## Dangerous Curves

Dangerous Curves by Zack Budryk: https://www.insidehighered.com/news/2013/02/12/students-boycott-final-challenge-professors-grading-policy-and-get

Zack Budryk’s article *Dangerous Curves *appearing in the online journal “Higher Ed” is the extraordinary story of how John Hopkins University students unanimously boycotted their final exam in order to all get A’s. The grading curve at John Hopkins functions by giving the highest score on any final exam an A and then adjusting all lower scores accordingly. Students realized that if they collectively came together and refused to enter the exam room, the highest score would be a zero by default, and thus everyone would be entitled to an A. Surprisingly the students pulled it off. Their ability to take advantage of the grading curve loophole is a prime example of a Game Theory, specifically called The Nash Equilibrium.

Andre Kelly, one of the student organizers of the boycott explained, “if you were able to walk into the exam with 100 percent confidence of answering every question correctly, then your pay-off would be the same for either decision. Just consider the impact on your other exam performances if you studied for [the final] at the level required to guarantee yourself 100. Otherwise, it’s best to work with your colleagues to ensure a 100 for all and a very pleasant start to the holidays.”

This protest is an example of game theory outcome that is exemplified by two types of Bayesian Nash Equilibria. The Nash Equilibrium is a list of strategies, one for each player, such that each player’s strategy is a “best response” to each of the other players. In the described example both equilibria depend on what all the students believe there peers will do. For example, 1) If all students believe that everyone will boycott with 100% certainty then everyone should go through with the boycott; and 2) If anyone presumes that at least one of their peers will break the boycott, then anyone may alter their choice and be forced/decide to take the exam. In this rare example, a stable outcome occurs where no student has an incentive to change his/her strategy after considering the strategies of the other “player”/ student. The only flaw in The Nash Equilibrium is that it doesn’t demonstrate what students are likely to do. Other than that the first equilibrium is highly unlikely.

If someone caves under Equilibrium #1 (in which no one takes the test) and proceeds to take the test despite knowing others have agreed to refrain, then that equilibrium collapses and everyone will end up having to take the test after all. This scenario will devolve into Equilibrium #2 (in which everyone takes the test and gets the grade they deserve). This conjecture is a prime example of The Nash Equilibrium game theory. The irony, at the end of the day, is not the students’ cooperation in order to achieve a rare equilibrium, it is their professor’s decision to honor the original grading system and award everyone an A.