Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    A strategy that is not strictly dominated need not be adm... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    A strategy that is not strictly dominated need not be admissible

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

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.For a strategy to not be strictly dominated, it is sufficient for it to be a best response to some belief about opponents' choices, whatever that belief is
      ?

      Think about whether this reason is strong or weak

    • 2.Admissibility requires the strategy to be a best response to a belief that does not explicitly rule out any of the opponents' choices — i.e., a full-support probability measure
      ?

      Think about whether this reason is strong or weak

    • 3.A strategy can be a best response to some particular belief without being a best response to any full-support probability measure
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.A strategy weakly dominated by no pure strategy can still be admissible, collapsing the gap the claim presupposes between non-domination and admissibility.
      ?

      Think about whether this reason is strong or weak

    • 2.Pearce (1984) shows that in finite games, iterative elimination of weakly dominated strategies converges to the same set as admissibility, suggesting the two criteria are extensionally equivalent in relevant cases.
      ?

      Think about whether this reason is strong or weak

    • 3.If non-domination and admissibility coincide in the class of games where the distinction matters most, the claim identifies a merely formal rather than substantive divergence.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 1.The supporting argument's P3 smuggles in a contentious Bayesian assumption: that rationality requires beliefs representable as single probability measures rather than sets of measures.
      ?

      Think about whether this reason is strong or weak

    • 2.Under Levi's and Walley's imprecise probability frameworks, a strategy counts as admissible when it is a best response to some measure within a credal set, dissolving the strict full-support requirement in P2.
      ?

      Think about whether this reason is strong or weak

    • 3.If the full-support condition in P2 is not a necessary feature of admissibility but an artifact of orthodox Bayesianism, the logical gap between non-domination and admissibility that grounds the claim does not hold generally.
      ?

      Think about whether this reason is strong or weak

    Topics

    Modality & PossibilityTruth & Knowledge

    Related

    A strategy can be a best response to some particular belief without being a best...A strategy weakly dominated by no pure strategy can still be admissible, collaps...Admissibility requires the strategy to be a best response to a belief that does ...For a strategy to not be strictly dominated, it is sufficient for it to be a bes...
    +5 moreShow less
    If non-domination and admissibility coincide in the class of games where the dis...If the full-support condition in P2 is not a necessary feature of admissibility ...Pearce (1984) shows that in finite games, iterative elimination of weakly domina...The supporting argument's P3 smuggles in a contentious Bayesian assumption: that...Under Levi's and Walley's imprecise probability frameworks, a strategy counts as...

    Similar

    No strategy can be a Nash equilibrium strategy if it is strictly domin...87%For a strategy to not be strictly dominated, it is sufficient for it t...86%A strictly dominated strategy fails to be a best response to any belie...86%If a strategy is weakly dominated with respect to X, it does not follo...85%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemic-game
    View source passageHide passage
    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