Teaching the Key Concepts

Carmela Lutmar
New York University

Game Theory

[Editor's Note: Originally prepared for the second edition of Principles of International Politics]

When I teach the material from Principles, I am often asked questions about game theory, such as: “How do you get these trees?” or “How do you know what numbers to give to the policy options that you mention?” or “Do policy makers really make these calculations?” Indeed, I think this is one of the main issues in teaching this material–the ability to translate the technical terms to real-life examples.

I have used two particularly effective examples in the past to address these questions:

I ask students to think about a decision they make every day. They wake up in the morning, and since it’s winter, the last thing they feel like doing is going to classes. That’s pretty natural. But they also know that if they don’t go, they might miss something important, and this might even influence their final grade. So I tell them to think about this ‘imaginary’ decision tree. The question is, ”Should I go to school today or not?” The possible ‘branches’ are ‘yes’ and ‘no’. If a student answers yes and goes, there are again two possible ‘branches’ --leave after half a day (attend only one class) or stay all day and go to class. On the other hand, if the student decides not go to school,  two different possible ‘branches’ present themselves--stay home and read some assignments while sipping hot cocoa or go to a basketball game.

Obviously, all of these ‘endless’ decisions are made very quickly in our heads, and they all depend on the utility (or units of happiness) and probability we attach to each option. Together they make the expected utility. For example, if I personally can’t stand basketball, for me any option is better than seeing a basketball game. Going to school is definitely preferable. However, this is obviously not the case for everybody.

Alternatively, since we are all in political science, I ask the students to think about the following ‘current affairs’ example:

You know that the possible actions available to Arafat and Sharon in the current Middle East crisis are the following:

Arafat can favor UN intervention or not, and

Sharon can expel Arafat or not.

Their preference orderings are as follows:

Arafat prefers not to be expelled and to have the UN intervene over not being expelled and the UN not intervening over being expelled and the UN intervening over being expelled and the UN not intervening.

Arafat’s preferences are thus: Not expelled, UN intervention > Not expelled, no UN intervention > Expulsion, UN intervention > Expulsion, no UN intervention

Sharon prefers to expel Arafat and to block UN intervention over Arafat’s staying in the territories and no UN intervention over expelling Arafat but failing to prevent UN intervention over not expelling Arafat and the UN intervening.

Sharon’s preferences are: Expel Arafat, no UN intervention > Arafat not expelled, no UN intervention > Expel Arafat, UN intervention > Arafat not expelled, UN intervention

I ask them to build the game based on the preferences above and solve it. Then, I ask them whether it reminds them of any game previously encountered. Does it have Nash equilibrium?

This might seem like a very complicated analysis of a ‘simple’ question. But think about it–each leader also considers the other leader’s possible actions. After all, this is what we mean when we say ‘strategic interaction’. Each leader’s actions depend not only on his or her preferences but also on the opponent’s preferences.