holds with strict inequality. Hence, no qiL ≠ qi can be weakly dominated.
Therefore, given an qiL = qi + ε, posterior beliefs will be updated to ρ(q[ ) = 1,
and consequently, given this new set of beliefs, only qiL = qi is an undominated
separating equilibrium.
Proof of result 5: First we note that if γ=0, then UA is not relevant (result 1 and
2) in the sense that a unilateral increase in reductions by one country will not
increase reductions abroad. On the other hand, given proposition 2, given γ=1,
UA is profitable. From (4) we have that
∂[qj (qU ) — qj (P)]
∂γ
> 0 , which says that
the higher the correlation, the more the other countries will increase their reduc-
∂qUA
tions (i.e. the larger will be qj (qUA) - qj(ρ)). Next, due to the SCP, —— < 0.
∂γ
Hence, increased γ implies less UA is needed to get a higher response, and
hence,
∂NBi ( qU, qj∙ ( qUU ))
∂γ
>0. Q.E.D.
45
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