If a player observes a deviation from backward induction, this constitutes evidence that common knowledge of rationality has already failed, making the assumption vacuous at that point.

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Deviation(game theory): When someone acts in a way that goes against what the rationality assumption would predict they should do.
backward induction(Game theory solution concept applied to sequential games): A method of solving extensive-form games by reasoning from terminal nodes backward to earlier decision nodes, determining optimal play at each node given optimal play at all subsequent nodes
common knowledge of rationality(Epistemic game theory): An epistemic condition in which all players are rational, all players know all players are rational, all players know that all players know all players are rational, and so on ad infinitum
knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.): Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

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