Iterative deletion procedures derive their justification from common knowledge of rationality, but weak dominance deletion requires stronger assumptions that are not grounded in that basis.
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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.