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    The invariance property of strict dominance under additio... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    The invariance property of strict dominance under additional information does not hold for weak 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.Weak dominance is defined existentially: a strategy is weakly dominated with respect to a set X if there exists some subset of X witnessing the dominance.
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    • 2.If a strategy is weakly dominated with respect to X, it does not follow that it is weakly dominated with respect to every subset X' of X.
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    • 3.The analogue of the strict dominance observation (that dominance is preserved under refinement of the opponent strategy set) therefore fails for weak dominance.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Weak dominance preserves a conditional invariance property: if the witnessing subset X' is itself closed under best response, dominance holds stably.
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    • 2.The failure of invariance under arbitrary refinement does not negate invariance under epistemically relevant refinements such as correlated equilibrium supports.
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    • 3.Thus the claim overstates the failure—it is refinement-type-relative, not absolute, as Brandenburger and Dekel's rationalizability framework implies.
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    Reason against 2 of 2
    ?
    • 1.Samuelson (1992) demonstrated that iterated weak dominance can yield stable solutions when the elimination order is restricted to simultaneous rounds.
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    • 2.If elimination order is constrained rather than arbitrary, the loss of invariance is a procedural artifact, not a feature of weak dominance itself.
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    • 3.The claim therefore conflates a property of unrestricted elimination procedures with an intrinsic semantic defect in weak dominance as a solution concept.
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    Related

    If a strategy is weakly dominated with respect to X, it does not follow that it ...If elimination order is constrained rather than arbitrary, the loss of invarianc...Samuelson (1992) demonstrated that iterated weak dominance can yield stable solu...The analogue of the strict dominance observation (that dominance is preserved un...
    +5 moreShow less
    The claim therefore conflates a property of unrestricted elimination procedures ...The failure of invariance under arbitrary refinement does not negate invariance ...Thus the claim overstates the failure—it is refinement-type-relative, not absolu...Weak dominance is defined existentially: a strategy is weakly dominated with res...Weak dominance preserves a conditional invariance property: if the witnessing su...

    Similar

    Strict dominance implies weak dominance, but weak dominance does not n...86%The analogue of the strict dominance observation (that dominance is pr...83%Defining dominance only over pure strategies would fail to detect such...76%Weak dominance is defined existentially: a strategy is weakly dominate...75%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemic-game
    View source passageHide passage
    If a strategy is strictly dominated, it remains so if the player gets more information about what her opponents (might) do. Thus, if a strategy \(s_i\) is strictly dominated in a game \(G\) with respect to the entire set of her opponents’ strategies \(S_{-i}\), then it will never be rational (according to the above definitions) in any epistemic (-plausibility) model for \(G\). I.e., there are no beliefs player \(i\) can have that makes \(s_i\) rational. The same observation does not hold for wea
    Extraction notes

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

    Details

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