Bonus Friday link: the greatest example of applied game theory EVER

Just saw this and it’s too good to wait for our next linkfest to share: computer science students at Johns Hopkins are graded on a curve, with the highest mark in the class being an “A” and the other marks defined accordingly. So students in one class all decided to skip the final, thereby ensuring they all received zeroes–and thus A’s! And they got away with it!

For anybody out there who teaches game theory (say, in an animal behavior class) and wants to drive home its relevance in the real world, now you have your go-to example!

I wish I could say that this is why I don’t grade on a curve (which I don’t), but now I have one more reason not to do so.😉

HT Economist’s View

8 thoughts on “Bonus Friday link: the greatest example of applied game theory EVER

  1. The only way this would be a better story is if it had occurred in a class on game theory. If it had, and if I was the instructor, I’d be totally fine with giving these students A’s!

    • Brilliant! I’d say it’s not too bad to let them all have their A’s anyway, even if the class wasn’t about game theory. If they’re able to figure this out and make it work, they’re probably also smart enough to have studied anyway, just in case anyone would ‘cheat’ and take the exam🙂

  2. Great story! I’m not so sure about the analysis suggesting that the “everyone skips” equilibrium is unstable in this case. Everyone was waiting outside the room, so everyone could see for themselves that no-one was cheating (cheating in this case being writing the exam, oddly enough). This greatly increases the incentive to hold firm. Furthermore, this situation invites threats beforehand and repraisals (e.g., ostracism) afterwards, against anyone who might choose to write the exam.

    I once risked promoting collusion by telling a class that I would use the maximum number of questions answered as the denominator in their midterm exam grade. I was a bit worried that they might all decide to answer one easy question, but I figured this would be too open to cheating (i.e., answering more questions), so I didn’t worry about it. And everyone just answered as many questions as they could. I think the main difference was that the number of questions each student answered was anonymous so there was no opportunity for social punishment. Later in the course, I used the midterm rules to explain the Prisoner’s Dilemma.

    Here’s to more game theory on Dynamic Ecology!

    • Wow, consciously and explicitly incorporating game theory into the structure of your midterm exam is really cool–and really gutsy!

      Yeah, you’re right that one can quibble about the analysis of the game the students are playing, but to me that just makes it an even better example. Because that too is a key feature of pretty much any real application of game theory in science–deciding exactly what game is being played.

      I know it’s common for game theory profs in economics to make students play pretend games, which is also fun but less gutsy. For instance, there’s the game where the prof offers a $20 bill to the highest bidder, with the condition that both the highest and second-highest bidders have to pay the prof their bids. So you get one student who hasn’t thought things through bidding, say, $1. And then some other student who hasn’t thought things through bids $2. So now the first student is out $1 unless he raises his bid. So he does the rational thing and bids $3, prompting the other student to raise his bid to $4. The students keep going like this until one of them is forced to bid $21 for a $20 bill, so now even if you “win” the auction you lose money. But that doesn’t even stop the game, because the winning bidder at least is losing only $1 net, while the losing bidder is out $20. So he raises his bid to $22…at which point the prof presumably has mercy on them and calls a halt, explaining that the rational thing to do was not to bid in the first place. And then the prof presumably shows a YouTube clip of the climax of “War Games”.😉

  3. What’s interesting here, is the fact that it is really cooperation. Any one non-cooperative student, ie, a student who would have taken the exam, would have got the best mark, and all others would have received a bad mark. Hence, in a classroom where most students were ready to skip the exam, the best strategy would have been to do the exam. And still, no one did.

    • True. Although the students were all gathered outside the classroom door, watching each other. Had any student decided to go in and take the exam, the other students all would’ve been able to follow–and also enforce social sanctions later, if they’d wanted. As another commenter remarked, these kinds of details are part of what make applications of game theory challenging (and interesting). It’s often difficult to say exactly what game the players are playing and exactly what the available strategies are.

      • Sure, social pressure is what can favor cooperation here. Regarding the game, if, besides the mark, we take the rankings of students into account, I do think that “everyone skips” is unstable (and hence requires another mechanism, like policing, to be reached). This is because defecting (= taking the exam) is always a better strategy. If all others skip, and you take the exam, you will still get an A (as you would have if you had not skipped), but you are ranked 1st (while you would otherwise have the same mark as all others). If one other takes the exam, you’d better take it too, because, either you are better than that other, and you still get an A, or, if you know less than the other, you still get a relatively better mark than if you skip if you can answer at least one question.

  4. Pingback: Friday links: gaming a game theory exam, “alpha females” in academia, and more | Dynamic Ecology

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