Game Theory Behind Grading on a Curve
Grading on a curve is a method many college professors, including most at Cornell, use to grade their students’ assignments and exams. It is a method used to adjust the students’ scores to better match their performance based on the performance of other students in the class rather than a hard grade scale. There are many ways that a professor can “grade on a curve,” a common one is distributing a percentage of grades across the letter grade scale. For example, only 20% of students in the class would get an A, 30% would get Bs, and so on. Professor Caplan discusses in his post how he encourages his students to try collusion, where everyone relatively studies less but gets the same grade, and discusses why he is so confident that they will not collude because they are in a Prisoners’ Dilemma.
While often this method of grading results in setting the students to compete with each other, the students can actually use the system to their advantage if they teamed up to agree to study less and would still get the same grade. While Professor Caplan believes it is a Prisoners’ Dilemma, this situation seems to have two Nash Equilibria rather than one. The first Nash Equilibrium is where all students study and get the grade they deserve, and the other is where they all collude to study less.
While Professor Caplan is not worried or afraid that his student would collude, a group of students at John Hopkins University unanimously boycotted their final exam in order to all get A’s. However, this Nash Equilibrium is rare because if they suspect that even one student is going to study more, then all students will end up studying more and lead to everyone doing the first Nash Equilibrium.
Link: https://www.econlib.org/archives/2007/02/collusion_in_th.html