Who Sets the Curve?

Even though extra study time will improve only one's absolute position but not one's relative position in the grading curve, competitive pressure will ensure that any agreement to not out-study each other will be broken.

In my high school Anatomy and Physiology class, I or my friend Adam always got the highest score on the tests. The tests were curved based on the highest grade so either I or Adam would set the curve. Our grades were very close and always in the A range, even before the curve was applied. After the curve, one of us would always have a 100% and the other would be slightly below 100%. The rest of the class generally scored poorly on the tests so we did not have to worry about any competition from them. Our primary goal was to get an A in the class and maintain a high GPA. However, we also competed to get the highest score on the test. We simply wanted to be able to brag to the other person. The Anatomy and Physiology tests were very comprehensive and sometimes consisted of 200 questions. It took a large amount of time and effort studying in order to get a very high raw score.

It would have been possible for us to both achieve our primary goal of getting an A without studying if we both made an agreement to not study. Without studying, both of us might have scored around 80%. Then our grades would be curved up roughly 20%, with one of us having a 100% and the other having slightly below 100%. That outcome is the same as if we had both studied furiously, yet we got there without having to study. Unfortunately, an agreement between us would be extremely unstable. The temptation to cheat on the agreement would be very strong. With only a small amount of studying I might have been able to raise my score up to a 90% and set the curve at 10%. Adam would then only have a curved score of 90% or possibly even less, while I would have a curved score of 100%. He would then be stuck with a low final score and a score much lower than mine, which would subject him to friendly verbal abuse and taunting from me. In this case the opportunity to gain a bragging right as well as the risk of losing face is too large. Both parties have a large incentive to cheat on the grade-fixing agreement, so both of us will.

This situation clearly shows a prisoner's dilemma. It would be easier for us to both agree to not study, yet still get A's after the curve. However, the agreement is unstable and we will both end up studying a lot to get the same grades as if we had not studied. In other words, studying hard is the dominant strategy for both of us. But there is a twist here. Most PD games assume that pursuing the dominant strategy will lead to an individually smart but collectively dumb result. However, if studying harder helps us understand the subject matters better, then both of us would be better educated for the extra efforts. So whether the collective result is dumb or smart really depends on one's perspective.