I actually had a professor rant about this yesterday. But, If all students believe that everyone will boycott with 100 percent certainty, then everyone should boycott (#1). But if anyone suspects that even one person will break the boycott, then at least someone will break the boycott, and everyone else will update their choices and decide to take the exam (#2). While this is sound game theory, it's extremely silly to apply it to this situation. If the students were "blind" (i.e. not in the building) and were actually going on faith, this analysis would be relevant. But since every student was standing next to the door, all that gets thrown out. It's no longer remotely improbable for the students to land on the less likely of the two Nash equilibria -- cooperation.In this one-off final exam, there are at least two Bayesian Nash equilibria (a stable outcome, where no student has an incentive to change his strategy after considering the other students’ strategies). Equilibrium #1 is that no one takes the test, and equilibrium #2 is that everyone takes the test. Both equilibria depend on what all the students believe their peers will do.