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    Made withinDC&Austin
    Nash Equilibrium (NE) is both necessary and sufficient as... — Carmelics
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    Home/Modality & Possibility
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    Nash Equilibrium (NE) is both necessary and sufficient as a solution concept for finite perfect-information zero-sum games.

    ConsequentialismModality & Possibility
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.In a zero-sum game, any improvement for one player requires making the other player worse off.
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    • 2.If each player is playing a strategy such that neither can do better given the other's strategy, then any deviation by either player would make the other worse off.
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    • 3.No solution compatible with mutual economic rationality can exist other than the unique NE in such conditions.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Finite perfect-information zero-sum games with more than one NE require a selection principle NE alone cannot supply.
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    • 2.Zermelo's theorem guarantees a unique value for such games, but multiple strategy profiles can realize that value as NEs.
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    • 3.Sufficiency fails whenever the equilibrium set is non-singleton, since NE provides no internal criterion for coordinate selection.
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    Reason against 2 of 2
    ?
    • 1.Bernheim's rationalizability and Pearce's correlated equilibrium show NE imposes mutual-best-response constraints stronger than common knowledge of rationality alone requires.
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    • 2.A solution concept is necessary only if rational agents could not converge on non-NE outcomes through legitimate epistemic routes such as pre-play communication or correlated devices.
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    • 3.Therefore NE is not necessary, since correlated equilibria outside the NE set can dominate it in expected value while remaining consistent with full rationality.
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    Modality & PossibilityConsequentialism

    Related

    A solution concept is necessary only if rational agents could not converge on no...Bernheim's rationalizability and Pearce's correlated equilibrium show NE imposes...Finite perfect-information zero-sum games with more than one NE require a select...If each player is playing a strategy such that neither can do better given the o...
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    In a zero-sum game, any improvement for one player requires making the other pla...No solution compatible with mutual economic rationality can exist other than the...Sufficiency fails whenever the equilibrium set is non-singleton, since NE provid...Therefore NE is not necessary, since correlated equilibria outside the NE set ca...Zermelo's theorem guarantees a unique value for such games, but multiple strateg...

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    Source

    AI-extracted1/3 agreementValid
    SEP: game-theory
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    We can specify one class of games in which NE is always not only necessary but sufficient as a solution concept. These are finite perfect-information games that are also zero-sum. A zero-sum game (in the case of a game involving just two players) is one in which one player can only be made better off by making the other player worse off. (Tic-tac-toe is a simple example of such a game: any move that brings one player closer to winning brings her opponent closer to losing, and vice-versa.) We can
    Extraction notes

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

    Details

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