Game theory says that no one cheating and deciding to take the final would be the obvious outcome because the students have no incentive to cheat the system. If they skip the test, they get 100. If they take the test, they get up to 100. No advantage from taking the test.
Now, if the maximum score for everyone skipping the test was lower than 100, then things would be interesting.
Everybody skipping the exam is a Nash equilibrium, but assuming perfectly rational behaviour (and that everybody has a utility function which depends solely on final exam grade) is dangerous.
This is, of course, why students turned up and waited outside to see if they needed to write the exam rather than just assuming that other students would all do the "obvious" thing.
Excellent username/post combo. What if some students believed that the professor would change his mind and change the rules when he realized what was going on?
Now, if the maximum score for everyone skipping the test was lower than 100, then things would be interesting.