This story blows me away. Last Saturday, the undergraduate students in Val Lambson's upper division game theory course at BYU arrived early for their final. They somehow convinced everyone in the course to not take the exam. So they all received scores of zero. But because the course grading is curved, their grades now depend entirely on the work done up to that point in the course. Thus, by this coordinated action, the students lowered their workload while decreasing the set of assignments upon which to base their grades. What blows my mind is that no one deviated--especially the students who were in the middle of the grade distribution going into the final.
Analyzing this equilibrium is interesting. Let's look at a number of cases.
Analyzing this equilibrium is interesting. Let's look at a number of cases.
1) Imagine that, going into the final exam, you are the student with the lowest score in the class. Why would you choose to not take the final, when deviating from the group and even getting a very low score (20 out of 100) might increase your grade by a letter grade because of the curve being based on a smaller number of assignments for everyone else? This student clearly stood to gain the most. However, the fact that he or she did not deviate belies the reality that his or her position at the bottom of the class represents a lack of knowledge of game theory.
2) Imagine that, going into the final, you are the best student in the class. You don't care if a small number of people deviate because, unless they are in the top of the grade distribution, they will not likely displace your ranking. And even if they displace you from the top spot, your probability of you still finishing with an A is still very high. However, if the number of people deviating also includes students from the middle or high end of the distribution, then the equilibrium unravels and the top ranked student takes the test.
3) Lastly, imagine that you are ranked somewhere in the middle of the grade distribution going into the final. You are smart enough to get a descent score on the final. For this reason, you have the most to gain from deviating. And because one of you deviating poses the biggest threat to the rest of the class in terms of ranking in the distribution, it takes fewer mid-range student deviations to unravel the equilibrium.
Key pieces of the full collusion outcome are the ability to monitor whether anyone deviated (although not perfect information on how game theory works), the way in which the information was communicated (starting value), and that no student feels that he or she would imrove in the course by taking the test if everyone took the test. Students waited around to see if anyone renegged on their commitment to not take the exam. Also, the students waited outside the classroom, and the major proponents of the action met the other students at the door and explained the proposed action while they walked to the class. The outcome probably would have been different if the students were all seated in the exam room and the tests had been passed out.
Val told me that nearly every section of this class that he has ever taught has brought up this idea. However, the students taking last Saturday's game theory final were the first to get the full collusion equilibrium to hold. Although my first reaction was a desire to congratulate the students, I think it might actually be a case of a poorly informed decision on the part of a significant number of students. But in any case, they certainly learned the power of strategic behavior on a number of levels.
2) Imagine that, going into the final, you are the best student in the class. You don't care if a small number of people deviate because, unless they are in the top of the grade distribution, they will not likely displace your ranking. And even if they displace you from the top spot, your probability of you still finishing with an A is still very high. However, if the number of people deviating also includes students from the middle or high end of the distribution, then the equilibrium unravels and the top ranked student takes the test.
3) Lastly, imagine that you are ranked somewhere in the middle of the grade distribution going into the final. You are smart enough to get a descent score on the final. For this reason, you have the most to gain from deviating. And because one of you deviating poses the biggest threat to the rest of the class in terms of ranking in the distribution, it takes fewer mid-range student deviations to unravel the equilibrium.
Key pieces of the full collusion outcome are the ability to monitor whether anyone deviated (although not perfect information on how game theory works), the way in which the information was communicated (starting value), and that no student feels that he or she would imrove in the course by taking the test if everyone took the test. Students waited around to see if anyone renegged on their commitment to not take the exam. Also, the students waited outside the classroom, and the major proponents of the action met the other students at the door and explained the proposed action while they walked to the class. The outcome probably would have been different if the students were all seated in the exam room and the tests had been passed out.
Val told me that nearly every section of this class that he has ever taught has brought up this idea. However, the students taking last Saturday's game theory final were the first to get the full collusion equilibrium to hold. Although my first reaction was a desire to congratulate the students, I think it might actually be a case of a poorly informed decision on the part of a significant number of students. But in any case, they certainly learned the power of strategic behavior on a number of levels.
How interesting! I'm sure that like most classes we considered doing this for any test in VEL's repeated games & reputation course a few years back.
Perhaps most of the students viewed the event as one that would be repeated in the future?
It's like the grad school basketball team when we all agreed not to score.
Oh wait. That's not how it works, is it?
In response to your bullet point one, while it may be true that the student at the bottom of the class lacks an understanding of game theory, I believe it is irrelevant. An understanding of game theory is not a pre-requisite for participating, self-interest is. I posit that as the lowest-performing student in the class, his/her interest more likely tends toward "not studying (in general)" or "not spending additional effort on a class that you probably hated," which interests align perfectly with a plan that involves no incremental work and results in no net loss.
My post is in agreement with ClarkW's comment above. The realized outcome in this class was clearly not a full-information equilibrium in which the agents' objectives were based on grade maximization.
Here's how I interpret it. Each student was faced with two alternatives:
1. Go along with the collusion and maintain my current place in the grade distribution.
2. Deviate and drastically improve my grade.
However, due to the monitoring that was going on, each student knew that if they picked option 2, everyone else would also take the final, and he or she would probably end up with the same grade as under option 1. If taking the test is costly in time and energy, then option 1 is clearly better (same grade without the cost).
The only remaining issue is "what happens to me if someone deviates and I collude?" Since this was a relatively large class, a single deviator is unlikely to do very much to everyone else's standing in the distribution. While the deviator moves way up in the distribution, most of the students are left unaffected.
I find it interesting that no one felt that they had a good chance of improving their spot in the distribution if everyone took the final.