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    Rationality and common knowledge of rationality in extens... — Carmelics
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    Home/Moral Responsibility
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    Rationality and common knowledge of rationality in extensive games does not necessarily imply players will play according to the backward induction solution

    Moral ResponsibilityTruth & Knowledge
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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    Topics

    Moral ResponsibilityTruth & Knowledge

    Key Terms

    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

    Connections

    2 topics

    Causation1 linkedSkepticism1 linked

    Related

    A self-undermining assumption cannot serve as a stable epistemic foundation for ...Aumann's (1995) proof presupposes that rationality is common knowledge even at c...Epistemic conditions that cannot be jointly satisfied throughout a game's play c...If a player observes a deviation from backward induction, this constitutes evide...
    +3 moreShow less
    Reny (1992) demonstrated that in games like Centipede, maintaining common knowle...Stalnaker (1998) showed that under a different model of belief revision, backwar...

    Similar

    The paradox of backward induction only generates a problem when game t...86%The paradox of backward induction is primarily a problem for normative...86%Player II can solve the game using backward induction only by taking a...85%Aumann's Theorem states that common knowledge of substantive rationali...85%

    Source

    AI-extracted1/3 agreementValid
    SEP: epistemic-game
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    The most well-known illustration of this is through the comparison of two apparently contradictory results regarding the consequences of assuming rationality and common knowledge of rationality in extensive games. Aumann (1995) showed that this epistemic condition implies that the players will play according to the backward induction solution while Stalnaker (1998) argued that this is not necessarily true. The crucial difference between these two results is the way in which they model the player
    Extraction notes

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

    Details

    The modeling of players' belief change upon learning an opponent has deviated fr...
    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit