Imagine a world where education is of no intrinsic value, and serves only as a signal of an unobservable character trait called "ability." Performance (which can be observed) is determined by both ability and effort. Effort is costly. Some students have a high level of ability, and some have a low level of ability. A professor's job is to rank them. Professors cannot recognize absolute excellence, only relative excellence, and so grade on a curve.
To keep things simple, imagine there are just two students, a high ability student, Alice, and a moderate ability student, Betty. The professor will always give out one A and one B.
The optimal strategy for the students depends upon their relative ability. Suppose that Alice's ability so much exceeds Betty's that she will always does best, no matter how hard Betty studies, and how little Alice does, as shown in the table below:
The first part of each cell describes Betty's outcome, and the second Alice's. So, for example, when both work, Betty's outcome is (B, effort) and Alice's outcome is (A, effort). In this scenario, Alice's superior ability means that the relative performance of the students is unaffected by studying, so there is no point in either of them putting out any effort. We arrive at the slacker solution.
The professor might complain about his students' shirking, but he would be wrong to do so. The students are shirking because mastery of the course material is not of intrinsic value to them. Since the purpose of education is to signal ability, coordinated shirking is a good thing, because it allows students to transmit an accurate signal of their ability at a lower cost.
The more interesting game is the student's dilemma. In this game, if Betty works and Alice shirks, Betty can outperform Alice.
The outcome of this game depends upon how the two students value effort and grades. There are three possible scenarios.
If Betty would rather get a B than study, so she prefers (B, no effort) to (A, effort), the optimal strategy for both is to shirk. If Betty is shirking, there is no point in Alice working, because she can get an A without studying. If Alice is shirking, Betty could achieve an A by working, but it's not worth it to her, because the cost of studying is greater than the benefits of an A. The slackers' equilibrium will prevail unless Alice actually gets positive enjoyment from studying. As long as Betty is shirking, there is no point in Alice ever working, as she will get an A regardless.
If the cost of effort is low enough (or the value of grades high enough) that both Alice and Betty would rather study than settle for a B, the game has no pure strategy equilibrium. If both start off shirking, Betty has an incentive to start working, because she can get an A rather than a B. But if Betty works, Alice has an incentive to work too. However, if Betty figures that Alice is going to work, there's no point in her working, so she shirks. Yet, if Betty shirks, then Alice figures she might as well too. We have the students' dilemma.
A final possibility is that, perhaps because Alice has attention deficit disorder, the cost of studying is lower for Betty than Alice. Betty prefers (A, effort) to (B, no effort), but Alice prefers (B, no effort) to (A, effort). They can both get what they want when Betty works and Alice shirks. This is an equilibrium because, if Betty is working, Alice doesn't bother, because she would rather settle for a B than put in the time and effort to get an A. If Alice isn't working, Betty does, in order to get a solid grade.
In this final scenario, when Betty works and Alice doesn't, the usefulness of education as a signal is restored. However it no longer serves as a signal of innate ability. Instead, it signals the cost to an individual of exerting effort. Those who get As are those are able to get organized, study, and hand things in on time at a low personal cost, and thus are likely to be able to get organized and hand things in on time in the workplace also. This, from an employer's point of view, is as good a reason as any to hire someone with a university degree.
The picture presented here is a caricature of education. In the real world, grades are determined by both relative and absolute performance. Yet, when relative performance matters, there is always the possibility of the student's dilemma.