lazy and grieving students: I'm very confused about your use of utility numbers here, and your implication that one player's utility can be traded for another. That's not how it works. If you have a term for the other player's happiness, that's your utility, not theirs. If you have a utility cost for failing a student because of a late assignment, you need to include that in your plan.

It was mentioned that the teacher is a utilitarian. That means that they would like to maximize overall net utility, imagining that it can be summed over people. There has been a bit of discussion about the difference between the 'utility' of economists and the 'utility' of ethicists, but I think we still need a thorough post on this, and if I weren't so busy I'd have done it already.