Gaming the System

“The desire to be seen as clever often prevents us from becoming so.” — La Rochefoucauld

Some college students used game theory to get an A by exploiting a loophole in the grading curve.

Catherine Rampell explains:

In several computer science courses at Johns Hopkins University, the grading curve was set by giving the highest score on the final an A, and then adjusting all lower scores accordingly. The students determined that if they collectively boycotted, then the highest score would be a zero, and so everyone would get an A.

Inside Higher Ed, writes:

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,” [Peter Fröhlich, the professor,] said. “After about 20-30 minutes I would give up…. Then we all left.” The students waited outside the rooms to make sure that others honored the boycott, and were poised to go in if someone had. No one did, though.

Andrew Kelly, a student in Fröhlich’s Introduction to Programming class who was one of the boycott’s key organizers, explained the logic of the students’ decision via e-mail: “Handing out 0’s to your classmates will not improve your performance in this course,” Kelly said.

“So if you can walk in with 100 percent confidence of answering every question correctly, then your payoff 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.”

Bayesian Nash equilibria

In this one-off final exam, there are at least two Bayesian Nash equilibria (a stable outcome, where no student has an incentive to change his strategy after considering the other students’ strategies). 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.

If all students believe that everyone will boycott with 100 percent certainty, then everyone should boycott (#1). But if anyone suspects that even one person will break the boycott, then at least someone will break the boycott, and everyone else will update their choices and decide to take the exam (#2).

Two incomplete thoughts

First, exploiting loopholes ensures increasing rules, laws, and language (to close previous loopholes), which lead to creating more complexity. More complexity, in turn, leads to more loopholes (among other things). … you see where this is going.

Second, ‘gaming the system’ is a form of game theory. What’s best for you, the individual (or in this case, a small group), may not be best for society.

Today’s college kids are tomorrow’s bankers and CEO’s. Just because you can do something doesn’t mean you should.

Update (via metafilter): In 2009, Peter Fröhlich, the instructor mentioned above, published Game Design: Tricking Students into Learning More.

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Still curious? Learn more about game theory with the Prisoners’ Dilemma.