Applied game theory: Students boycott exam and all get an A

A piece on the New York Times Economix blog casts a story from Inside Higher Ed as a piece of applied game theory. Professor Peter Fröhlich of Johns Hopkins University has a grading system in which

each class’s highest grade on the final counts as an A, with all other scores adjusted accordingly. So if a midterm is worth 40 points, and the highest actual score is 36 points, “that person gets 100 percent and everybody else gets a percentage relative to it,” said Fröhlich.

Can you spot the problem? The Economix posts points out that this allows “at least two Bayesian Nash equilibria”:

Equilibrium #1 is that no one takes the test, and equilibrium #2 is that everyone takes the test. Both equilibria depend on what all the students believe their peers will do.

In equilibrium #1, everyone scores the same mark – zero – and the calibrated marking scheme maps this onto 100%. The students, realising this, arranged a complete boycott and were all awarded grade A.

Alas, this was not a game theory class! Prof Fröhlich has since changed his grading scheme.

Further information:

Dangerous Curves (Inside Higher Ed) has some detail of how the boycott was arranged (had just one taken the test, all would have been forced to follow suit).

Gaming the System (Economix) discusses the related game theory and economics concepts.