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    The trivial converse — that any strategy profile survivin... — Carmelics
    Home/Modality & Possibility
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    The trivial converse — that any strategy profile surviving IESDS is consistent with common knowledge of rationality — is not particularly interesting.

    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.One can always construct a type space that assigns probability 1 to any given strategy profile, making the converse hold vacuously.
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    • 2.A result that holds by arbitrary construction of a type space does not provide meaningful epistemic constraints.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The converse establishes a non-trivial necessary condition: no IESDS-eliminated strategy can ever be rational under CKR, which constrains the space of rational play.
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    • 2.Bernheim (1984) and Pearce (1984) showed that rationalizable strategies—not just Nash equilibria—are the proper solution concept under CKR, making the boundary IESDS draws theoretically load-bearing.
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    • 3.A result's interest is not diminished merely because its proof is constructive; the type-space construction reveals that CKR imposes no further constraints beyond IESDS survival, which is itself a substantive finding.
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    Reason against 2 of 2
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    • 1.Aumann and Brandenburger's (1995) framework shows that characterizing what CKR permits, not just what it requires, is essential to demarcating the epistemic content of solution concepts.
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    • 2.The converse's 'triviality' presupposes that only uniqueness results are interesting, but in modal epistemology, permissibility results—showing what is consistent with a knowledge state—carry independent theoretical weight.
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    Topics

    Modality & PossibilityTruth & Knowledge

    Key Terms

    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

    Connections

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    Skepticism1 linked

    Related

    A result that holds by arbitrary construction of a type space does not provide m...A result's interest is not diminished merely because its proof is constructive; ...Aumann and Brandenburger's (1995) framework shows that characterizing what CKR p...Bernheim (1984) and Pearce (1984) showed that rationalizable strategies—not just...
    +3 moreShow less
    One can always construct a type space that assigns probability 1 to any given st...The converse establishes a non-trivial necessary condition: no IESDS-eliminated ...

    Similar

    Any strategy profile that survives iterated elimination of strictly do...86%Given any strategy profile that survives iterated elimination of stric...83%Violation of common knowledge of rationality means either a player is ...78%Material rationality only requires rationality at decision nodes that ...78%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemic-game
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    This result establishes sufficient conditions for ISDS. It has also a converse direction: given any strategy profile that survives iterated elimination of strictly dominated strategies, there is a model in which this profile is played where all players are rational and this is common knowledge. In other words, one can always view or interpret the choice of a strategy profile that would survive the iterative elimination procedure as one that results from common knowledge of rationality. Of course
    Extraction notes

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

    Details

    The converse's 'triviality' presupposes that only uniqueness results are interes...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit