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    Identifying the solution to Selten's Horse on general pri... — Carmelics
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    Identifying the solution to Selten's Horse on general principles requires reasoning about players' beliefs about conditional probabilities, not merely strategic beliefs about actions.

    Truth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Player III, upon receiving a move, must reason about whether his action node was reached from node 11 or node 12.
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    • 2.This reasoning involves conditional probabilities: the probability that Player III is at node 13 or 14 given that he has a move.
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    • 3.If Player III reasons in terms of conditional probabilities, then Players I and II must conjecture about Player III's beliefs about those conditional probabilities.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Harsanyi's purification theorem shows that beliefs about mixed strategies reduce to beliefs about payoff perturbations, collapsing the distinction between strategic and probabilistic beliefs.
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    • 2.If conditional probability assessments are themselves derived from perturbed payoff structures, then reasoning about them is a special case of strategic belief, not a categorically distinct operation.
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    Reason against 2 of 2
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    • 1.Kreps and Wilson's sequential equilibrium framework encodes conditional probability beliefs as 'systems of beliefs' that are formally part of the equilibrium concept itself, not external to strategic reasoning.
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    • 2.Because sequential equilibrium makes beliefs about conditional probabilities constitutive of strategy profiles, the claim that such beliefs are non-strategic conflates a technical distinction with a conceptual one.
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    Topics

    Philosophy of LanguageTruth & Knowledge

    Key Terms

    Conditional probabilities(probability and strategy)
    The likelihood of something happening given that something else has already happened (for example, the probability it will rain tomorrow given that it's cloudy today).
    Game theory(mathematics and philosophy)
    The mathematical study of strategic interactions where each person's outcome depends not just on their own choices, but on what other people choose to do.
    Reinhard Selten(as the originator of the concept being discussed)
    A German economist and game theorist who won the Nobel Prize for his work on how people make strategic decisions in competitive situations.
    Selten's Horse(as a specific example in game theory)
    A famous thought experiment in game theory where a player must decide whether to enter a market and face competition, used to show that what seems logical in theory doesn't always match how rational players actually behave.
    strategic beliefs(Contrasted with beliefs about conditional probability in the context of Selten's Horse)
    Beliefs that concern only what players will do given a set of payoffs and game structures, as opposed to beliefs about the epistemic or probabilistic frameworks other players operate with.

    Connections

    1 topic

    Modality & Possibility1 linked

    Related

    Because sequential equilibrium makes beliefs about conditional probabilities con...Harsanyi's purification theorem shows that beliefs about mixed strategies reduce...If Player III reasons in terms of conditional probabilities, then Players I and ...

    Source

    AI-extracted1/3 agreementValid
    SEP: game-theory
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    Theorists who think of game theory as part of a normative theory of general rationality, for example most philosophers, and refinement program enthusiasts among economists, have pursued a strategy that would identify this solution on general principles. Notice what Player III in Selten’s Horse might wonder about as he selects his strategy. “Given that I get a move, was my action node reached from node 11 or from node 12?” What, in other words, are the conditional probabilities that Player III is
    Extraction notes

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

    Details

    If conditional probability assessments are themselves derived from perturbed pay...
    +5 moreShow less
    Kreps and Wilson's sequential equilibrium framework encodes conditional probabil...Player I must therefore conjecture about Player II's beliefs about Player III's ...Player III, upon receiving a move, must reason about whether his action node was...Strategic beliefs concern only what players will do given payoffs and game struc...This reasoning involves conditional probabilities: the probability that Player I...

    Similar

    Strategic beliefs concern only what players will do given payoffs and ...85%If Player III reasons in terms of conditional probabilities, then Play...80%The common belief assumption is a strong requirement on players in gam...80%If a principle commands belief of itself, it does not require a prior ...79%
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit