)

The game ends now. The United States chose the Tough strategy and the Soviet Union chose the Weak strategy. And the outcome is (W, T). The payoff to the two players is (-10.10). As we can see, this is a chicken game. The Soviet Union and the United States wanted to avoid, not choose, actions with the same labels. The coordination failure (T, T) is far more drastic than the coordination failure (W, W). Each of two countries most prefers to be tough, having the other be weak, and each least prefers the outbreak of a nuclear war. There are two pure strategy Nash equilibria in this game, which are (W, T) and (T, W). These are the outcomes in which exactly one of them is weak. There is no mixed strategy Nash Equilibrium in this game. The mixed strategy cannot be rationalized.Assume the United States would play tough with probability p, and play weak with probability (1-p). Then the payoff of the Soviet Union if it chose tough would be: p ( )+(1-p) 100, and its payoff using weak strategy would be: p (-100)+(1-p) 0. P ( ) + (1-p) 100 p (-100) + (1-p) 0 as long as p is not zero. There is no properly mixed strategy for the United States, and it can never make the Soviet Union indifferent. The Soviet Union and the United States both wanted to influence the outcome. It was the United States that successfully made a visible and irreversible commitment to be tough. The tough stance of Kennedy conveyed a clear message to Thrushes that the United States would play the pure strategy Tough with probability 1. Then the best response of the Soviet Union was Weak. And finally, the equilibrium stayed at (W, T).

This event ended with the success of the United States. Kennedy showed courage and intelligence in this challenge. Unfortunately, the Soviet Union became the coward. And Khrushev gained the reputation of a timid speculator.

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