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    Strict dominance implies weak dominance, but weak dominan... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    Strict dominance implies weak dominance, but weak dominance does not necessarily imply strict dominance

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.A strictly dominated strategy fails to be a best response to any belief
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    • 2.A weakly dominated (inadmissible) strategy may still be a best response to beliefs that assign probability one to states where the player is indifferent between the weakly dominated action and the admissible one
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    • 3.These conditions are not symmetric
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Under Savage's framework, rational preference requires complete state-space specification, making the strict/weak dominance distinction dependent on how states are individuated.
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    • 2.If states are individuated finely enough to distinguish all payoff-relevant outcomes, every case of weak dominance collapses into strict dominance, dissolving the asymmetry.
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    • 3.The apparent non-implication from weak to strict dominance is therefore an artifact of coarse state descriptions, not a fundamental logical asymmetry.
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    Reason against 2 of 2
    ?
    • 1.Pearce's 1984 rationalizability framework demonstrates that iterated elimination of weakly dominated strategies is order-dependent in ways that iterated elimination of strictly dominated strategies is not.
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    • 2.This order-dependence reveals that weak dominance lacks the modal robustness required for genuine dominance reasoning, suggesting weak dominance is not a weakened form of the same relation but a categorically different one.
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    • 3.If strict and weak dominance are categorically distinct relations rather than stronger and weaker instances of one relation, the claim that strict dominance 'implies' weak dominance mischaracterizes their logical relationship.
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    Related

    A strictly dominated strategy fails to be a best response to any beliefA weakly dominated (inadmissible) strategy may still be a best response to belie...If states are individuated finely enough to distinguish all payoff-relevant outc...If strict and weak dominance are categorically distinct relations rather than st...
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    Pearce's 1984 rationalizability framework demonstrates that iterated elimination...The apparent non-implication from weak to strict dominance is therefore an artif...These conditions are not symmetricThis order-dependence reveals that weak dominance lacks the modal robustness req...Under Savage's framework, rational preference requires complete state-space spec...

    Similar

    The analogue of the strict dominance observation (that dominance is pr...86%The invariance property of strict dominance under additional informati...86%Weak dominance is defined existentially: a strategy is weakly dominate...84%Strict and weak dominance must be defined in terms of mixed strategies...83%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemic-game
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    The proof of this Lemma is more involved. See Bernheim (1984: Appendix A) for a proof. In order for a strategy \(s_i\) to not be strictly dominated, it is sufficient for \(s_i\) to be a best response to a belief, whatever that belief is, about the opponents’ choices. Admissibility requires something more: the strategy must be a best response to a belief that does not explicitly rule-out any of the opponents’ choices. Comparing these two Lemmas, we see that strict dominance implies weak dominance
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit