Unilateral Actions the Case of International Environmental Problems

With these assumptions in place, we turn to the description of the signalling
game that forms the basis for the unilateral actions, since we then assume that
updates are dependent on observed levels of reductions only.

6. The signalling game 2: Incentives to signal that
costs are low

The timing of events in the correlated model is as follows: Nature draws a
(common) type θ from the set {L, H}, according to a probability distribution
(ρ, 1-ρ) where ρ=prob (θ=L). One country, denoted country i, makes an effort
to reveal θ. Given this, this country is totally informed, whereas the other coun-
tries remain uninformed. Hereafter, this country chooses a reduction level
qi∈Qi. The other countries j ≠ i, observe qj, but not θ, and choose their reduc-
tion level qj∈Qj. The net benefit functions are still NB_i = NB_i(θ,q_i,q_j ) , but now
the type of the uninformed countries are determined by their posterior belief,
hence NBj = NBj(ρ(qi ),qi,qj(qi,ρ(qi )) . Note that compared to the non-
correlated situation, it is now the low cost country that needs to undertake
costly efforts in order to separate.

Under what conditions can a low cost country reveal its true costs and get the
uninformed to increase their reductions accordingly? First of all, a collection of
reduction levels and beliefs {q H, q L, ρ( q_i )} forms a sequential equilibrium if
the following conditions are satisfied:

i) Optimality for the country with costs θ:

qθ ∈ arg max NBi(θ^,qi^,q_j⁽q^^, ρ(q^ ))

ii) Beliefs are Bayes-consistent:

a) If qH ≠ q_L then ρ(qH ) = 0 and ρ(q_L ) = 1

b) I^f qH = qL thenρ(qH) = ρ(qL) = ρ^o

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