Information-Dependent Games: Can Common Sense Be Common Knowledge?

This paper attempts to study the consistency of several basic gametheoretic axioms. We focus on two of these: _q_qmmon_.knowledge (CK) and common sense (CS). Common knowledge assumes that the game itself and all other game-theoretic axioms imposed on the model are common knowledge~ Common sense assumes that when a player has a strictly dominant strategy, he/she will play it. We use the following version of the surprise-test paradox to show that the axioms CK and CS may be inconsistent. Suppose there are two players, the teacher and the class. The teacher should choose on which out of two days, say Thursday and Friday, a test will be given. The ctass is a dummy player, that is, it has a single strategy. The rules of the "game" are that the teacher has to be able to prove that, the evening before the day of the test, the class could not have proven that it would be taking place the following day. The teacher's payoff is 1 if he can prove it, and 0 otherwise. The class' payoff is irrelevant. If we assume both CK and CS, we can follow the usual argumentation of the paradox: if the teacher decides to give the test on Friday, his payoff is bound to be zero, and that is common knowledge. The paradox lies in the