To Give a Surprise Exam, Use Game Theory

This paper proposes a game-theoretic solution to the surprise examination problem. It is argued that the game of " matching pennies " provides a useful model for the interaction of a teacher who wants her exam to be surprising and students who want to avoid being surprised. A distinction is drawn between prudential and evidential versions of the problem. In both, the teacher should not assign a probability of zero to giving the exam on the last day. This representation of the problem provides a diagnosis of where the backwards induction argument, which " proves " that no surprise exam is possible, is mistaken. 1. The Problem and its Game-Theoretic Setting Before the semester begins, a teacher announces to her class that she will give exactly one exam during the semester and that the exam will come as a surprise to the students when it occurs. One of the students in the class reasons as follows: If the teacher wants to give a surprise exam, she won't wait until the last day of the semester to give the exam, because the students will be expecting an exam then, if none has been given earlier. So the teacher won't give the exam on the last day. But if the last day is ruled out, the