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The student’s dilemma

A professor in the USA recently posed an interesting dilemma to students taking his psychology exam. At the end of the exam students were provided with a bonus question in order to gain extra credit. All they had to do was decided whether they would like two or six additional marks adding on to their final score. The twist was that if more than 10% of the class opted for an additional six marks then everyone would get nothing added on!

The professor had placed the students in a prisoner’s dilemma scenario. To see this consider an individual student weighing up which option to choose; if more than 90% of the class chose two additional marks, then this student is better off choosing six additional marks. Whereas if more than 90% of the class chose six additional marks, then this student is indifferent between the two options (the student will get no additional marks regardless of their choice). It follows that choosing six additional marks is a weakly dominant strategy.

In a similar fashion, in the classic prisoners setting keeping quiet is collectively better, however, each criminal has a strong individual incentive to confess. Likewise, in oligopoly markets the interdependence between firms results in a tension between cooperation and competition. Firms collectively benefit from keeping prices high, but an individual firm has an incentive to undercut its rivals and steal a large share of the market. A strong prediction when self-interested participants play the prisoner’s dilemma game just once and choose their strategies independently is therefore that the prisoners will confess to the crime and that firms will set low prices.

So did the US professor end up giving away many bonus marks? No, about 20% of the class opted for six additional marks and as a result all the students ended up with no extra marks. In fact, the professor claims to have been running the same experiment for the previous seven years and only once has he ended up giving away any bonus marks. On the one hand, this result is consistent with what is predicted in the prisoner’s dilemma game. However, running contrary to this is the fact that around 80% of the students opted for just two additional marks. It would certainly be interesting to see what would happen if in future years the professor relaxed the threshold above which all students get no extra marks.

UMD ‘tragedy of the commons’ tweet goes viral The Baltimore Sun, Quinn Kelley (09/07/15)
A professor tested the ‘Prisoner’s Dilemma’ on his students by bribing them with extra credit points Tech Insider, Will Haskell (17/07/15)

Questions

  1. Draw the payoff matrix for the student’s dilemma.
  2. What are some of the possible explanations for around 80% of the class choosing two extra marks?
  3. How do you think the outcome of the game might have changed if students were allowed to communicate with each other before making their choice on the number of additional marks to ask for?
  4. How do you think student choices would change if the threshold above which all students get no extra marks was varied?
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