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    Knowledge games with universal goals have equilibria in p... — Carmelics
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    Home/Modality & Possibility
    HistoryEditSee Inverse

    Knowledge games with universal goals have equilibria in pure strategies.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Universal goal statements are constructed from literals using only conjunction, disjunction, knowledge operators, and dynamic modalities with universal announcements.
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    • 2.Truth of universal formulas is preserved when transitioning from a model to a submodel.
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    • 3.Because truth is preserved under submodel transitions, epistemic uncertainty becomes less harmful for universal goals.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Preserving truth under submodel transitions does not guarantee equilibrium existence, since equilibria require strategic best-response consistency, not merely semantic monotonicity.
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    • 2.Aumann's agreement theorem shows that common knowledge constraints can prevent agents from coordinating on pure strategies even when goal conditions are universally preserved.
      ?

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    Reason against 2 of 2
    ?
    • 1.Universal goal formulas can include disjunctions over knowledge operators, creating indeterminacy in agent preference rankings across epistemic states that precludes pure strategy equilibria.
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    • 2.Hintikka's game-theoretic semantics demonstrates that disjunctive epistemic goals shift strategic choice to a verifier-falsifier structure where pure strategy solutions systematically collapse under imperfect information.
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    Topics

    Modality & Possibility

    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

    3 topics

    Truth & Knowledge2 linkedPhilosophy of Language1 linkedSkepticism1 linked

    Related

    Aumann's agreement theorem shows that common knowledge constraints can prevent a...Because truth is preserved under submodel transitions, epistemic uncertainty bec...Hintikka's game-theoretic semantics demonstrates that disjunctive epistemic goal...Preserving truth under submodel transitions does not guarantee equilibrium exist...
    +3 moreShow less
    Truth of universal formulas is preserved when transitioning from a model to a su...Universal goal formulas can include disjunctions over knowledge operators, creat...

    Similar

    Pure Coordination games may have multiple equilibria.83%Under natural conditions on goals, iterated games admit equilibria tha...81%If iterative elimination of strictly dominated strategies leads to a u...81%If a game has a unique Nash equilibrium outcome, that outcome must be ...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: logics-for-games
    View source passageHide passage
    These games are conducted under imperfect information, as players may not know the true state of their epistemic model. Accordingly, the relevant strategies need to be uniform. Players must say the same thing in all states they cannot distinguish. In general, then, many solution concepts produce mixed strategy outcomes. In fact, it can be shown that there exists simple announcement games without any unique equilibrium in pure strategies. However, there is a relevant role for logic to play. Suppo
    Extraction notes

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

    Details

    Universal goal statements are constructed from literals using only conjunction, ...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit