The Game Theory Behind Acing an Exam

By Anne Evered. Stanford University. 

Last December, students at Johns Hopkins University took advantage of their computer science professor’s grading policies to essentially “game” the system and receive full marks on an exam without ever filling out a single answer.

Professor Fröhlich, who teaches courses in computer science, grades the exams for his classes on a curved scale with the highest grade of the class counted as a 100% and the rest of the scores scaled accordingly. This system leaves open a loophole: if all students get 0’s, then a 0 is the highest score, so all students would receive a 100%. This year, students in three of Fröhlich’s classes took advantage of this loophole and set up a boycott of the test, the catch being that the plan would only work if everyone stuck to it.

What happened on the day of the test is an all but miraculous show of collaboration. As Professor Fröhlich recounts, “The students refused to come into the room and take the exam, so we sat there for a while: me on the inside, they on the outside…After about 20-30 minutes I would give up…. Then we all left.” Some of the students stuck around, though, to ensure that everyone held to the agreement. Ultimately, the boycott held. No one took the test; all students received A’s.

According to economists, the achievement of this agreement is somewhat unexpected. Examination of how this situation worked in game theory terms reveals why.

Read the full paper here.