Stalnaker (1998) demonstrates that common knowledge of rationality is consistent with non-backward-induction play when rationality is construed as belief-relative rather than strategy-profile-relative.
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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.
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.