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    The pursuer-fugitive game is not strictly competitive whe... — Carmelics
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    The pursuer-fugitive game is not strictly competitive when the utility functions reflect the players' actual preferences about outcomes

    ConsequentialismModality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.A strictly competitive game requires that every gain in expected utility by one player represents a precisely symmetrical loss by the other
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    • 2.The pursuer ranks outcomes as: capturing the fugitive herself > fugitive dies by other means > fugitive escapes
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    • 3.The fugitive ranks outcomes as: escape > death by gunshot > death by rockfall or snakebite
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Von Neumann's original definition of strictly competitive games requires only that one player's gain in *ordinal* ranking entails the other's loss, not cardinal symmetry.
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    • 2.If we restrict the outcome space to {capture, escape}, the pursuer-fugitive game satisfies this ordinal zero-sum condition regardless of how intermediate outcomes are ranked.
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    • 3.The SEP argument conflates the richer preference structure of the *extended* game with the defining structure of the *core* competitive interaction.
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    Reason against 2 of 2
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    • 1.Harsanyi's utility aggregation framework holds that interpersonal utility comparisons can be normalized so that any two-player game with opposed interests is representable as zero-sum under an appropriate cardinal rescaling.
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    • 2.If utility functions can always be affinely transformed to yield strict competition without loss of strategic content, then the claim that 'actual preferences' break strict competitiveness is an artifact of the chosen representation, not a deep feature of the game.
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    Modality & PossibilityConsequentialism

    Related

    A strictly competitive game requires that every gain in expected utility by one ...Harsanyi's utility aggregation framework holds that interpersonal utility compar...If utility functions can always be affinely transformed to yield strict competit...If we restrict the outcome space to {capture, escape}, the pursuer-fugitive game...
    +5 moreShow less
    The SEP argument conflates the richer preference structure of the *extended* gam...The fugitive ranks outcomes as: escape > death by gunshot > death by rockfall or...The pursuer ranks outcomes as: capturing the fugitive herself > fugitive dies by...These rankings are not mirror images of each other, so gains and losses are not ...Von Neumann's original definition of strictly competitive games requires only th...

    Similar

    The pursuer-fugitive game cannot be solved purely on the basis of ordi...85%The utility functions are the dependent variables, so the games must b...75%The fugitive in the river-crossing game cannot rely on a pure strategy...75%The pursuer's choice cannot affect the distribution of the fugitive's ...75%

    Source

    AI-extracted1/3 agreementValid
    SEP: game-theory
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    We were able to solve this game straightforwardly because we set the utility functions in such a way as to make it zero-sum, or strictly competitive. That is, every gain in expected utility by one player represents a precisely symmetrical loss by the other. However, this condition may often not hold. Suppose now that the utility functions are more complicated. The pursuer most prefers an outcome in which she shoots the fugitive and so claims credit for his apprehension to one in which he dies of
    Extraction notes

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

    Details

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