The name is absent

At any time t, full rationality requires that individual i is aware of the
history up to that time, insofar as it determines the truth value of proposi-
tions in Nⁱ. That is, full rationality in a bounded domain precludes imperfect
recall.

Thus, the event observed by individual i at time t is summed up by the
truth value of elementary propositions pⁿ where n E N = Nⁱ ∩ N_t . We have
a corresponding representation of: the history

hⁱ (t) = ∑ 2~⁽ⁿ⁺¹⁾ (uⁿ + 1) ;

n∈N_t^l

the associated compound proposition p_t, consisting of the conjunction

pⁱ_t =    Λ    pⁿ    Λ    -pⁿ ;

{n∈Np.vⁿ=1}   {n∈N_t⅛"=-1}

and the corresponding event E^.

Given full rationality in a bounded domain, any proposition p may be
written from the external viewpoint as pⁱ Λ p ⁱ where pⁱ E Pⁱ ,p^t E P ⁱ.
In particular, the proposition p_t characterizing the time t event E_t may be
written as

pt = pⁱt ^λ p_t^l.

5 Probabilities

Suppose that we are given a measure μ on Ω, which may be taken to represent
the prior beliefs that would be held by the decisionmaker in the absence
of bounds on rationality, including bounds on the set of propositions under
consideration. Given such a measure, the structure of the state space derived
above is sufficient to give a complete characterization of Bayesian updating.
For any event E, we have, at time t, a derived measure

μ (E ∩ Et)
μ ^(Et)

Note that we can now derive μ_t+₁ (E) in two ways. First, we can repeat the
definition above, yielding

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