January 22, 2007
The Prisoner's Dilemma and the Curve
Posted by Jeff Lipshaw
I watched this play out in front of me last Wednesday.
We all know the Prisoner's Dilemma of game theory. Two prisoners are being interrogated separately and cannot communicate with each other. Each must make the decision whether to confess or stay quiet, not knowing what the other will do. There are three possible payoffs: if both prisoners confess each gets a moderate sentence; if both stay quiet they walk; but if one confesses and the other stays quiet, the confessing prisoner gets a light sentence, and the hold-out gets the full term. The irony of the game is that the dominating strategy for each prisoner is to confess, but the best result for each of them individually is if each of them holds out, which means that there needs to be cooperation.
At the end of Secured Transactions class, one of the students in the back row asked "how many students do you have in this class?" The reason is that Tulane has a mandatory curve if there are twenty-one or more students in the class, and we seemed to be hovering around that number. Assume the desired payoff is that the class not have the mandatory curve, but each student wants to take the course (no snide remarks, please). If there are exactly twenty-one students, and one of them drops, all the remaining students have the benefit (?) of there being no mandatory curve.
Actually, I think the game model only works if the students see a significant payoff in staying in the course. Which probably explains why I expected to walk in the next day and find that I had a four-person class.
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You can keep enrollment up by telling students that, if you don't have to follow the mandatory curve, you will actually give LOWER grades than the curve suggests!
Posted by: Andrew Perlman | Jan 22, 2007 9:58:55 AM