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    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that 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.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.Intermediate outcome rankings determine strategy selection; different rankings produce different equilibria, violating game equivalence.
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    • 2.If intermediate outcomes have asymmetric value to players (e.g., near-capture favors pursuer), payoff structure is contextually modified.
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    • 3.Zero-sum game definition requires all outcomes maintain constant sum; allowing variable intermediate preferences may violate this at sub-terminal points.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Zero-sum requires only final payoff opposition: one player's capture-win equals fugitive's escape-loss, independent of path.
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    • 2.Intermediate outcome rankings affect decision-making but not the mathematical structure of the restricted outcome space itself.
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    • 3.Any ordinal ranking of intermediate states preserves the binary opposition at closure, making zero-sum invariant across preferences.
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