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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The fourth Nash Equilibrium (R, r2, r3) arises because Player III's entire information set is off the path of play when Player I plays R and Player II plays r2, making Player III's action inconsequential to the outcome.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Off-path beliefs are not arbitrary: Kreps and Wilson's sequential equilibrium (1982) requires beliefs at off-path nodes to be epistemically consistent with strategies.
      ?

      Think about whether this reason is strong or weak

    • 2.Player III's off-path action constitutes a credible threat only if it is a best response given some coherent belief system over the unreached information set.
      ?

      Think about whether this reason is strong or weak

    • 3.An equilibrium sustained by an off-path action that would never be rational given any consistent belief is eliminated by forward induction, undermining the equilibrium's stability.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Consequential irrelevance in a single play does not establish strategic irrelevance: Selten's (1975) trembling-hand perfection requires strategies to be best responses even against small perturbations that reach off-path nodes.
      ?

      Think about whether this reason is strong or weak

    • 2.If Player III's action at the off-path set is not a best response when that set is reached with positive probability under any perturbation, the equilibrium (R, r2, r3) fails the perfection test and cannot be considered fully rational.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.When Player I plays R and Player II plays r2, Player III's information set is off the path of play.
      ?

      Think about whether this reason is strong or weak

    • 2.When a player's information set is off the path of play, that player's action does not affect the outcome.
      ?

      Think about whether this reason is strong or weak

    Next step

    Based on where you are in your exploration

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