The caution requirement reflects Brandenburger and Dekel's correlated rationalizability refinement, which is a substantive additional constraint beyond common knowledge of rationality itself.
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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
constraint(canonical formulations of general relativity and electromagnetism)
A condition encoding the fact that canonical variables cannot be specified independently of one another.
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.
substantive(classification of linguistic forms by their role in expressing categories of thought)
The linguistic form required to express thought's apprehension of independent objects