^H = q(H,0)
(7.b)
And will, under the given assumptions, always exist:
Result 3: Given the single crossing condition, there always exists a separating
equilibrium given by (7.a) and (7.b). Proof, see appendix 2.
This result is reproduced in figure 4, where RiL and RiH are indicated by the dot-
ted lines as defines above. The interception indicated by the bold line indicates
the set of separating equilibrium outcomes, all representing an increase in re-
duction levels for the low cost compared to the full information situation.
Again, as in section 3, the requirement on belief formation will be that if a sig-
nal q’ is weakly dominated for one type θ, but not for the other type, the unin-
formed players’ belief should place zero probability that θ has sent q’, i.e. q’
must be followed by posterior ρ(θ∣q,)=0. The result of doing this is stated be-
low:
Result 4: There exists one undominated separating equilibrium,
( qL, qH ) = ( qU, q ( H ,0)), where
qiUA =suparg{qi ∈Qi | NBi(L,qi ,1)=NBi(L,q(L,1),0)}.
Proof, see appendix 2
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