Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Deleting weakly dominated strategies just like strictly d... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Deleting weakly dominated strategies just like strictly dominated strategies has odd consequences

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Weak dominance lacks the epistemic robustness of strict dominance: a weakly dominated strategy remains rational under at least one opponent belief.
      ?

      Think about whether this reason is strong or weak

    • 2.Savage's sure-thing principle requires dominance reasoning to hold across all states, not merely most; weak dominance violates this by permitting tied outcomes.
      ?

      Think about whether this reason is strong or weak

    • 3.Iterative deletion procedures derive their justification from common knowledge of rationality, but weak dominance deletion requires stronger assumptions that are not grounded in that basis.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Selten's perfectness criterion shows that rational equilibrium selection must be stable under small perturbations, which Kreps's payoff examples directly demonstrate weak dominance deletion fails to satisfy.
      ?

      Think about whether this reason is strong or weak

    • 2.A solution concept that reverses its recommendations under arbitrarily small payoff changes cannot track the modal facts about what players would rationally do, violating Lewis's constraint on counterfactual stability.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If s2 is deleted because s1 weakly dominates it, then column t1 becomes strictly dominated
      ?

      Think about whether this reason is strong or weak

    • 2.This process selects s1-t2 as the unique Nash Equilibrium solution
      ?

      Think about whether this reason is strong or weak

    • 3.Kreps demonstrates via payoff perturbation that this selection procedure yields counterintuitive results when payoffs are changed slightly
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

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

    Topics

    Modality & PossibilityTruth & Knowledge

    Connections

    1 topic

    Skepticism1 linked

    Related

    A solution concept that reverses its recommendations under arbitrarily small pay...If s2 is deleted because s1 weakly dominates it, then column t1 becomes strictly...Iterative deletion procedures derive their justification from common knowledge o...Kreps demonstrates via payoff perturbation that this selection procedure yields ...
    +4 moreShow less
    Savage's sure-thing principle requires dominance reasoning to hold across all st...Selten's perfectness criterion shows that rational equilibrium selection must be...This process selects s1-t2 as the unique Nash Equilibrium solutionWeak dominance lacks the epistemic robustness of strict dominance: a weakly domi...

    Similar

    If a strategy is weakly dominated with respect to X, it does not follo...90%Elimination of weakly dominated strategies and correlation are distinc...85%Elimination of weakly dominated strategies refines away the NE s2-t185%Strict and weak dominance must be defined in terms of mixed strategies...85%

    Source

    AI-extracted1/3 agreementValid
    SEP: game-theory
    View source passageHide passage
    Here, no strategy strictly dominates another. However, Player I’s top row, s1, weakly dominates s2, since I does at least as well using s1 as s2 for any reply by Player II, and on one reply by II (t2), I does better. So should not the players (and the analyst) delete the weakly dominated row s2? When they do so, column t1 is then strictly dominated, and the NE s1-t2 is selected as the unique solution. However, as Kreps goes on to show using this example, the idea that weakly dominated strategies
    Extraction notes

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

    Details

    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit