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    Carmelics

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

    It is not the case that Rationality and common knowledge of rationality in extensive games does not necessarily imply players will play according to the backward induction solution

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The modeling of players' belief change upon learning an opponent has deviated from the backward induction path affects the conclusion
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    • 2.Stalnaker (1998) showed that under a different model of belief revision, backward induction is not entailed
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Aumann's (1995) proof presupposes that rationality is common knowledge even at counterfactual nodes, a condition that is self-undermining when deviation occurs.
      ?

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    • 2.If a player observes a deviation from backward induction, this constitutes evidence that common knowledge of rationality has already failed, making the assumption vacuous at that point.
      ?

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    • 3.A self-undermining assumption cannot serve as a stable epistemic foundation for deriving unique equilibrium behavior in extended sequential play.
      ?

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    Reason against 2 of 2
    ?
    • 1.Reny (1992) demonstrated that in games like Centipede, maintaining common knowledge of rationality is impossible to sustain consistently across all information sets.
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    • 2.Epistemic conditions that cannot be jointly satisfied throughout a game's play cannot coherently entail any particular solution concept as uniquely rational.
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