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    The pair of randomizing strategies — each player rolling ... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    The pair of randomizing strategies — each player rolling a three-sided die — constitutes a Nash equilibrium.

    ConsequentialismModality & Possibility
    ?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 fugitive has a 2/3 probability of escaping and the pursuer a 1/3 probability of catching the fugitive under mutual randomization.
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    • 2.Neither player can improve their probability given that the other player is playing a uniform random strategy.
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    • 3.When one player randomizes uniformly, the other player is indifferent among all mixed strategies, so no deviation improves their outcome.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.A Nash equilibrium requires that no player can *strictly* improve by deviating, but indifference among strategies entails the equilibrium is not uniquely action-guiding.
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    • 2.When a player is indifferent across all mixed strategies, the equilibrium condition fails to provide a rational basis for choosing the specific equilibrium mixture over any other.
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    • 3.Harsanyi's purification theorem notwithstanding, the epistemic conditions justifying mixed-strategy equilibria as rational prescriptions remain contested in the literature on equilibrium selection.
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    Reason against 2 of 2
    ?
    • 1.Causal decision theory (Lewis, Gibbard & Harper) evaluates strategies by their causal consequences, and a randomizing device produces no causal mechanism linking one's choice to improved outcomes.
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    • 2.If the pursuer's bridge selection is causally independent of the fugitive's die roll, the mixed strategy provides no consequentialist justification superior to any pure strategy yielding equal expected utility.
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    Topics

    Modality & PossibilityConsequentialism

    Connections

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    Free Will & Foreknowledge1 linked

    Related

    A Nash equilibrium requires that no player can *strictly* improve by deviating, ...Causal decision theory (Lewis, Gibbard & Harper) evaluates strategies by their c...Harsanyi's purification theorem notwithstanding, the epistemic conditions justif...If the pursuer's bridge selection is causally independent of the fugitive's die ...
    +4 moreShow less
    Neither player can improve their probability given that the other player is play...The fugitive has a 2/3 probability of escaping and the pursuer a 1/3 probability...When a player is indifferent across all mixed strategies, the equilibrium condit...When one player randomizes uniformly, the other player is indifferent among all ...

    Similar

    When one player randomizes uniformly, the other player is indifferent ...80%Repeatedly applying a mixed strategy based on an n-sided die (where n ...78%A set of strategies is a Nash equilibrium if and only if no player cou...77%Applying Bayes's rule to sequential equilibrium requires that players ...76%

    Source

    AI-extracted1/3 agreementValid
    SEP: game-theory
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    Suppose that we ignore rocks and cobras for a moment, and imagine that the bridges are equally safe. Suppose also that the fugitive has no special knowledge about his pursuer that might lead him to venture a specially conjectured probability distribution over the pursuer’s available strategies. In this case, the fugitive’s best course is to roll a three-sided die, in which each side represents a different bridge (or, more conventionally, a six-sided die in which each bridge is represented by two
    Extraction notes

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

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit