Unilateral Actions the Case of International Environmental Problems

ter what the true state of costs is, the informed country always has a strong in-
centive to announce that costs are high. The only way a country can convince
the relevant parties that it has high costs, is by engaging in a unilateral deviation
from the non-cooperative optimum by such an amount that only a country with
high costs will find it worthwhile undertaking.

Now an abstract signalling game model is setup. In period 1, the informed
country can choose to signal its costs by deviating from non-cooperative reduc-
tion path. The other countries choose their output on the basis of their best reply
function (which is based on their prior cost estimates). Next they evaluate the
chosen outcomes, and update their beliefs by use of Bayes rule. On the basis of
these new beliefs, they play their best reply in the second period.

The following notation will be used:

Choice in period 1:
Updating of beliefs:

Choice in period 2:

Superscripts denote periods and q¹ = (q_i,q¹_-i) is the total vector of outputs in pe-
riod 1. Note that second period choices are fully determined by first-period ac-
tions and prior beliefs. Initially, nature draws a type θ from the set {L, H}, ac-
cording to a probability distribution (ρ, 1-ρ) where ρ=prob (θ=L).
NBi(θ,qi,ρ)=NBi(qi¹,q-¹i,ρi,θi)+NBi(qi²(ρi(q¹)),q-²i(ρ-i(q¹)),θi) is the two-
period net benefit for country i from playing qi, and the optimal response from
country j, given country i’s type in both periods.¹⁰ Moreover, let q(L,1) and
q(H,0) be the full information maximizer of NBi for the low costs and the high
cost types, respectively. Note that q(H,0) < q(L,1), see figure 3 for an example.

10 Assume no discounting. In general including discounting makes unilateral actions less likely,
since it reduces the second period gains from a unilateral action.

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