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    Home/Original/inverse
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    Inverse View

    It is not the case that The pair of randomizing strategies — each player rolling a three-sided die — constitutes a Nash equilibrium.

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

    Reasons For

    2 perspectives
    Reason for 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.
      ?

      Think about whether this reason is strong or weak

    Reason for 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.
      ?

      Think about whether this reason is strong or weak

    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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    Next step

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