Game Theory And Cold War

GAME THEORY AND COLD WAR

Katerina Ploussiou

War has been with us ever since the dawn of civilization. Nothing has been more constant in history than war. An American psychologist, William Janes, suggested that war creates a sense of unity in the face of a collective threat. It binds people together, it brings a sense of cohesion, with communal goals, and inspires individual citizens to behave honourably and unselfishly, in the service of a greater good. Robert J. Aumann, a mathematician known for his research and breakthroughs on repeated games, argues that there isn’t a theory which can avoid wars; however, game theory provides the strategies to help decision makers in conflict situations to hopefully avoid war and devastation. In the framework of repeated games, Aumann explains that if rivals give the impression of willingness to fight then there will be no war. Mutual Assured Destruction is based on the theory of deterrence which explains that the threat of using strong weapons against rivals prevents the enemy’s use of those weapons. Aumann points to Cold War as an example of Mutual Assured Destruction.

Cold war was an ongoing geopolitical rivalry between the United States and the Soviet Union who had disparate ideologies.

Let’s model out the Cold War in a game to find out how it had ended.

Mutual Assured Destruction is based on the theory of deterrence which explains that the threat of using strong weapons against rivals prevents the enemy’s use of those weapons.

In the game below, let’s consider that the Soviet Union makes the first move. It has to decide whether to utilize its nuclear weapons and attack, or not utilize its weapons and therefore choose don’t attack. If the Soviet Union, choose don’t attack, the game ends, and results in a stalemate where no nuclear weapons are used. However, if the Soviet Union choose to attack, the USA must then decide its move; whether to retaliate, or don’t retaliate.

The payoffs for each player are shown at the end of the branches. In this game the payoffs are measured in “utility” to the player. The number are fairly arbitrary, and only matter in their relation to each other. If the two players choose don’t attack the game ends with both players getting a payoff of 0, which is not better or worse off than before. If the Soviet Union attacks, and the USA retaliates, both players receive a payoff of negative infinity, and the game ends in mutual destruction for both players. This leads to both players losing. If on the other hand, the Soviet Union chooses to attack, and the USA chooses don’t retaliate, the Soviet Union receives a payoff of 500 and the USA receives a payoff of -500. In this case both players are better off than receiving a payoff of negative infinity.

In order to solve the game, we must work out which action the Soviet Union will take to start the game. So, the Soviet Union has two choices, the first choice is to don’t attack, and receiving a payoff of 0, and the second choice is to attack, however the payoff it will receive will depend on its rival’s choice of action. Consequently, the Soviet Union, before it decides what to do, it must work out what the USA will do so it can work out its payoff and make rational decisions.

USA choice is simple, if it retaliates, it will receive a payoff of negative infinity, if it doesn’t retaliate, it receives a payoff of -500, given that the Soviet Union attacks. The best choice and solution to this game is for the Soviet Union to attack and the USA to not retaliate.

However, an important component was left out. What if the USA could promise the Soviet Union that if it attacked the USA it would retaliate? No rational player would choose a payoff of negative infinity over -500. This is what game theorist call a “doomsday device’’, a device in the game that triggers retaliation if the first player attacks. Therefore, if the Soviet Union knows that the USA will retaliate if it attacks then its choices become: if it attacks it receives a payoff of negative infinity and if it doesn’t attack, it receives a payoff of 0. So, the best choice for the Soviet Union is to not attack, and we have a Cold War stalemate. The threat of complete nuclear destruction acted as a deterrent for either side using the weapons. Fortunately, neither nation was willing to play the final stage of a game in which the best possible outcome involved a victory that could only be celebrated by a handful of survivor’s underground.

This idea is what roughly happened in the real war which had ended it. To prevent a war, one would think to disarm or lower the levels of armaments. However, that would be a mistake, doing the exact opposite would be the correct thing to do. This is highlighted by the fact that both the USA and Soviet Union used a few strategies equivalent to the doomsday device. They both established nuclear submarines all over the world, ready to strike back if their main bases were hit, the USA kept nuclear armed planes in the air for 3 decades ready to respond. As well as this, both sides adopted what is known as the madman strategy, convincing the other player that they are not rational thinkers and they will respond with retaliation even if it is not in their best interests. The atmosphere was tense, and there was a constant threat of miscommunication leading to disastrous results.

This result is the tipping point of a nuclear war, it leads to a situation called Mutual Assured Destruction. It is a situation in which neither side has an incentive to either attack or disarm. The guaranteed mutual destruction that would follow a nuclear war prevents both sides from using the weapons. The threat of complete nuclear destruction acted as a deterrent for either side using weapons. Aumann points to the Cold War as an example, which turned into a scientific model and national security policy, aptly called Mutual Assured Destruction. Simply put, any possible nuclear attack would be retaliated in the same way. This would lead to a situation in which neither side could win and therefore to an armistice. “The possibility of disaster has to be serious. You can’t make other people believe it’s serious, unless it is serious,” Aumann explains, stressing the core factor that led to the Mutual Assured Destruction during the Cold War: an equilibrium of horror.

The threat of complete nuclear destruction acted as a deterrent for either side using the weapons. Fortunately, neither nation was willing to play the final stage of a game in which the best possible outcome involved a victory that could only be celebrated by a handful of survivor’s underground.

References

Erickson, Paul, Judy L. Klein, Lorraine Daston, Rebecca Lemov, Thomas Sturm, and Michael D. Gordin. How reason almost lost its mind: The strange career of Cold War rationality. University of Chicago Press, 2013.

How Game Theory Works? -Science. Available online at: https://science. howstuffworks.com/game-theory5.htm.

The Washington Post, 2017: What Game theory tells us about nuclear war with North Korea. Available online at: https://www.washingtonpost.com/news/wonk/ wp/2017/08/16/what-game-theory-tells-us-about-nuclear-war-with-north-korea/ .

UBS: Can game theory end world conflict? Available online at: https:// www.ubs.com/microsites/nobel-perspectives/en/laureates/robert-aumann. html?campID=PR-NOBELCONTENTPARTNERSHIP-GLOBAL-ENG-BI-CUSTOMPOST2- AUMANN.

UBS: Can game theory avoid wars? Available online at: https://www.ubs.com/ microsites/nobel-perspectives/en/latest-questions/2019/game-theory-avoid-wars. html .

Weintraub, E. Roy. “Game theory and cold War rationality: A review essay.” Journal of Economic Literature 55, no. 1 (2017): 148-61.