After teaching a class on game theory, the instructor announces that if every student skips the last question on the next exam, everyone will receive full credit for that question. However, if one or more students answer the last question, all responses will be graded and those who skip the question will get a zero Will the entire class skip the last question if there is no chance for classmates to discuss the situation before taking the exam?

No they wouldn't, some students will for sure answer the question.

Explanation:

The best prepared (the ones that study a lot) students' dominant strategy will be to answer the question since they know they do not need to skip.

The dominant strategy in game theory refers to the strategy that will result in the highest gain for a player regardless of what course of action the other player (or players) take.

Not all the students in the class will have a dominant strategy, nor all the players in a game have one either. But those who have a dominant strategy will usually follow it regardless of what happens to others.