Epistemic robustness is not the only criterion for rationality. A weakly dominated strategy can be epistemically justified if the opponent belief is well-founded through credible information.
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A cognitive virtue and hallmark of the scientific method, intimately tied to requirements of consistency, justification, warrant, and evidence for beliefs.
weakly dominated strategy(Strategic game theory, Lemma 3.2)
A strategy s_i in S_i is weakly dominated (possibly by a mixed strategy) with respect to a subset X of the opponent strategy space S_{-i} if and only if there is no full support probability measure p in the interior of the simplex over X such that s_i is a best response with respect to p.