The Game Theory of Extra Credit

There are few phrases that college students love to hear more than "extra credit." However, one professor at the University of Maryland found a way to turn extra credit against his students by asking a very simple question at the end of one of his psychology exams:

"Here you have the opportunity to earn some extra credit on your final paper grade. Select whether you want 2 points or 6 points added onto your final paper grade. But there's a small catch: if more than 10% of the class selects 6 points, then no one gets any points. Your responses will be anonymous to the rest of the class, only I will see the responses."

We can examine the potential payoffs of the possible decisions each student faces.

While this is not a true prisoners' dilemma because each student doesn't have a dominant strategy, the chances of you being the deciding vote are very slim, and only decreases as the class size increases. Thus, in a large class, each (rational) student is most likely to choose 6 points, ultimately leading to the entire class receiving zero extra credit points.

This is very cool, but I think that a teacher could combine this tactic with another phrase that college students love to hear - "the class is curved" - in order to create a true prisoner's dilemma and ensure that, for any size class, the end result will be that no one receives extra credit. Curves mean that the absolute value of your grade means nothing, and what really matters is your grade relative your other classmates. Thus, the potential payoffs become:

Each student now has a dominant strategy to choose 6 points. If less than 10% of the class chooses 6 points, then choosing 2 points would give you at best 0 relative points (if the entire class chooses 2 points) and most likely negative relative points (if at least one other person chooses 6 points). The same thing occurs if you are the deciding vote. Therefore, each student is at least as good off by choosing 6 points as they would have been if they chose 2 points.

In the end, the professor looks benevolent because he offered extra credit to his students, and the students learn a valuable lesson about game theory. The only thing irrational about this is why more professors don't use it in their classes.