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It is not the case that Weak dominance lacks the epistemic robustness of strict dominance: a weakly dominated strategy remains rational under at least one opponent belief.
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Reasons For
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1.
The distinction between strict and weak dominance is pragmatically irrelevant: both require eliminating strategies that could harm rational players under plausible beliefs.
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2.
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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3.
Real strategic situations rarely feature perfectly uniform belief distributions. Weak dominance reflects realistic constraints better than strict dominance does.
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Reasons Against
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Reason against
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1.
Strict dominance guarantees optimality regardless of opponent beliefs, while weak dominance requires specific belief assumptions to justify play.
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2.
Rational agents should prefer strategies that perform well under uncertainty. Strictly dominated strategies fail this test; weakly dominated strategies pass it sometimes.
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3.
Epistemic robustness means a strategy remains rational across wider ranges of belief assignments. Strict dominance satisfies this; weak dominance does not.
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