Nishka Mittal October 2, 2012



Yüklə 30,63 Kb.
tarix15.08.2018
ölçüsü30,63 Kb.
#63006

Nishka Mittal

October 2, 2012

Math 89S GTD

Paper #1


Game Theory and War

From October 16 to October 28, 1962, the world waited for nuclear disaster while the Soviets and the Americans played a game. In the game, each side was equipped with weapons with the potential to wipe out entire cities. Global nuclear destruction was not the only thing at stake; the Soviet Union and the United States were both highly concerned about maintaining their reputation among their enemies and allies. For this reason, neither side wished to yield to the other for fear of being viewed as the weaker player. However both sides knew that if neither of them yielded, the result would be the worst possible outcome for everyone. Thus, by escalating their threats, each side pushed the other closer and closer to the brink of war (hence the term brinkmanship, a term coined during the height of the Cold War), hoping that the other guy would crack first (“The World on the Brink”).

Using a simpler example, game theory can explain the thought processes of John F. Kennedy and Nikita Khrushchev during the thirteen-day-long crisis. Suppose two drivers are driving rapidly towards each other on a single-lane road. If neither driver swerves, they will both crash. If one swerves and the other remains going straight, the one who swerves gets called “chicken” because he or she is presumably a coward. Therefore, the most ideal situation for each driver would be if they remain going straight while the other driver swerves. This way, they would avoid the embarrassment of being called “chicken” and the crash would be avoided. Consider a table of the possible outcomes of this game:





Driver B

Swerve

Straight

Driver A

Swerve

Tie, Tie

Lose, Win

Straight

Win, Lose

Crash, Crash

Now consider the same table of outcomes, this time with point values assigned to each decision made by the drivers:






Driver B

Swerve

Straight

Driver A

Swerve

0, 0

-1, 1

Straight

1, -1

-10, -10

The cost of crashing (-10 points) is so much greater than the cost of swerving (-1 point), so you would think that the most reasonable strategy would be to swerve so that crashing is eliminated from the possible outcomes. However, Driver A may logically assume that Driver B is a lunatic with a death wish and will therefore swerve to avoid crashing. Driver A may then decide, “Since Driver B will probably swerve if he is a rational human being, I should go straight so that I can win the game.” Similarly, Driver B may think the same of Driver A and decide to go straight. Simultaneously aiming for the most desirable outcome, highlighted in red on the above table, the drivers would crash (Poundstone).

Over the course of those thirteen days, Kennedy and Khrushchev were driving two cars head-on towards each other. They, too, were aware of this most desirable outcome and tried to get the other person to swerve by threatening to keep going straight. If they had crashed, they would have affected millions of lives apart from their own. Thankfully, they were eventually successful in their attempts to negotiate a peace agreement that put an end to the Cuban Missile Crisis.

It was Bertrand Russell who first saw the “game of chicken” as a metaphor for the nuclear stalemate in his 1959 book, Common Sense and Nuclear Warfare. When I read about the game of chicken and it’s relation to the Cold War, I was amazed by how perfectly it described the situation of the nuclear stalemate. I wondered if there were other current or past wars that had been examined through the lens of game theory. Indeed, I came across another interesting example of how game theory principles govern the decisions that leaders make. In the long-lasting Arab-Israeli conflict, the Israelis and the Arabs are playing a different game from Kennedy and Khrushchev. In the game, which I am simplifying for the sake of this explanation, the two sides are fighting over a resource: land. Professor Robert Aumann, who was awarded the Nobel Prize in 2005 for his work on conflict and cooperation through game theory analysis, suggests that the Arabs’ strategy during this conflict is based on something that in game theory is called “Blackmailer’s Paradox.” Here, he uses a suitcase full of cash to serve as a metaphor for a resource that is caught in between a power struggle (“Israel’s Conflict As Game Theory”).

Blackmailer’s paradox describes the following situation: two players, let’s name them Alex and Bob, are put in a room with a suitcase containing $100,000. They may keep the money in the suitcase provided they can negotiate an agreement on how to divide it. Alex, thinking rationally, suggests that they simply split the money evenly so that each of them walks away with $50,000. But Bob, to Alex’s surprise, demands 90% of the money, leaving Alex with only 10%. Alex points out that this is not fair, but Bob declares “take it or leave it.” Alex, knowing that he will end up with no money if he does not accept Bob’s terms, surrenders and Bob leaves the room with $90,000. I had never heard of Blackmailer’s Paradox before and was surprised by how easy it was for Bob to make away with 90% of the money using an unreasonable and unjustifiable argument. My interest piqued, I decided to do a survey of Duke students, presenting them with the same scenario and asking them what they thought the most likely outcome would be given five different options. Here is what my survey looked like; note that I did not include the ending to Blackmailer’s Paradox:



Survey:

Two people (not necessarily acquaintances) are put in a room with a suitcase containing $100,000. The owner of the suitcase tells them that they can only have the money if they can negotiate an agreement on how to divide it. What do you think will happen? Please rank 1 through 5 where you think 1 is most likely and 5 is least likely.



  1. They will immediately agree to split it 50/50

  2. One person will demand significantly more than 50% or the deal is off, and the other person will eventually agree because they know their choices are to give in or to walk away with no money.

  3. One person will demand significantly more than 50% or the deal is off, and the other person will stubbornly protest because that is not fair. There will be no resolution.

  4. Both people will demand significantly more than 50% or the deal is off, and neither will give in. There will be no resolution.

  5. Both people will demand significantly more than 50% or the deal is off, and they will slowly negotiate (for example 90/10, 80/20, okay fine 70/30…) until they end up splitting 50/50

By the six methods for determining the winner of a preferential ballot, A won half the time and E won the other half of the time. A and E both result in a 50/50 split between the two players. It is very logical to make the prediction that no matter what happens, the end result will be that one person gets half of the money and the other person gets the other half. That would be fair, reasonable, and in no way surprising. However, if we look at disagreements across state borders or between any two competing entities, a fair 50/50 split is rarely the outcome. Relating this back to the Arab-Israeli conflict, Aumann puts forth the idea that the Israelis have fallen into the trap of the Blackmailer’s Paradox. This is evidenced by the fact that though the Israelis are willing to negotiate, they end up losing every attempt at a negotiation because the Palestinians repeatedly adopt positions that are either blatantly unfair or just not practicable. For example, the Palestinians have asserted that while Arabs have the right to live within Israel, Jews cannot live in areas that are controlled by the Palestinians (Jager). Israel has been forced to abide by their terms because otherwise they would emerge from the negotiation empty-handed (this particular example is synonymous with choice B in my survey). This would also jeopardize their relationship with the United States and certain European countries that support them. Thus, the conflict has still not been resolved. As the game continues, we actually see something similar to choices C and D of my survey, which end in no resolution. The conflict has persisted for so many years with only talks of peace without actual implementation, proving that options C and D are entirely plausible and in fact very likely. Despite this, C and D received the least number of votes.

The outcome of a war largely depends on decisions made by political leaders that hold considerable power. If there are two or more players in the game (or two or more leaders in a power struggle), and all the players use game theory strategy to decide the best course of action, an outcome that should be simple could suddenly become complex. Whether it is the Cold War, the Arab-Israeli conflict, or any other dispute, unexpected results can emerge when game theory principles are applied. Before I began this paper, war was a seemingly one-dimensional game of greed and power. But looking at it through the lens of game theory, war becomes a multifaceted game of infinite and startling outcomes.

Works Cited

"Israel's Conflict as Game Theory." Israel National News. N.p., 2010. Web. 04 Oct. 2012. .

Jager, Ron. "Israel Is Playing With Peace Talks." Reporting on the Middle East, Science, and Education. N.p., 2011. Web. 04 Oct. 2012. .

Poundstone, William. "Chicken." Heretical.com. N.p., 1992. Web. 04 Oct. 2012. .



"The World on the Brink." John F. Kennedy Presidential Library & Museum. N.p., n.d. Web. 04 Oct. 2012. .
Yüklə 30,63 Kb.

Dostları ilə paylaş:




Verilənlər bazası müəlliflik hüququ ilə müdafiə olunur ©www.genderi.org 2024
rəhbərliyinə müraciət

    Ana səhifə