Unilateral Actions the Case of International Environmental Problems

The intuition is that when country 1’s costs increases, this leads to smaller re-
ductions by country 1, smaller reductions increase the marginal benefit for
country 2 of the same level of reductions, and, hence, it will reduce more in re-
sponse.

Appendix 2

Proof of result 1: We will show that a q_i^' < q(H,0) exists that satisfies both 4.a
and 4.b. Define qi^' =min arg{NBi(L, qi,0) = NBi(L,q(L,1),1)}, i.e. q_i^' is the smallest
qi satisfying 4.b. If at the same time, qi^' satisfies 4.a with strict inequality, then
existence is guaranteed. Given that NBi(H,q^'i,0) > NBi(H,q(H,0),1), then also
NB_i(H,q_i^',0) > NB_i(H,q(L,1),1) , since q(H,0) is the unique maximizer of
NBi(H,ρ,0).

From this we have that

NBi(H,q^'i,0)-NBi(H,q(L,1),1)>NBi(L,qi^',0)-NBi(L,q(L,1),1). Hence, in order
to get separation, there must exist a q_i^' < q_i (H,0), such that
NBi(H,qi^',0)-NBi(H,q(L,1),1)>NBi(L,qi^',0)-NBi(L,q(L,1),1).

Proof of result 2: Weak domination for the low cost type in this set-up corre-
sponds to the following inequality. If NB_i (L,q(L,1),1) ≥ NBi (L, q_i ,0), then all q_i
are weakly dominated by q(L,1). But this expression is equal to 3.2, the condi-
tion satisfied by all separating equilibria. Hence, all q_i are weakly dominated by
c(L,1) for the low cost type.

Define qH = minarg{NB_i (H, q ¹H ,0) = NB_i (H, q(H,0),1)}. We now show that no
q ¹H ≠ qH is weakly dominated. This amounts to showing that

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