Unilateral Actions the Case of International Environmental Problems



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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