## The Cold War and Prisoner’s Dilemma

The idea of Prisoner’s Dilemma was first brought up in 1950s. The prisoner’s dilemma is a standard example of a game analyzed in game theory that shows why two completely “rational” individuals might not cooperate, even if it appears that it is in their best interests to do so.

It was intended to use for economics, however, both the Soviet and the United States use it to form war strategies during Cold War. Even though the two nations did not conduct major fights, they armed heavily in nuclear weapons. A balance would strike when the two nations have similar amount of nuclear weapons and vulnerabilities, since nuclear war would be devastating for both of them. However, according to prisoner’s dilemma, the two nations are only concerned about their own interest. Suppose the United States and Soviet Union can both choose from preparing 100 units of weapons and 0 units of weapons. From the Unites States’ point of view, preparing 100 units would be a better choice regardless of the Soviet Union’s decision. Same works for the Soviet Union. However, the optimal outcome can only be reached when both countries prepare 0 unit of weapons, against what happened in real life: both nations prepare 100 units of weapons. The real-life outcome is a Nash Equilibrium, which is logical yet not optimal.

The Cold War is similar to the Game of Chicken, lest it was much more complicated and devastating. The principle of Chicken Game is a game that “while each player prefers not to yield to the other, the worst possible outcome occurs when both players do not yield.” (Chicken Game, Wikipedia, https://en.wikipedia.org/wiki/Chicken_(game) ) The only way to win this game is to make the other player believes that you are so irrational that you are willing to sacrifice anything to win this game. The underlying philosophy is the same as a nuclear arm race. It is certainly the worst outcome that both countries fire all their nuclear weapons, leading to millions of people killed. Then why the arm race took place and lasted so long? Nash Equilibrium trapped both sides in a situation where the combined optimal choices of two sides will ultimately lead to the worst outcome.

Source: http://math.ucdenver.edu/~lorencobb/docs/Cobb-ColdWar-2011.pdf