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    Carmelics

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

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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 It cannot be common knowledge among A and B at state w that both A and B are substantively rational

    ?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.Stalnaker (1998) demonstrates that common knowledge of rationality is consistent with non-backward-induction play when rationality is construed as belief-relative rather than strategy-profile-relative.
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    • 2.Aumann's proof smuggles in a substantive assumption that players' beliefs are derived from a common prior, which is a stronger condition than common knowledge of rationality alone.
      ?

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    • 3.Therefore the claim conflates common knowledge of rationality with common knowledge of rationality plus common priors, making the impossibility result an artifact of an overly enriched epistemic model.
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    Reason for 2 of 2
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    • 1.Substantive rationality requires acting on one's actual strategy, but a player's strategy encodes dispositions at nodes never reached, making off-path rationality assessments counterfactually indeterminate.
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    • 2.If backward induction requires evaluating rationality at unreached nodes, the epistemic conditions for common knowledge collapse because there is no fact of the matter about what a rational agent would do at those nodes.
      ?

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    Reasons Against

    1 perspective
    Reason against
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    • 1.The backward induction profile in the game is (I1I3, I2) leading to outcome o4 with payoffs of 3 for both players
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    • 2.The epistemic model has a single state w where the strategy profile σ(w) = (O1I3, O2)
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    • 3.The strategy profile σ(w) = (O1I3, O2) is not the backward induction profile
      ?

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    Next step

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