Christian Rogers Math 89S: Game Theory and Democracy



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Christian Rogers

Math 89S: Game Theory and Democracy

Professor Bray
October 4, 2012

Nuclear Weapons: Then and Now

Politics, especially on an international level, is a complex and messy subject. One simply has to open up a newspaper or tune into the evening news for evidence. While many problems can be resolved peacefully through negotiations, there are problems in international relations that manage to escalate quickly and result in a war between two or more countries. From revolutionary wars to World Wars, violence has always been part of international relations. However, with recent technological advancements, wars have taken an especially deadly turn. Advanced weaponry has allowed soldiers to become more “efficient” when fighting a battle allowing them to kill many more enemy combatants and innocent bystanders. The most devastating of these newly created weapons are nuclear weapons such as the atomic and hydrogen bombs. These weapons have the capacity to eliminate hundreds of thousands of people, obliterate cities, and possibly end life on earth, as we know it. The most destructive of these weapons was tested by the Soviets in 1961 during the Cold War. The hydrogen bomb that was being tested had a destructive power of approximately 60 megatons. The Soviets formally named the bomb Ivan, but nicknamed it the “King of Bombs.” Originally, Ivan was going to be constructed with a power of 100 megatons, but the Soviets decided it was too risky and dangerous. To put this in perspective, a single megaton can create temperatures that are five times as intense as the center of the sun. These weapons essentially contain enough power to devastate if not completely destroy our planet.

Due to the potential dangers and stigma of using nuclear weapons, they have fortunately been used only a handful of times. A bomb as powerful as Ivan has not been built since let alone used in actual warfare. In fact, only two atomic bombs have ever been used in combat. These two bombs were dropped on the Japanese cities of Nagasaki and Hiroshima by the US to end World War II. Although these bombs were successful in ending the war, there were many arguments over whether using such force was justified. They took the lives of thousands of innocent people and completely leveled Hiroshima and Nagasaki. The nuclear weapons used by the US in World War II gave the world a tangible example of the destructive power of these types of weapons.

Shortly following the end of World War II, the US became involved in a conflict with the Soviet Union that became known as the Cold War. Both nations were contending to be the dominant power in the world. Each tried to exert influence over the other as much as possible and tried to demonstrate their nation was superior in every way. In World War II, the US was the only country that had operating nuclear weapons at the time. As a result, President Truman never had to worry about the possibility of a nuclear weapon being used as retaliation for bombing Japan. During the Cold War, however; the Soviets managed to successfully construct their own arsenal of nuclear weapons. By having these destructive weapons in their possession, the Soviets completely transformed the situation. No longer could the US simply use its own nuclear weapons without fearing some retaliation from the Soviets. If the US were to try and take out all the weapons the Soviets possessed there would be no guarantee that they would have all been destroyed and even a single missile would be enough to exact a devastating blow on the US. The Soviets possessed a similar mindset, believing that they could not inflict a strike on the US without expecting some sort of violent and devastating response. The two nations were thus in a situation similar to what is known as the Prisoner’s Dilemma.

Figure 1:





Player 2 - Cooperate

Player 2 - Defect

Player 1 - Cooperate

-1, -1

-10, 0

Player 1 - Defect

0, -10

-5, -5

The Prisoner’s Dilemma is a game involving two players that can be best explained by using a diagram as shown in figure one. The “traditional” story for the Prisoner’s Dilemma is that each player is being sent to jail for drug use, however; the police know each player is actually a big time drug dealer. The police lack the evidence to convict the players, so they present them with a choice: either testify against the other player and go free or keep silent and go to jail for a year. The player who is testified against is given ten years in prison. In addition, if both players choose to testify, they both go to jail for five years. Lastly, the players may not communicate with one another. This is where the figure becomes helpful in sorting everything out. The chart displays the options each player can choose. Each player can either choose to cooperate, which means they choose to remain silent, or defect, which means they choose to testify.

Few situations can perfectly align with the model of the Prisoner’s Dilemma. For instance, the players may somehow be able to communicate with one another, they may not make decisions based on rational reasoning, or they might introduce another variation. The situation faced by the Soviets and the US was very similar to Prisoner’s Dilemma. They could cooperate, use their nuclear weapons (defect), or do nothing. However, the situation between these two countries did have some major differences from the traditional story of the Prisoner’s Dilemma. The two nations did have some communication and they faced the possibility of playing multiple games of the Prisoner’s Dilemma due to their many interactions. Playing multiple games has a huge impact on how a player approaches the Prisoner’s Dilemma. In the traditional setting of the Prisoner’s Dilemma, it is best to defect because a player avoids the maximum penalty. Also, since the game is only played once, it does not matter what your opponent thinks about your actions. However, the since the US and the Soviet Union played a new game of the Prisoner’s Dilemma every time they interacted, they had to take their opponent’s feelings into consideration. For example, if the US were to defect by using its nuclear weapons in the first game, the Soviets would be likely to retaliate in the next game. The US would do well it the first game, but future games would be compromised due to each player wanting to exact revenge upon the other. Neither player can trust the other and so neither wishes to cooperate even though it would be the best strategy for the both of them. Choosing to cooperate would make either one of them vulnerable while defecting would create problems in the future; as a result both countries refrained from using their nuclear weapons. Their choice to refrain from using violence is a modified form of both players defecting and choosing the middle path rather than taking a risk. As mentioned earlier, the situation varies slightly from the standard Prisoner’s Dilemma.

Seeing as how these world leaders decided to avoid risks and play it safe, I wanted to see what other people would have done in similar situations. I decided to take a survey of approximately nineteen college students to see how others would react in the Prisoner’s Dilemma. Since many people are not well versed about history or current events, I decided to create my own Prisoner’s Dilemma scenario. I made the scenario relatable to the lives of college students so as to help make their choices more realistic. The scenario I proposed involved students coming back from a night out on the town to their dorm only to discover a cake along with another person sitting in the common room. Both the student returning and the student quietly sitting in the common room were the two players in the scenario. I also reminded the students participating in the survey that there would be a good chance that they would have another encounter with this person to help simulate playing multiple games of the Prisoner’s Dilemma. I provided various options that students could choose from in deciding how to react in this situation. Some choices were traditional Prisoner’s Dilemma solutions while others had certain twists to them. The choices varied from safe choices such as both players cooperating and taking small pieces of cake to risky choices in which one player would defect by taking the whole cake and hope the opposing player did not defect as well by telling on the person. I even included options for the players to “cheat” by allowing them to communicate, but at a cost of losing the cake. The students then ranked these choices in order of preference. The results produced similar outcomes to the Cold War. In each method I used to tally the votes, the students tended to choose choices that were typically seen as safer. Options that involved a great deal of risk tended to be placed lower. Therefore, it seems as though the rational choice tends to be to use a safe strategy that involves little risk and reward rather than a strategy involving high stakes. To be able to confirm this, I asked a follow up question. I asked the students if they would choose the same type of strategy if the scenario were something much more important or crucial. The majority responded that they would, which helps to confirm the idea that people prefer to use safer strategies rather than take risks. In the traditional Prisoner’s Dilemma, the rational and thus safer choice tends to be to defect while cooperating poses many risks and makes a player vulnerable. There are times when there are multiple ways to defect as well. The actions taken by leaders in the Cold War and the voting results of the students surveyed confirm that choosing safe options is the rational choice.

Knowing that people tend to choose safer decisions when confronted with a Prisoner’s Dilemma style scenario, we can try to predict how people and nations will act in the future. The conflict between Israel and Iran is one that stretches back many years, however; recently nuclear weapons have made their way into the conflict. Israel currently has a small amount of nuclear weapons, but Iran is currently believed to be constructing its own set of nuclear weapons. Israel fears that Iran will amass a nuclear arsenal greater than that of Israel. As a preventative measure, President Netanyahu of Israel has sought support from countries such as the US to help control Iran. The Prisoner’s Dilemma between Iran and Israel is similar to the one that took place during the Cold War, but at a much smaller level. The arsenal’s of Iran and Israel were nothing like those of the US and the Soviets, but even so, it should not be forgotten how dangerous a single bomb can be. In the highly unlikely event either country chooses to defect by using their nuclear weapons, it would stray from past precedent. Although it is certainly not impossible, it is simply improbable. For instance, if either leader begins to no longer act rationally, then there is no telling what could possibly happen. At this point cooperation between the two countries also seems unlikely. The more likely scenario is that the two leaders will both defect by choosing to simply refrain from using their weapons. As with the Cold War, the nuclear weapons are more of a deterrent than anything else. Using them is simply not practical and considering that Iran and Israel will have many interactions in the future, it is not a rational decision to use nuclear weapons. Despite these predictions, there is always the possibility that the countries might deviate from past precedent for one reason or another. No matter what though, one thing is certain and that is that nuclear weapons have the capacity to completely destroy the world.

The Prisoner’s Dilemma is undoubtedly a complex and messy game. There are usually differences in each scenario that make it unique from the others. These unique traits make it difficult to make predictions based on past events because we can only compare similar events, not identical ones. It is important though to study past events so that we are not completely unaware of the possible outcomes of a situation. In short, studying the past better equips us to deal with the present.

Bibliography

Bellows, Alan. "The Most Powerful Bomb Ever Constructed." Damn Interesting. N.p., 13 Jan. 2006. Web.3 Oct. 2012. .

Nye, Joseph S., Jr. Understanding Global Conflict and Cooperation: An Introduction to Theory and History. 8th ed. Boston: Longman, 2011. Print.

Solomon, Jay. "Netanyahu Demands 'Red Line' on Iran." Wall Street Journal 28 Sept. 2012, World News:A1+. Print.




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