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    Made withinDC&Austin
    The fourth Nash Equilibrium (R, r2, r3) arises because Pl... — Carmelics
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    Home/Consequentialism
    HistoryEditSee Inverse

    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.

    Social Contract
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.When Player I plays R and Player II plays r2, Player III's information set is off the path of play.
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    • 2.When a player's information set is off the path of play, that player's action does not affect the outcome.
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    Reasons Against

    2 perspectives
    Reason against 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.
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    • 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.
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    • 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.
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    Reason against 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.
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    • 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.
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    Topics

    ConsequentialismSocial Contract

    Key Terms

    Nash equilibrium(Applied here to the pair of uniform randomizing strategies in the fugitive-pursuer bridge game.)
    A combination of strategies in which neither player can improve their expected outcome by unilaterally deviating, given the other player's strategy.
    Player I, Player II, Player III(game theory)
    The different decision-makers or participants in a game being analyzed; each player makes choices that affect the outcome.
    R, r2, r3(game theory notation)
    Symbols representing specific strategic choices or moves that each player can make in the game.
    information set(Extensive-form game theory)
    A set of nodes (here n and n') that a player cannot distinguish between, represented by the player's inability to discern her actual situation
    off the path of play(Extensive-form game analysis)
    A node or information set that is not reached given the strategies chosen by the players; e.g., node 7 is off the path of play when Player I chooses L at node 4, ensuring node 7 is never reached.

    Connections

    1 topic

    Causation1 linked

    Related

    An equilibrium sustained by an off-path action that would never be rational give...Consequential irrelevance in a single play does not establish strategic irreleva...If Player III's action at the off-path set is not a best response when that set ...

    Source

    AI-extracted1/3 agreementValid
    SEP: game-theory
    View source passageHide passage
    This game has four NE: (L, l2, l3), (L, r2, l3), (R, r2, l3) and (R, r2, r3). Consider the fourth of these NE. It arises because when Player I plays R and Player II plays r2, Player III’s entire information set is off the path of play, and it doesn’t matter to the outcome what Player III does. But Player I would not play R if Player III could tell the difference between being at node 13 and being at node 14. The structure of the game incentivizes efforts by Player I to supply Player III with inf
    Extraction notes

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

    Details

    Off-path beliefs are not arbitrary: Kreps and Wilson's sequential equilibrium (1...
    +3 moreShow less
    Player III's off-path action constitutes a credible threat only if it is a best ...When Player I plays R and Player II plays r2, Player III's information set is of...When a player's information set is off the path of play, that player's action do...

    Similar

    When Player I plays R and Player II plays r2, Player III's information...86%When a player's information set is off the path of play, that player's...74%If Player II plays L at node 6, Player I's best response is to play L ...72%Player B's only rational strategy is to choose l2 at informational cel...70%
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit