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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that A strategy that is not strictly dominated need not be admissible

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

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

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    Reasons Against

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

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