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

    It is not the case that The invariance property of strict dominance under additional information does not hold for weak dominance.

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 2 of 2
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    • 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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    Reasons Against

    1 perspective
    Reason against
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    • 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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