Mathematics

### Paper 2, due Monday, April 5

Three-to-five page paper.

Use 2-person game theory models to analyze a political or interpersonal situation of your choice. Use either (1) game trees, which represent situations in which players move one after the other; or (2) game tables, which represent situations in which players choose strategies simultaneously. Or use both types of models if both are helpful.
1. Describe the situation.
2. Create some game theory models to describe it. Make sure that that you clearly explain the assumptions that go into your models. For example, clearly describe the players' preferences, so that the reader understands their ranking of the outcomes. You may want to create several models, since there may be several realistic possibilities for the players preferences. (Don't go overboard, just consider the possibilities you think are most important.)
3. Analyze your models using rollback (for trees) or by finding dominated strategies and Nash equilibria (for tables). Predict the outcome, or at least the most likely outcomes.
4. What are some ways a player could try to improve her outcome? Describe these in detail in the context of your models so that the reader understands exactly what you mean. Some possibilities are trying to change the game so the player moves first; trying to change the game so the other player moves first; trying to change the payoffs; using commitments, promises, or threats.
5. From among the possibilities you identified in part 4, which might realistically be successful?
6. Criticize your model. Have you captured enough important features of the situation so that your model is useful, or are there critical aspects of the situation that your model does not capture?
Here are some ideas for the subject of this paper. I prefer that you use your own idea instead of one of these, but I suggest you pass it by me first.
1. Two people get on a bus, but there is only one seat left. Each can either sit in it or offer it to the other. People are different--some are happiest when they can sit (due to selfishness or need), some are happiest when they can make someone else happy (altruists). Sometimes there are issues of pride: A person can need help, but not want to appear to need help. There are thus a number of possibilities for the preferences of the two players.

2. Two pedestrians come walking down a block from opposite directions. In the middle of the block, a crime is in progress: A boy is lying on the sidewalk, a hoodlum is kicking him and taking his wallet. Each pedestrian can run to the boy's aid, or he can stop and do nothing. If he tries to help, he may get hurt by the hoodlum; if he doesn't try to help, he may feel afterward that he has behaved dishonorably. Of course, people are different in how important these considerations are to them, and neither pedestrian knows the other. If both try to help, there is less likelihood of getting hurt by the hoodlum. Again, there are a number of possibilities for the preferences of the two pedestrians and how they size up the situation (for example, how likely they are to get hurt if they try to help).

3. Consider the rivalry between the United States and the Soviet Union during the Cold War. One interpretation of this rivalry is that the Soviet Union was striving for world domination, whereas the United States wanted to prevent the Soviet Union from dominating the world but was not itself striving for world domination. Each country had a choice of two strategies, aggressive or restrained. In analyzing this situation, you may want to consider both the possibility that the two countries choose their strategies simultaneously, and the possibility that one country or the other chooses first.

4. The following opinion column by Charles Krauthammer appeared in the Washington Post on March 19, and was reprinted in the Raleigh News and Observer on March 21:

In the 1930s Europe chose appeasement. Today Spain has done so again. Europe may follow.

One can understand Europe's reaction in the 1930s. First, it could almost plausibly convince itself that Hitler could be accommodated. Perhaps he really was only seeking what he sometimes said he was -- the return of territory, the unification of the German volk, a place in the sun -- and not world conquest.

Today there is no doubting the intentions of Arab-Islamic radicalism. It is not this grievance or that (U.S. troops in Saudi Arabia). It is not this territory or that (Palestine, Andalusia). The intention, endlessly repeated, is the establishment of a primitive, messianic caliphate -- redeeming Islam and dominating the world. They have seen the future: Taliban Afghanistan, writ large.

Moreover, Europe in the 1930s had a second excuse. The devastation of the first world war, staggering and fresh in memory (France and Germany lost a third of their young men of military age), had made another such war unthinkable. This does not excuse appeasement -- it cost millions more lives in the second world war -- but provides context and possibly humility. One has to ask oneself: Am I sure I would not have chosen the cowardly alternative?

Nonetheless, it was still the cowardly alternative. And today Spain has chosen it -- having suffered not Europe's 20 million dead of World War I but 200 dead in the Madrid bombings.

The Socialist Party placed the blame for the attack not on the barbarians who detonated the bombs but on the Spanish government that stood with the United States in its war against the barbarians. The Spanish electorate then voted into office the purveyors of precisely that perverse view.

Spain will now withdraw from Iraq, sever its alliance with America and, as Prime Minister-elect Jose Luis Rodriguez Zapatero has promised, "restore magnificent relations with France and Germany."

Nonetheless, Spain is just Spain. The really big prize is Europe. Which is why the most ominous development of the week was the post-Madrid pronouncements of Romano Prodi, the president of the European Commission.

"It is clear that force alone cannot win the fight against terrorism." Sounds reasonable until you hear Prodi's amplification of the idea just two days earlier. "We know that international terrorism wants to spread fear," he said. "Fear generates not so much justice but rather vengeance, which chooses war to answer the need of security. . . . We become prisoners of terror and of terrorists." In other words, making war on terror is unjust, fearful, mere vengeance and ultimately a victory for terrorism.

If not war, then what? A centerpiece to Prodi's solution to terrorism: a new European constitution. I'm not making this up: "to defeat fear we only have democracy and politics. . . . Today for us, politics means building Europe completely with its constitution and its institutions."

This is beyond appeasement. This is decadence: Terror rages and we tend our garden.

Prodi is right that the war on terror is not resolved by force alone. How is it won apart from hunting down terrorists and destroying terrorist regimes? By reversing the Arab-Islamic world's tragic collapse into oppression, intolerance and destitution, in which popular grievances are cynically deflected by repressive regimes and clergy into the virulent anti-Americanism that exploded upon us on Sept. 11, 2001. Which means trying to give desperate and oppressed people a chance at the kind of freedom and prosperity that we helped construct after World War II in Europe and East Asia.

Where on this planet is this project most engaged? Iraq, where day by day the U.S.-led coalition is trying to build a new civil order characterized by pluralism, the rule of law and constitutional restraints. Even a modicum of success in this enterprise would constitute a monumental strategic advance, a historic change in the very culture of the Middle East.

Spain's response to this challenge? Abandon the effort.

So when Zapatero and, more important, Prodi speak of nonmilitary means to combat terrorism, they don't mean draining the swamp by gradually building free institutions. They mean buying off the terrorists, distancing themselves from America and seeking a separate peace.

Sure, they will continue to track down individual al Qaeda terrorists. But that's no favor to anyone. They want to make sure there's not another Madrid, in case European appeasement is not quite thorough enough to satisfy the terrorists. But on the larger fight, the reordering of the Arab world that produced the terrorists, they choose surrender.

Discuss the strategy of appeasement as a two-person game. Are there circumstances where it is a good strategy?