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    The single-state epistemic-probability model assigning pr... — Carmelics
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    The single-state epistemic-probability model assigning profile (u, l) does not satisfy common knowledge of rationality in the relevant sense.

    SkepticismTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.Common knowledge of rationality in epistemic-probability models requires that players hold cautious beliefs.
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    • 2.Cautious beliefs require that a player cannot know which option her opponent will choose from a set of choice-worthy options.
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    • 3.In the described game, Bob's beliefs in the single-state model are not cautious.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Common knowledge of rationality is satisfiable by any model where each player's strategy is a best response given their actual beliefs, without requiring caution.
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    • 2.Aumann's original formalization of common knowledge of rationality in 'Agreeing to Disagree' (1976) does not impose caution as a necessary condition on belief profiles.
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    • 3.The caution requirement reflects Brandenburger and Dekel's correlated rationalizability refinement, which is a substantive additional constraint beyond common knowledge of rationality itself.
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    Reason against 2 of 2
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    • 1.A single-state epistemic model can satisfy common knowledge of rationality if the state space is constructed so that each player's strategy is optimal given the probability-one beliefs held at that state.
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    • 2.Restricting legitimate models of common knowledge of rationality to those with cautious beliefs conflates rationality under certainty with rationality under uncertainty, as Savage's expected utility framework permits degenerate probability-one beliefs as a limiting case.
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    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

    Free Will & Foreknowledge1 linkedMoral Responsibility1 linked

    Related

    A single-state epistemic model can satisfy common knowledge of rationality if th...Aumann's original formalization of common knowledge of rationality in 'Agreeing ...Cautious beliefs require that a player cannot know which option her opponent wil...Common knowledge of rationality in epistemic-probability models requires that pl...
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    Common knowledge of rationality is satisfiable by any model where each player's ...In the described game, Bob's beliefs in the single-state model are not cautious.

    Similar

    The epistemic model has a single state w where the strategy profile σ(...82%The single state epistemic model may be insufficient for fully assessi...80%Therefore the single-state model fails the caution requirement and doe...79%Specifying an epistemic-probability model requires only a prior probab...76%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemic-game
    View source passageHide passage
    The extent of this conflict is nicely illustrated in Samuelson (1992). In particular, Samuelson (1992) shows that there is no epistemic-probability model[14] of the above game with a state satisfying common knowledge of rationality (where “rationality” means that players do not choose weakly dominated strategies). Prima facie, this is puzzling: What about the epistemic-probability model consisting of a single state \(w\) assigned the profile \((u, l)\)? Isn’t this a model of the above game whe
    Extraction notes

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

    Details

    Restricting legitimate models of common knowledge of rationality to those with c...
    The caution requirement reflects Brandenburger and Dekel's correlated rationaliz...
    Therefore the single-state model fails the caution requirement and does not coun...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit