Of common knowledge (Common Knowledge of Rationality, CKR) is a sufficient condition for backward induction. Rational meaning is very clear here is that participants are "learning
Sex up "(habitual) to pay to maximize, that is, at any vertex, the premise that he would not knowingly cause to continue the implementation of a strategy to pay less than the other strategies. However, Aumann acknowledged, CKR is a very stringent requirements, rarely encountered in practice, if CKR not met, then the backward induction may not only be unreasonable and unwise, and there may still be irrational! Therefore, Aumann pointed out that despite CKR backward induction can guarantee results, but he does not guarantee to meet the CKR.
In the following short essay which, Aumann (1998a) shows that in Rosenthal's Centipede Game (centipede game), if from the game beginning, the proposition A is a common knowledge, then the traditional backward induction results will appear, namely a first step on the choice of participants down, the game ended. which proposition A is: participants in their actual arrival only rational choice vertex.