Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

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

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    It cannot be common knowledge among A and B at state w th... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Skepticism
    HistoryEditSee Inverse

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

    Skepticism
    ?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.The backward induction profile in the game is (I1I3, I2) leading to outcome o4 with payoffs of 3 for both players
      ?

      Think about whether this reason is strong or weak

    • 2.The epistemic model has a single state w where the strategy profile σ(w) = (O1I3, O2)
      ?

      Think about whether this reason is strong or weak

    • 3.The strategy profile σ(w) = (O1I3, O2) is not the backward induction profile
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

    Reason against 2 of 2
    ?
    • 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.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

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

    Topics

    SkepticismTruth & 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

    2 topics

    Modality & Possibility3 linkedFree Will & Foreknowledge1 linked

    Related

    Aumann's Theorem states that common knowledge of substantive rationality implies...Aumann's proof smuggles in a substantive assumption that players' beliefs are de...If backward induction requires evaluating rationality at unreached nodes, the ep...Stalnaker (1998) demonstrates that common knowledge of rationality is consistent...
    +5 moreShow less
    Substantive rationality requires acting on one's actual strategy, but a player's...

    Similar

    It is not common knowledge that both Ann and Bob are rational90%Violation of common knowledge of rationality means either a player is ...80%It does not make sense to speak of a universal standard of rationality...80%Aumann (1995) and Stalnaker (1998) share the same epistemic condition ...80%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemic-game
    View source passageHide passage
    In the above game the backward induction profile is \((I_1I_3, I_2)\) leading to the outcome \(o_4\) with both players receiving a payoff of \(3\). Consider an epistemic model with a single state \(w\) where \(\sigma(w)=(O_1I_3,O_2)\). This is not the backward induction profile, and so, by Aumann’s Theorem (Theorem 4.7) it cannot be common knowledge among \(A\) and \(B\) at state \(w\) that both \(A\) and \(B\) are substantively rational.
    Extraction notes

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

    Details

    The backward induction profile in the game is (I1I3, I2) leading to outcome o4 w...
    The epistemic model has a single state w where the strategy profile σ(w) = (O1I3...
    The strategy profile σ(w) = (O1I3, O2) is not the backward induction profile
    Therefore the claim conflates common knowledge of rationality with common knowle...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit