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    Off-path beliefs are not arbitrary: Kreps and Wilson's se... — Carmelics
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    Challenges→The fourth Nash Equilibrium (R, r2, r3) arises because Player III's entire information set is off the path of play when Player I plays R and Player II plays r2, making Player III's action inconsequential to the outcome.

    Off-path beliefs are not arbitrary: Kreps and Wilson's sequential equilibrium (1982) requires beliefs at off-path nodes to be epistemically consistent with strategies.

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    Reasons For

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    Reason for
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    • 1.Sequential equilibrium's consistency requirement prevents players from holding beliefs contradicting observed play, eliminating purely arbitrary belief assignments.
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    • 2.Bayesian consistency forces off-path beliefs to derive from rational updating rules, grounding them in logical inference rather than arbitrary stipulation.
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    • 3.Without epistemic constraints on off-path beliefs, equilibria become indeterminate since infinitely many belief profiles could rationalize identical on-path play.
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    Reasons Against

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    Reason against
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    • 1.Sequential equilibrium still permits multiple belief systems satisfying consistency at off-path nodes, so non-arbitrariness is relative, not absolute.
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    • 2.Players may rationally hold diverse beliefs about unreached nodes; consistency merely restricts the set without uniquely determining beliefs through reason alone.
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    • 3.The requirement remains substantively indeterminate because limit arguments used to justify off-path beliefs often rely on unspecified perturbation sequences.
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    Social Contract1 linkedConsequentialism1 linked

    Related

    Bayesian consistency forces off-path beliefs to derive from rational updating ru...Players may rationally hold diverse beliefs about unreached nodes; consistency m...Sequential equilibrium still permits multiple belief systems satisfying consiste...Sequential equilibrium's consistency requirement prevents players from holding b...
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    The fourth Nash Equilibrium (R, r2, r3) arises because Player III's entire infor...The requirement remains substantively indeterminate because limit arguments used...Without epistemic constraints on off-path beliefs, equilibria become indetermina...

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