The professor announces an exam to be held at the end of the semester and hopes this will induce his students to learn. Given his students have indeed studied, the best decision for the professor would be to cancel the exam to save himself the hassle of grading the exam papers. Thus, his optimal discretionary behaviour is time-inconsistent.
But if the students see through the professor’s incentive, they 2/8  BIS central bankers' speeches  might not study hard, and all of them end up worse off. What’s the way out of this dilemma? University examination rules which make end-of-semester tests compulsory instead of leaving them to the discretion of the professor.