If backward induction requires evaluating rationality at unreached nodes, the epistemic conditions for common knowledge collapse because there is no fact of the matter about what a rational agent would do at those nodes.
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common knowledge(Condition for the formation of a joint commitment)
A state in which each party knows the relevant fact, knows that the others know it, and so on — used here as the threshold condition for a joint commitment coming into force.
epistemic conditions
Conditions such as space and time, without which we cannot cognize any object
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.
rationality(Traditional conception being challenged by epistemic relativists)
A cognitive virtue and hallmark of the scientific method, intimately tied to requirements of consistency, justification, warrant, and evidence for beliefs.