Game Theory at Work

The article “Gaming The System” gives a real life example of game theory at work. The article is about a programming course at Johns Hopkins university, and how the students used game theory to beat the grading system. The story goes that a class was scheduled to take a final, but decided to boycott the exam because of a loophole in the grading schematic. The loophole was that the instructors grading system was one that curved, the curve in this case was giving the highest score in the class an A and adjusting all the lower scores based on the highest one. So by all students boycotting the exam and receiving 0’s, they would all actually receive A’s. The decision for all students to boycott is a Nash equilibrium in that if all the students expected one another to boycott they would all receive the highest payoff of an A. Conversely the other Nash equilibrium was if the students believed that even one person would deviate from this strategy and take the test they would all decided to change their strategy and take the test. The strategy to boycott the test though is the dominant strategy in the fact that they would all get A’s. So they really had no reason to switch that strategy because there was a chance of a lower payoff if they took it, but not a higher one. 

Even more fascinating was the professors decisions to honor the curve and give all students A’s! He likely accepted that he got outsmarted, and thus honored the grade. But the article does say that he amended his syllabus to prevent being duped in the future. Non the less it was a fascinating real life example of game theory at work.

 

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1 thought on “Game Theory at Work”

  1. This is a great discussion of a real world application of game theory, and I was especially interested in Rampell’s description of “trembling hand perfect” equilibria. Rampell describes two Bayesian Nash Equilibria, one in which no one takes the test and one in which everyone takes the test. She says that the second equilibrium is “trembling hand perfect” because even if someone fails to take the test by mistake, they cannot affect the payoffs of other students. On the other hand, she says that the first equilibrium is NOT “trembling hand perfect” because one student’s failure to adhere to the boycott has the potential to ruin every other student’s payoff and thus cause the equilibrium to unravel.

    I find it a bit odd, however, that she is so surprised by the students’ success. There seems to be a significant amount of research on the importance of communication in producing cooperative outcomes. For example, there is big difference in the results of the standard prisoner’s dilemma game and a the prisoner’s dilemma game played with the added element of communication (http://www.dklevine.com/lectures/evolution/bachi.pdf). It may be that what the students did was surprising and the result was certainly not a trembling hand perfect equilibrium, but may also be that those of us interested in economic game theory just tend to discount the importance of communication in games.

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