To give a surprise exam, use game theory

Synthese 115 (3):355-373 (1998)
Abstract
This paper proposes a game-theoretic solution of 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.
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