Unilateral Actions the Case of International Environmental Problems

c) Ifqθ ≠{qH^,qL}thenρ(qθ) = 0

Regarding the beliefs again let any out-of-equilibrium moves be followed by
the worst possible beliefs from the point of view of the informed country. This
now means that q_θ ≠ qL then ρ(q_θ ) = 0. If costs turn out to be low, the informed
country will try to convince the uninformed that costs are low. It can do so by
unilaterally increasing its reductions to such an extent that only a low cost
country could profit from such a move, even if beliefs are updated most favora-
bly from the point of view of the informed country. If costs turn out to be low,
the following two conditions are necessary for the low cost country to separate.

NBi(L,qi^UA,1)≥NBi(L,q(L,1),0)

NBi(H,qi^UA,1)≤ NBi(H,q(H,0),0)

In order to describe the set of separating equilibrium outcomes, it is convenient
to define the following two sets:

RL = {q* ∈ Qi | NBi(L,q* ,1) ≥ NB,(L.q(LJ)β)}

RH = {q* ∈ Qi | NBi(H,q*,1) ≤ NB_l(H ,q(H 0)0)}

The intersection of these two sets is given by R^SC = {q_i | q_i ∈ R^L ∩ R^H } . In or-
der for the low cost type to accomplish this, assume the following single cross-
ing condition (SCC): For all ρ^'' > ρ^' and all q¹,q² ∈ Q_i :
NB_i(L,q_i²,ρ^'' )-NB_i(L,q_i¹,ρ^' ) > NB_i(H,q_i²,ρ^'' )-NB_i(H,q_i¹,ρ^' ) . The SCC says that
an increase in beliefs (beliefs that costs are higher), increases the NB more for a
low cost country than for a high cost country.

The set of separating equilibrium outcomes is given by

L  _RSC

^qi ∈ ^r

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