Uncertainty in the Nuclear Arms Race

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threat on the nation. If the United States and the Soviet Union cannot trust each other to mutually disarm, and decide to continue nuclear armament, this would yield a payoff of -1. This payoff is considerably lower than all the other actions because the United States would suffer from economic hardship while dealing with their hazardous relationship with China, besides never having national security.

The Soviet Union’s payoffs are different in each game because the numbers are determined by the ultimate desire/goal of the U.S.S.R. In the game in which the Soviet Union’s ultimate goal is to have nuclear supremacy, the Soviet Union’s preferences are: U.S. Disarm/ U.S.S.R. armament > mutual armament > mutual disarmament >U.S. armament/U.S.S.R disarm. In the second game (the Soviet Union’s goal is to have mutual disarmament with the United States) the Soviet Union’s preferences are: mutual disarmament > U.S. disarm/ U.S.S.R armament > U.S. armament/ U.S.S.R disarmament > mutual armament. If the Soviet Union’s goal is to have nuclear control, and the U.S. decides to disarm, the Soviet Union would receive a payoff of 3 because it has accomplished what it desires most. Its second best payoff (2) would be if both countries continue to increase nuclear armament because the race will not guarantee a winner and the Soviet Union will not be left defenseless. If the Soviet Union disarms and the United States continues armament, this would yield the Soviet Union the worst payoff of -1, since it is the opposite of what the country wants. The Soviet Union would rather have mutual disarmament (with a payoff of 1) because then, at least, neither country will have nuclear control. In contrast, in the second game, the Soviet Union aims for mutual nuclear reduction (for the same reasons as the United States (e.g. economy and political relationship with China)). If the country can achieve an agreement with the United States, it will receive a payoff of 3. If the United States alone decides to disarm, the Soviet Union will yield a payoff of 2 because the country will have national security, but also the cost of nuclear weapons. If the United States arms and the Soviet Union disarms this will yield 1 because although, the economy would improve, national security would be threatened. The worst outcome (mutual armament) will receive a payoff of -1 because the Soviet Union will impose the cost of the weapons and security will always be threatened.

The game is drawn as follows on the following page.

Solving the two games, the United States discovers that in the first game, the country would receive the highest payoff by continuing armament. In the second game the country would receive the highest payoff by mutually disarming with the Soviet Union. In order to determine what was the Soviet Union’s ultimate goal, the United States had to first find the expected utility of both arming and disarming by the probability that the Soviet Union did not have a preference or goal in mind (indifference). The United States would then have to compare the expected utilities by making them equal to each other and solving for the probability threshold of indifference. We can conclude that the United States believed that the U.S.S.R would agree to disarm because of the economic hardship and political instability that they shared. So its assessment of the probability that the U.S.S.R would disarm was very close to 1. The calculations are below:

KEY

EU = Expected Utility

p -=probability that U.S.S.R prefers nuclear supremacy

1 - p = probability that the U.S.S.R prefers mutual disarmament

Subgame perfect of 1st game= {U.S.S.R nuclear supremacy; disarm, arm}

Subgame perfect of 2nd game={U.S.S.R mutual disarm; disarm, disarm}

EU (disarming) = EU (arming)

P (1)+(1-p)(3)=P (2)+(1-p)(-1)

Player 1 indifferent between his actions = 4/5

The threshold reveals that if the United States believed that the true probably was greater than p, it would have disarm. On the other hand, if the true probably had been less than p, the United States would have found it better to arm. The outcome on the equilibrium path, given the signal that the U.S.S.R would disarm, would be that the United States disarms as well.

As history shows, in 1958, both countries agreed to informally suspend nuclear testing to limit the growth of the arms race (A Global History of the Nuclear Arms Race). Starting in the 1970s, both powers started control agreements. This period was known as détente (Weapons of Peace: the Nuclear Arms Race). The period allowed the countries to reduce their nuclear spending and opened way for the SALT I and SALT 11 agreement (which limited the size of the country’s arsenals) (A Global History of the Nuclear Arms Race). At the end of the Cold War, the U.S-Soviet relationship greatly improved and after the governmental change in Russia (no longer the Soviet union) both countries cut down on nuclear spending. Fewer systems were created and there was new control over nuclear weapons. Both countries, although, still have nuclear missiles reaching the thousands (Weapons of Peace: the Nuclear Arms